Physics Book - User contributions [en]

Real Systems

2016-04-18T03:44:24Z

Mwyatt6: /* Connectedness */

This topic has been claimed by mwyatt6

==The Main Idea==
[[File:RealPointParticleDifference.PNG|thumb|left]]
In [[Point Particle Systems]], the only change in energy is from translational kinetic energy because every force is assumed to act on the center of mass. Up until Week 10, we have been measuring change in energy of systems using the Point Particle Method. From what we learned in Week 10 though, we know that translational kinetic energy is not the only type of energy there can be a change in (see: [[Thermal Energy]] and [[Translational, Rotational and Vibrational Energy]]). In a real system, you must consider the point of application of each force when calculating the change in energy. Also in real systems, forces may also occur over a different displacement than the displacement of the center of mass. These two key differences lead to an interesting mathematical model that differs from that used for the Point Particle Method.

===A Mathematical Model===

The mathematical equation used for Real Systems can vary depending on what his happening within and on the system. For the sake of flow with the WikiPhysicsBook, we will be analyzing real systems with the energy principle.

[[File:EnergyPrinEqn.png]]

(We are ignoring Q for the sake of simplicity. It will not be taken into account in the subsequent examples despite the possible transfer of energy from temperature differences).
'''E''' is the total energy of the system and '''W''' is the net work done from the surroundings on system. The major difference of a point particle system versus a real system is in the calculation of Work. In a point particle system, it is calculated by the net force dot product with the change in the position of the center of mass. However, Work in a real system is calculated by:

[[File:Workeq.PNG]]

This means that the summation of the all the external forces dot product with the distance each force was applied amounts to the total change in energy of the real system. The change in the mathematical equation for Work between a point particle system and a real system is important because now different forms of energy may be taken into account. In a real system, the change in energy of a system can be given by:

[[File:Realenergyeq.PNG]]

Where,
total change in internal energy ('''U''') is given by:

[[File:Utotaleq.PNG]]

total change in kinetic energy ('''K''') is given by:

[[File:Ktoteq.PNG]]

and change in Miscellaneous Energy is given by:

[[File:Emisceq.PNG]]

==Examples==

In order to better display the difference of Real Systems from [[Point Particle Systems]], the examples done here will be the same examples done from [[Point Particle Systems]].

===Jumper Model (Simple)===
[[File:Jumper.png]]
'''Problem:''' You jump up so that your center of mass has moved a distance '''h'''. How much chemical energy did you expend?

From the Point Particle System analysis, we know that [[File:Jumpktrans.PNG]] and [[File:Fnetjump.PNG]].

System: Person Surroundings: Earth+Floor

Initial State: Crouched down

Final State: Extended and moving with speed v

[[File:Jumpsteps.PNG]]

Assuming negligent change in thermal energy and relative kinetic energy, the change in thermal energy is approximately equal to the normal force multiplied by height.

===Yo-Yo (Middling)===

[[File:Simple.png|650px]][http://www.example.com link title](Chabay)

'''Step 1:''' Solve for translational kinetic energy using the Point Particle System

(The equation for translational kinetic energy here is different than that in [[Point Particle Systems]], so the derivation has been provided.)

[[File:Middling.png|650px]]

[[File:Simple Part Two.png|650px]]

'''Step Two:''' Solve for rotational kinetic energy using a Real System

[[File:Difficult.png]]

Here is where the true difference between Real and Point Particle Systems can be seen. In the Point Particle system, there is no value to account for the change of rotational kinetic energy from the work done the hand. By changing the Work equation to [[File:Workeq.PNG]] rather than [[File:Wppeq.PNG]], the rotational kinetic energy can now be found.

===Spring In a Box (Difficult)===

Suppose a thin box contains a ball of clay with the mass '''M''' connected to a relaxed spring with a stiffness '''ks'''. The masses of the box and the spring are negligible. It is initally at rest, and then a constant force of '''F'''. The box moves a distance '''b''' and the spring stretches a distance '''s''' so that the clay sticks to the box. What is the change in thermal energy of the clay after colliding with the wall of the box?

[[File:Springbox.png]]

From the analyzation of the [[Point Particle Systems]] of the Spring in a Box, we know that [[File:Ktransbox.PNG]]. Because the system is a spring, we also know that [[File:Uspring.PNG]].

[[File:Bssol.PNG]]

Assuming there is no relative kinetic energy (none based on diagram) and no change in chemical energy (there is no change in substance), the change in thermal energy of the clay can be found. Finding the change in thermal energy is important because you can determine whether there was enough energy to change the temperature of the clay or whether there is enough energy given off by the clay to change the temperature of a surrounding substance by a degree. Problems like this show the importance of analyzing real systems versus point particle systems.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

This topic interests me because from one single system you can mathematically determine the other forms of energy that can occur in various physical interaction. From the other forms of energy, you can determine whether there is enough energy to maybe change the temperature of another substance via thermal energy or even change the substance that is in the system given a big enough change in chemical energy.

'''How is it connected to your major?'''

As a chemical engineering major, the application of Real Systems is largely used for the majority of mathematics in my major dealing with energy balances. From only analyzing a system from a point particle method, one would only be able to find the change in the translational kinetic energy. In my major, it is very important to consider the entire system in order to find important values such as the change in thermal and kinetic energy because these values are often associated with the amount of work and heat produced in many chemical engineering processes.

'''Is there an interesting industrial application?'''

There is an absolute overload of interesting industrial applications for the analysis of real systems. In fact, the analysis of real systems in terms of energy balances is the entirety of what I've done in my chemical engineering classes thus far (I am currently a second year). There are many interesting (depending on your taste) uses of the real system analysis on a multitude of different turbines and chemical reactors.

===External links===
[http://www.physicsbook.gatech.edu/Point_Particle_Systems]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." <i>Matter & Interactions</i>. N.p.: n.p., n.d. N. pag. Print.

Wiki Commons Picture

--[[User:Nfortingo3|Nfortingo3]]([[User talk:Nfortingo3|talk]]) 19:26, 28 November 2015 (EST)

[[Category:Energy]]

Real Systems

2016-04-18T03:43:38Z

Mwyatt6: /* Connectedness */

This topic has been claimed by mwyatt6

==The Main Idea==
[[File:RealPointParticleDifference.PNG|thumb|left]]
In [[Point Particle Systems]], the only change in energy is from translational kinetic energy because every force is assumed to act on the center of mass. Up until Week 10, we have been measuring change in energy of systems using the Point Particle Method. From what we learned in Week 10 though, we know that translational kinetic energy is not the only type of energy there can be a change in (see: [[Thermal Energy]] and [[Translational, Rotational and Vibrational Energy]]). In a real system, you must consider the point of application of each force when calculating the change in energy. Also in real systems, forces may also occur over a different displacement than the displacement of the center of mass. These two key differences lead to an interesting mathematical model that differs from that used for the Point Particle Method.

===A Mathematical Model===

The mathematical equation used for Real Systems can vary depending on what his happening within and on the system. For the sake of flow with the WikiPhysicsBook, we will be analyzing real systems with the energy principle.

[[File:EnergyPrinEqn.png]]

(We are ignoring Q for the sake of simplicity. It will not be taken into account in the subsequent examples despite the possible transfer of energy from temperature differences).
'''E''' is the total energy of the system and '''W''' is the net work done from the surroundings on system. The major difference of a point particle system versus a real system is in the calculation of Work. In a point particle system, it is calculated by the net force dot product with the change in the position of the center of mass. However, Work in a real system is calculated by:

[[File:Workeq.PNG]]

This means that the summation of the all the external forces dot product with the distance each force was applied amounts to the total change in energy of the real system. The change in the mathematical equation for Work between a point particle system and a real system is important because now different forms of energy may be taken into account. In a real system, the change in energy of a system can be given by:

[[File:Realenergyeq.PNG]]

Where,
total change in internal energy ('''U''') is given by:

[[File:Utotaleq.PNG]]

total change in kinetic energy ('''K''') is given by:

[[File:Ktoteq.PNG]]

and change in Miscellaneous Energy is given by:

[[File:Emisceq.PNG]]

==Examples==

In order to better display the difference of Real Systems from [[Point Particle Systems]], the examples done here will be the same examples done from [[Point Particle Systems]].

===Jumper Model (Simple)===
[[File:Jumper.png]]
'''Problem:''' You jump up so that your center of mass has moved a distance '''h'''. How much chemical energy did you expend?

From the Point Particle System analysis, we know that [[File:Jumpktrans.PNG]] and [[File:Fnetjump.PNG]].

System: Person Surroundings: Earth+Floor

Initial State: Crouched down

Final State: Extended and moving with speed v

[[File:Jumpsteps.PNG]]

Assuming negligent change in thermal energy and relative kinetic energy, the change in thermal energy is approximately equal to the normal force multiplied by height.

===Yo-Yo (Middling)===

[[File:Simple.png|650px]][http://www.example.com link title](Chabay)

'''Step 1:''' Solve for translational kinetic energy using the Point Particle System

(The equation for translational kinetic energy here is different than that in [[Point Particle Systems]], so the derivation has been provided.)

[[File:Middling.png|650px]]

[[File:Simple Part Two.png|650px]]

'''Step Two:''' Solve for rotational kinetic energy using a Real System

[[File:Difficult.png]]

Here is where the true difference between Real and Point Particle Systems can be seen. In the Point Particle system, there is no value to account for the change of rotational kinetic energy from the work done the hand. By changing the Work equation to [[File:Workeq.PNG]] rather than [[File:Wppeq.PNG]], the rotational kinetic energy can now be found.

===Spring In a Box (Difficult)===

Suppose a thin box contains a ball of clay with the mass '''M''' connected to a relaxed spring with a stiffness '''ks'''. The masses of the box and the spring are negligible. It is initally at rest, and then a constant force of '''F'''. The box moves a distance '''b''' and the spring stretches a distance '''s''' so that the clay sticks to the box. What is the change in thermal energy of the clay after colliding with the wall of the box?

[[File:Springbox.png]]

From the analyzation of the [[Point Particle Systems]] of the Spring in a Box, we know that [[File:Ktransbox.PNG]]. Because the system is a spring, we also know that [[File:Uspring.PNG]].

[[File:Bssol.PNG]]

Assuming there is no relative kinetic energy (none based on diagram) and no change in chemical energy (there is no change in substance), the change in thermal energy of the clay can be found. Finding the change in thermal energy is important because you can determine whether there was enough energy to change the temperature of the clay or whether there is enough energy given off by the clay to change the temperature of a surrounding substance by a degree. Problems like this show the importance of analyzing real systems versus point particle systems.

==Connectedness==
How is this topic connected to something that you are interested in?

This topic interests me because from one single system you can mathematically determine the other forms of energy that can occur in various physical interaction. From the other forms of energy, you can determine whether there is enough energy to maybe change the temperature of another substance via thermal energy or even change the substance that is in the system given a big enough change in chemical energy.

How is it connected to your major?

As a chemical engineering major, the application of Real Systems is largely used for the majority of mathematics in my major dealing with energy balances. From only analyzing a system from a point particle method, one would only be able to find the change in the translational kinetic energy. In my major, it is very important to consider the entire system in order to find important values such as the change in thermal and kinetic energy because these values are often associated with the amount of work and heat produced in many chemical engineering processes.

Is there an interesting industrial application?

There is an absolute overload of interesting industrial applications for the analysis of real systems. In fact, the analysis of real systems in terms of energy balances is the entirety of what I've done in my chemical engineering classes thus far (I am currently a second year). There are many interesting (depending on your taste) uses of the real system analysis on a multitude of different turbines and chemical reactors.

===External links===
[http://www.physicsbook.gatech.edu/Point_Particle_Systems]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." <i>Matter & Interactions</i>. N.p.: n.p., n.d. N. pag. Print.

Wiki Commons Picture

--[[User:Nfortingo3|Nfortingo3]]([[User talk:Nfortingo3|talk]]) 19:26, 28 November 2015 (EST)

[[Category:Energy]]

Real Systems

2016-04-18T03:33:44Z

Mwyatt6: /* Spring In a Box (Difficult) */

This topic has been claimed by mwyatt6

==The Main Idea==
[[File:RealPointParticleDifference.PNG|thumb|left]]
In [[Point Particle Systems]], the only change in energy is from translational kinetic energy because every force is assumed to act on the center of mass. Up until Week 10, we have been measuring change in energy of systems using the Point Particle Method. From what we learned in Week 10 though, we know that translational kinetic energy is not the only type of energy there can be a change in (see: [[Thermal Energy]] and [[Translational, Rotational and Vibrational Energy]]). In a real system, you must consider the point of application of each force when calculating the change in energy. Also in real systems, forces may also occur over a different displacement than the displacement of the center of mass. These two key differences lead to an interesting mathematical model that differs from that used for the Point Particle Method.

===A Mathematical Model===

The mathematical equation used for Real Systems can vary depending on what his happening within and on the system. For the sake of flow with the WikiPhysicsBook, we will be analyzing real systems with the energy principle.

[[File:EnergyPrinEqn.png]]

(We are ignoring Q for the sake of simplicity. It will not be taken into account in the subsequent examples despite the possible transfer of energy from temperature differences).
'''E''' is the total energy of the system and '''W''' is the net work done from the surroundings on system. The major difference of a point particle system versus a real system is in the calculation of Work. In a point particle system, it is calculated by the net force dot product with the change in the position of the center of mass. However, Work in a real system is calculated by:

[[File:Workeq.PNG]]

This means that the summation of the all the external forces dot product with the distance each force was applied amounts to the total change in energy of the real system. The change in the mathematical equation for Work between a point particle system and a real system is important because now different forms of energy may be taken into account. In a real system, the change in energy of a system can be given by:

[[File:Realenergyeq.PNG]]

Where,
total change in internal energy ('''U''') is given by:

[[File:Utotaleq.PNG]]

total change in kinetic energy ('''K''') is given by:

[[File:Ktoteq.PNG]]

and change in Miscellaneous Energy is given by:

[[File:Emisceq.PNG]]

==Examples==

In order to better display the difference of Real Systems from [[Point Particle Systems]], the examples done here will be the same examples done from [[Point Particle Systems]].

===Jumper Model (Simple)===
[[File:Jumper.png]]
'''Problem:''' You jump up so that your center of mass has moved a distance '''h'''. How much chemical energy did you expend?

From the Point Particle System analysis, we know that [[File:Jumpktrans.PNG]] and [[File:Fnetjump.PNG]].

System: Person Surroundings: Earth+Floor

Initial State: Crouched down

Final State: Extended and moving with speed v

[[File:Jumpsteps.PNG]]

Assuming negligent change in thermal energy and relative kinetic energy, the change in thermal energy is approximately equal to the normal force multiplied by height.

===Yo-Yo (Middling)===

[[File:Simple.png|650px]][http://www.example.com link title](Chabay)

'''Step 1:''' Solve for translational kinetic energy using the Point Particle System

(The equation for translational kinetic energy here is different than that in [[Point Particle Systems]], so the derivation has been provided.)

[[File:Middling.png|650px]]

[[File:Simple Part Two.png|650px]]

'''Step Two:''' Solve for rotational kinetic energy using a Real System

[[File:Difficult.png]]

Here is where the true difference between Real and Point Particle Systems can be seen. In the Point Particle system, there is no value to account for the change of rotational kinetic energy from the work done the hand. By changing the Work equation to [[File:Workeq.PNG]] rather than [[File:Wppeq.PNG]], the rotational kinetic energy can now be found.

===Spring In a Box (Difficult)===

Suppose a thin box contains a ball of clay with the mass '''M''' connected to a relaxed spring with a stiffness '''ks'''. The masses of the box and the spring are negligible. It is initally at rest, and then a constant force of '''F'''. The box moves a distance '''b''' and the spring stretches a distance '''s''' so that the clay sticks to the box. What is the change in thermal energy of the clay after colliding with the wall of the box?

[[File:Springbox.png]]

From the analyzation of the [[Point Particle Systems]] of the Spring in a Box, we know that [[File:Ktransbox.PNG]]. Because the system is a spring, we also know that [[File:Uspring.PNG]].

[[File:Bssol.PNG]]

Assuming there is no relative kinetic energy (none based on diagram) and no change in chemical energy (there is no change in substance), the change in thermal energy of the clay can be found. Finding the change in thermal energy is important because you can determine whether there was enough energy to change the temperature of the clay or whether there is enough energy given off by the clay to change the temperature of a surrounding substance by a degree. Problems like this show the importance of analyzing real systems versus point particle systems.

==Connectedness==
How is this topic connected to something that you are interested in?
#This topic interest me because from one single particle you can mathematically determine the other form of energy that can occur in various physical interaction. In addition, being able to take a large complex interactions whether springs, gravitational potential or rotational energies are involved, you can solve and break down the interactions
How is it connected to your major?

#This topic is not directly connected to my major, but the underlying ideas connect very closely to my major. By first looking at a point particle we have a starting point to looking and breaking down a complex system. As a biochemist there are large complex biological systems that I will encounter in my studies.

[[File:Biochem.png]]

While I may not be able to break everything down to one single point, starting off with the simplest path way to understand and comprehend the largest and most complex systems is a similar method to my topic. Like with real and Point particle systems, you start off with a simple point so that one part of the interaction can be understood, from there the rest of the system can be dissected and other interactions can be solved for. With biochemical system, understanding one path, than moving from their to larger paths will help you understand the whole system.

Is there an interesting industrial application?

#I do not really know if their is a physical industrial application that can be seen from looking at real and Point particle systems. However, the methodology and thought process behind looking at a real system can be applied to many problem solving situations.

===External links===
[http://www.physicsbook.gatech.edu/Point_Particle_Systems]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." <i>Matter & Interactions</i>. N.p.: n.p., n.d. N. pag. Print.

Wiki Commons Picture

--[[User:Nfortingo3|Nfortingo3]]([[User talk:Nfortingo3|talk]]) 19:26, 28 November 2015 (EST)

[[Category:Energy]]

Real Systems

2016-04-18T03:28:00Z

Mwyatt6:

This topic has been claimed by mwyatt6

==The Main Idea==
[[File:RealPointParticleDifference.PNG|thumb|left]]
In [[Point Particle Systems]], the only change in energy is from translational kinetic energy because every force is assumed to act on the center of mass. Up until Week 10, we have been measuring change in energy of systems using the Point Particle Method. From what we learned in Week 10 though, we know that translational kinetic energy is not the only type of energy there can be a change in (see: [[Thermal Energy]] and [[Translational, Rotational and Vibrational Energy]]). In a real system, you must consider the point of application of each force when calculating the change in energy. Also in real systems, forces may also occur over a different displacement than the displacement of the center of mass. These two key differences lead to an interesting mathematical model that differs from that used for the Point Particle Method.

===A Mathematical Model===

The mathematical equation used for Real Systems can vary depending on what his happening within and on the system. For the sake of flow with the WikiPhysicsBook, we will be analyzing real systems with the energy principle.

[[File:EnergyPrinEqn.png]]

(We are ignoring Q for the sake of simplicity. It will not be taken into account in the subsequent examples despite the possible transfer of energy from temperature differences).
'''E''' is the total energy of the system and '''W''' is the net work done from the surroundings on system. The major difference of a point particle system versus a real system is in the calculation of Work. In a point particle system, it is calculated by the net force dot product with the change in the position of the center of mass. However, Work in a real system is calculated by:

[[File:Workeq.PNG]]

This means that the summation of the all the external forces dot product with the distance each force was applied amounts to the total change in energy of the real system. The change in the mathematical equation for Work between a point particle system and a real system is important because now different forms of energy may be taken into account. In a real system, the change in energy of a system can be given by:

[[File:Realenergyeq.PNG]]

Where,
total change in internal energy ('''U''') is given by:

[[File:Utotaleq.PNG]]

total change in kinetic energy ('''K''') is given by:

[[File:Ktoteq.PNG]]

and change in Miscellaneous Energy is given by:

[[File:Emisceq.PNG]]

==Examples==

In order to better display the difference of Real Systems from [[Point Particle Systems]], the examples done here will be the same examples done from [[Point Particle Systems]].

===Jumper Model (Simple)===
[[File:Jumper.png]]
'''Problem:''' You jump up so that your center of mass has moved a distance '''h'''. How much chemical energy did you expend?

From the Point Particle System analysis, we know that [[File:Jumpktrans.PNG]] and [[File:Fnetjump.PNG]].

System: Person Surroundings: Earth+Floor

Initial State: Crouched down

Final State: Extended and moving with speed v

[[File:Jumpsteps.PNG]]

Assuming negligent change in thermal energy and relative kinetic energy, the change in thermal energy is approximately equal to the normal force multiplied by height.

===Yo-Yo (Middling)===

[[File:Simple.png|650px]][http://www.example.com link title](Chabay)

'''Step 1:''' Solve for translational kinetic energy using the Point Particle System

(The equation for translational kinetic energy here is different than that in [[Point Particle Systems]], so the derivation has been provided.)

[[File:Middling.png|650px]]

[[File:Simple Part Two.png|650px]]

'''Step Two:''' Solve for rotational kinetic energy using a Real System

[[File:Difficult.png]]

Here is where the true difference between Real and Point Particle Systems can be seen. In the Point Particle system, there is no value to account for the change of rotational kinetic energy from the work done the hand. By changing the Work equation to [[File:Workeq.PNG]] rather than [[File:Wppeq.PNG]], the rotational kinetic energy can now be found.

===Spring In a Box (Difficult)===

Suppose a thin box contains a ball of clay with the mass '''M''' connected to a relaxed spring with a stiffness '''ks'''. The masses of the box and the spring are negligible. It is initally at rest, and then a constant force of '''F'''. The box moves a distance '''b''' and the spring stretches a distance '''s''' so that the clay sticks to the box. What is the change in thermal energy of the clay after colliding with the wall of the box?

[[File:Springbox.png]]

From the analyzation of the [[Point Particle Systems]] of the Spring in a Box, we know that [[File:Ktransbox.PNG]]. Because the system is a spring, we also know that [[File:Uspring.PNG]].

[[File:Bssol.PNG]]

==Connectedness==
How is this topic connected to something that you are interested in?
#This topic interest me because from one single particle you can mathematically determine the other form of energy that can occur in various physical interaction. In addition, being able to take a large complex interactions whether springs, gravitational potential or rotational energies are involved, you can solve and break down the interactions
How is it connected to your major?

#This topic is not directly connected to my major, but the underlying ideas connect very closely to my major. By first looking at a point particle we have a starting point to looking and breaking down a complex system. As a biochemist there are large complex biological systems that I will encounter in my studies.

[[File:Biochem.png]]

While I may not be able to break everything down to one single point, starting off with the simplest path way to understand and comprehend the largest and most complex systems is a similar method to my topic. Like with real and Point particle systems, you start off with a simple point so that one part of the interaction can be understood, from there the rest of the system can be dissected and other interactions can be solved for. With biochemical system, understanding one path, than moving from their to larger paths will help you understand the whole system.

Is there an interesting industrial application?

#I do not really know if their is a physical industrial application that can be seen from looking at real and Point particle systems. However, the methodology and thought process behind looking at a real system can be applied to many problem solving situations.

===External links===
[http://www.physicsbook.gatech.edu/Point_Particle_Systems]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." <i>Matter & Interactions</i>. N.p.: n.p., n.d. N. pag. Print.

Wiki Commons Picture

--[[User:Nfortingo3|Nfortingo3]]([[User talk:Nfortingo3|talk]]) 19:26, 28 November 2015 (EST)

[[Category:Energy]]

File:Bssol.PNG

2016-04-18T03:27:31Z

Mwyatt6:

File:Uspring.PNG

2016-04-18T03:26:02Z

Mwyatt6:

File:Boxspringsol.PNG

2016-04-18T03:24:12Z

Mwyatt6:

File:Ktransbox.PNG

2016-04-18T03:17:03Z

Mwyatt6:

Real Systems

2016-04-18T03:06:18Z

Mwyatt6:

This topic has been claimed by mwyatt6

==The Main Idea==
[[File:RealPointParticleDifference.PNG|thumb|left]]
In [[Point Particle Systems]], the only change in energy is from translational kinetic energy because every force is assumed to act on the center of mass. Up until Week 10, we have been measuring change in energy of systems using the Point Particle Method. From what we learned in Week 10 though, we know that translational kinetic energy is not the only type of energy there can be a change in (see: [[Thermal Energy]] and [[Translational, Rotational and Vibrational Energy]]). In a real system, you must consider the point of application of each force when calculating the change in energy. Also in real systems, forces may also occur over a different displacement than the displacement of the center of mass. These two key differences lead to an interesting mathematical model that differs from that used for the Point Particle Method.

===A Mathematical Model===

The mathematical equation used for Real Systems can vary depending on what his happening within and on the system. For the sake of flow with the WikiPhysicsBook, we will be analyzing real systems with the energy principle.

[[File:EnergyPrinEqn.png]]

(We are ignoring Q for the sake of simplicity. It will not be taken into account in the subsequent examples despite the possible transfer of energy from temperature differences).
'''E''' is the total energy of the system and '''W''' is the net work done from the surroundings on system. The major difference of a point particle system versus a real system is in the calculation of Work. In a point particle system, it is calculated by the net force dot product with the change in the position of the center of mass. However, Work in a real system is calculated by:

[[File:Workeq.PNG]]

This means that the summation of the all the external forces dot product with the distance each force was applied amounts to the total change in energy of the real system. The change in the mathematical equation for Work between a point particle system and a real system is important because now different forms of energy may be taken into account. In a real system, the change in energy of a system can be given by:

[[File:Realenergyeq.PNG]]

Where,
total change in internal energy ('''U''') is given by:

[[File:Utotaleq.PNG]]

total change in kinetic energy ('''K''') is given by:

[[File:Ktoteq.PNG]]

and change in Miscellaneous Energy is given by:

[[File:Emisceq.PNG]]

==Examples==

In order to better display the difference of Real Systems from [[Point Particle Systems]], the examples done here will be the same examples done from [[Point Particle Systems]].

===Jumper Model===
[[File:Jumper.png]]
'''Problem:''' You jump up so that your center of mass has moved a distance '''h'''. How much chemical energy did you expend?

From the Point Particle System analysis, we know that [[File:Jumpktrans.PNG]] and [[File:Fnetjump.PNG]].

System: Person Surroundings: Earth+Floor

Initial State: Crouched down

Final State: Extended and moving with speed v

[[File:Jumpsteps.PNG]]

Assuming negligent change in thermal energy and relative kinetic energy, the change in thermal energy is approximately equal to the normal force multiplied by height.

===Yo-Yo===

[[File:Simple.png|650px]][http://www.example.com link title](Chabay)

'''Step 1:''' Solve for translational kinetic energy using the Point Particle System

(The equation for translational kinetic energy here is different than that in [[Point Particle Systems]], so the derivation has been provided.)

[[File:Middling.png|650px]]

[[File:Simple Part Two.png|650px]]

'''Step Two:''' Solve for rotational kinetic energy using a Real System

[[File:Difficult.png]]

Here is where the true difference between Real and Point Particle Systems can be seen. In the Point Particle system, there is no value to account for the change of rotational kinetic energy from the work done the hand. By changing the Work equation to [[File:Workeq.PNG]] rather than [[File:Wppeq.PNG]], the rotational kinetic energy can now be found.

==Connectedness==
How is this topic connected to something that you are interested in?
#This topic interest me because from one single particle you can mathematically determine the other form of energy that can occur in various physical interaction. In addition, being able to take a large complex interactions whether springs, gravitational potential or rotational energies are involved, you can solve and break down the interactions
How is it connected to your major?

#This topic is not directly connected to my major, but the underlying ideas connect very closely to my major. By first looking at a point particle we have a starting point to looking and breaking down a complex system. As a biochemist there are large complex biological systems that I will encounter in my studies.

[[File:Biochem.png]]

While I may not be able to break everything down to one single point, starting off with the simplest path way to understand and comprehend the largest and most complex systems is a similar method to my topic. Like with real and Point particle systems, you start off with a simple point so that one part of the interaction can be understood, from there the rest of the system can be dissected and other interactions can be solved for. With biochemical system, understanding one path, than moving from their to larger paths will help you understand the whole system.

Is there an interesting industrial application?

#I do not really know if their is a physical industrial application that can be seen from looking at real and Point particle systems. However, the methodology and thought process behind looking at a real system can be applied to many problem solving situations.

===External links===
[http://www.physicsbook.gatech.edu/Point_Particle_Systems]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." <i>Matter & Interactions</i>. N.p.: n.p., n.d. N. pag. Print.

Wiki Commons Picture

--[[User:Nfortingo3|Nfortingo3]]([[User talk:Nfortingo3|talk]]) 19:26, 28 November 2015 (EST)

[[Category:Energy]]

File:Wppeq.PNG

2016-04-18T03:05:35Z

Mwyatt6:

Real Systems

2016-04-18T02:45:59Z

Mwyatt6: /* Examples */

This topic has been claimed by mwyatt6

==The Main Idea==
[[File:RealPointParticleDifference.PNG|thumb|left]]
In [[Point Particle Systems]], the only change in energy is from translational kinetic energy because every force is assumed to act on the center of mass. Up until Week 10, we have been measuring change in energy of systems using the Point Particle Method. From what we learned in Week 10 though, we know that translational kinetic energy is not the only type of energy there can be a change in (see: [[Thermal Energy]] and [[Translational, Rotational and Vibrational Energy]]). In a real system, you must consider the point of application of each force when calculating the change in energy. Also in real systems, forces may also occur over a different displacement than the displacement of the center of mass. These two key differences lead to an interesting mathematical model that differs from that used for the Point Particle Method.

===A Mathematical Model===

The mathematical equation used for Real Systems can vary depending on what his happening within and on the system. For the sake of flow with the WikiPhysicsBook, we will be analyzing real systems with the energy principle.

[[File:EnergyPrinEqn.png]]

(We are ignoring Q for the sake of simplicity. It will not be taken into account in the subsequent examples despite the possible transfer of energy from temperature differences).
'''E''' is the total energy of the system and '''W''' is the net work done from the surroundings on system. The major difference of a point particle system versus a real system is in the calculation of Work. In a point particle system, it is calculated by the net force dot product with the change in the position of the center of mass. However, Work in a real system is calculated by:

[[File:Workeq.PNG]]

This means that the summation of the all the external forces dot product with the distance each force was applied amounts to the total change in energy of the real system. The change in the mathematical equation for Work between a point particle system and a real system is important because now different forms of energy may be taken into account. In a real system, the change in energy of a system can be given by:

[[File:Realenergyeq.PNG]]

Where,
total change in internal energy ('''U''') is given by:

[[File:Utotaleq.PNG]]

total change in kinetic energy ('''K''') is given by:

[[File:Ktoteq.PNG]]

and change in Miscellaneous Energy is given by:

[[File:Emisceq.PNG]]

==Examples==

In order to better display the difference of Real Systems from [[Point Particle Systems]], the examples done here will be the same examples done from [[Point Particle Systems]].

===Jumper Model===
[[File:Jumper.png]]
'''Problem:''' You jump up so that your center of mass has moved a distance '''h'''. How much chemical energy did you expend?

From the Point Particle System analysis, we know that [[File:Jumpktrans.PNG]] and [[File:Fnetjump.PNG]].

System: Person Surroundings: Earth+Floor

Initial State: Crouched down

Final State: Extended and moving with speed v

[[File:Jumpsteps.PNG]]

Assuming negligent change in thermal energy and relative kinetic energy, the change in thermal energy is approximately equal to the normal force multiplied by height.

===Yo-Yo===

[[File:Simple.png]][http://www.example.com link title](Chabay)

===Step 1: Solve for Point Particle System===

[[File:Middling.png]]

[[File:Simple Part Two.png]]

In this part of the problem, when it the point particle is the only thing in the system, the only thing that can be solved for is the translational kinetic energy. Since there is only one thing in the system, there is no potential energy involved and the only thing the particle can do it move or translate. The forces acting on the point particle are equal in '''magnitude''' and '''direction''' to the real system. However, their is one key difference discussed in the next section (Chabay)

===Step Two: Solve for Real System===
[[File:Difficult.png]]

As stated before, the forces acting on the point particle are equal in magnitude and direction to the real system. However, the is one key difference is the displacement of the applied force.(Chabay)

==Connectedness==
How is this topic connected to something that you are interested in?
#This topic interest me because from one single particle you can mathematically determine the other form of energy that can occur in various physical interaction. In addition, being able to take a large complex interactions whether springs, gravitational potential or rotational energies are involved, you can solve and break down the interactions
How is it connected to your major?

#This topic is not directly connected to my major, but the underlying ideas connect very closely to my major. By first looking at a point particle we have a starting point to looking and breaking down a complex system. As a biochemist there are large complex biological systems that I will encounter in my studies.

[[File:Biochem.png]]

While I may not be able to break everything down to one single point, starting off with the simplest path way to understand and comprehend the largest and most complex systems is a similar method to my topic. Like with real and Point particle systems, you start off with a simple point so that one part of the interaction can be understood, from there the rest of the system can be dissected and other interactions can be solved for. With biochemical system, understanding one path, than moving from their to larger paths will help you understand the whole system.

Is there an interesting industrial application?

#I do not really know if their is a physical industrial application that can be seen from looking at real and Point particle systems. However, the methodology and thought process behind looking at a real system can be applied to many problem solving situations.

===External links===
[http://www.physicsbook.gatech.edu/Point_Particle_Systems]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." <i>Matter & Interactions</i>. N.p.: n.p., n.d. N. pag. Print.

Wiki Commons Picture

--[[User:Nfortingo3|Nfortingo3]]([[User talk:Nfortingo3|talk]]) 19:26, 28 November 2015 (EST)

[[Category:Energy]]

Real Systems

2016-04-18T02:45:36Z

Mwyatt6: /* Jumper Model */

This topic has been claimed by mwyatt6

==The Main Idea==
[[File:RealPointParticleDifference.PNG|thumb|left]]
In [[Point Particle Systems]], the only change in energy is from translational kinetic energy because every force is assumed to act on the center of mass. Up until Week 10, we have been measuring change in energy of systems using the Point Particle Method. From what we learned in Week 10 though, we know that translational kinetic energy is not the only type of energy there can be a change in (see: [[Thermal Energy]] and [[Translational, Rotational and Vibrational Energy]]). In a real system, you must consider the point of application of each force when calculating the change in energy. Also in real systems, forces may also occur over a different displacement than the displacement of the center of mass. These two key differences lead to an interesting mathematical model that differs from that used for the Point Particle Method.

===A Mathematical Model===

The mathematical equation used for Real Systems can vary depending on what his happening within and on the system. For the sake of flow with the WikiPhysicsBook, we will be analyzing real systems with the energy principle.

[[File:EnergyPrinEqn.png]]

(We are ignoring Q for the sake of simplicity. It will not be taken into account in the subsequent examples despite the possible transfer of energy from temperature differences).
'''E''' is the total energy of the system and '''W''' is the net work done from the surroundings on system. The major difference of a point particle system versus a real system is in the calculation of Work. In a point particle system, it is calculated by the net force dot product with the change in the position of the center of mass. However, Work in a real system is calculated by:

[[File:Workeq.PNG]]

This means that the summation of the all the external forces dot product with the distance each force was applied amounts to the total change in energy of the real system. The change in the mathematical equation for Work between a point particle system and a real system is important because now different forms of energy may be taken into account. In a real system, the change in energy of a system can be given by:

[[File:Realenergyeq.PNG]]

Where,
total change in internal energy ('''U''') is given by:

[[File:Utotaleq.PNG]]

total change in kinetic energy ('''K''') is given by:

[[File:Ktoteq.PNG]]

and change in Miscellaneous Energy is given by:

[[File:Emisceq.PNG]]

==Examples==

In order to better display the difference of Real Systems from [[Point Particle Systems]], the examples done here will be the same examples done from [[Point Particle Systems]].

===Jumper Model===
[[File:Jumper.png]]
'''Problem:''' You jump up so that your center of mass has moved a distance '''h'''. How much chemical energy did you expend?

From the Point Particle System analysis, we know that [[File:Jumpktrans.PNG]] and [[File:Fnetjump.PNG]].

System: Person Surroundings: Earth+Floor

Initial State: Crouched down

Final State: Extended and moving with speed v

[[File:Jumpsteps.PNG]]

Assuming negligent change in thermal energy and relative kinetic energy, the change in thermal energy is approximately equal to the normal force multiplied by height.

===Yo-Yo===

[[File:Simple.png]][http://www.example.com link title](Chabay)

===Step 1: Solve for Point Particle System===

[[File:Middling.png]]

[[File:Simple Part Two.png]]

In this part of the problem, when it the point particle is the only thing in the system, the only thing that can be solved for is the translational kinetic energy. Since there is only one thing in the system, there is no potential energy involved and the only thing the particle can do it move or translate. The forces acting on the point particle are equal in '''magnitude''' and '''direction''' to the real system. However, their is one key difference discussed in the next section (Chabay)

===Step Two: Solve for Real System===
[[File:Difficult.png]]

As stated before, the forces acting on the point particle are equal in magnitude and direction to the real system. However, the is one key difference is the displacement of the applied force.(Chabay)

==Connectedness==
How is this topic connected to something that you are interested in?
#This topic interest me because from one single particle you can mathematically determine the other form of energy that can occur in various physical interaction. In addition, being able to take a large complex interactions whether springs, gravitational potential or rotational energies are involved, you can solve and break down the interactions
How is it connected to your major?

#This topic is not directly connected to my major, but the underlying ideas connect very closely to my major. By first looking at a point particle we have a starting point to looking and breaking down a complex system. As a biochemist there are large complex biological systems that I will encounter in my studies.

[[File:Biochem.png]]

While I may not be able to break everything down to one single point, starting off with the simplest path way to understand and comprehend the largest and most complex systems is a similar method to my topic. Like with real and Point particle systems, you start off with a simple point so that one part of the interaction can be understood, from there the rest of the system can be dissected and other interactions can be solved for. With biochemical system, understanding one path, than moving from their to larger paths will help you understand the whole system.

Is there an interesting industrial application?

#I do not really know if their is a physical industrial application that can be seen from looking at real and Point particle systems. However, the methodology and thought process behind looking at a real system can be applied to many problem solving situations.

===External links===
[http://www.physicsbook.gatech.edu/Point_Particle_Systems]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." <i>Matter & Interactions</i>. N.p.: n.p., n.d. N. pag. Print.

Wiki Commons Picture

--[[User:Nfortingo3|Nfortingo3]]([[User talk:Nfortingo3|talk]]) 19:26, 28 November 2015 (EST)

[[Category:Energy]]

Real Systems

2016-04-18T02:43:53Z

Mwyatt6:

This topic has been claimed by mwyatt6

==The Main Idea==
[[File:RealPointParticleDifference.PNG|thumb|left]]
In [[Point Particle Systems]], the only change in energy is from translational kinetic energy because every force is assumed to act on the center of mass. Up until Week 10, we have been measuring change in energy of systems using the Point Particle Method. From what we learned in Week 10 though, we know that translational kinetic energy is not the only type of energy there can be a change in (see: [[Thermal Energy]] and [[Translational, Rotational and Vibrational Energy]]). In a real system, you must consider the point of application of each force when calculating the change in energy. Also in real systems, forces may also occur over a different displacement than the displacement of the center of mass. These two key differences lead to an interesting mathematical model that differs from that used for the Point Particle Method.

===A Mathematical Model===

The mathematical equation used for Real Systems can vary depending on what his happening within and on the system. For the sake of flow with the WikiPhysicsBook, we will be analyzing real systems with the energy principle.

[[File:EnergyPrinEqn.png]]

(We are ignoring Q for the sake of simplicity. It will not be taken into account in the subsequent examples despite the possible transfer of energy from temperature differences).
'''E''' is the total energy of the system and '''W''' is the net work done from the surroundings on system. The major difference of a point particle system versus a real system is in the calculation of Work. In a point particle system, it is calculated by the net force dot product with the change in the position of the center of mass. However, Work in a real system is calculated by:

[[File:Workeq.PNG]]

This means that the summation of the all the external forces dot product with the distance each force was applied amounts to the total change in energy of the real system. The change in the mathematical equation for Work between a point particle system and a real system is important because now different forms of energy may be taken into account. In a real system, the change in energy of a system can be given by:

[[File:Realenergyeq.PNG]]

Where,
total change in internal energy ('''U''') is given by:

[[File:Utotaleq.PNG]]

total change in kinetic energy ('''K''') is given by:

[[File:Ktoteq.PNG]]

and change in Miscellaneous Energy is given by:

[[File:Emisceq.PNG]]

==Examples==

In order to better display the difference of Real Systems from [[Point Particle Systems]], the examples done here will be the same examples done from [[Point Particle Systems]].

===Jumper Model===
[[File:Jumper.png]]
'''Problem:''' You jump up so that your center of mass has moved a distance '''h'''. How much chemical energy did you expend?

From the Point Particle System analysis, we know that [[File:Jumpktrans.PNG]] and [[File:Fnetjump.PNG]].

System: Person Surroundings: Earth+Floor

Initial State: Crouched down

Final State: Extended and moving with speed v

[[File:Jumpsteps.PNG]]

===Yo-Yo===

[[File:Simple.png]][http://www.example.com link title](Chabay)

===Step 1: Solve for Point Particle System===

[[File:Middling.png]]

[[File:Simple Part Two.png]]

In this part of the problem, when it the point particle is the only thing in the system, the only thing that can be solved for is the translational kinetic energy. Since there is only one thing in the system, there is no potential energy involved and the only thing the particle can do it move or translate. The forces acting on the point particle are equal in '''magnitude''' and '''direction''' to the real system. However, their is one key difference discussed in the next section (Chabay)

===Step Two: Solve for Real System===
[[File:Difficult.png]]

As stated before, the forces acting on the point particle are equal in magnitude and direction to the real system. However, the is one key difference is the displacement of the applied force.(Chabay)

==Connectedness==
How is this topic connected to something that you are interested in?
#This topic interest me because from one single particle you can mathematically determine the other form of energy that can occur in various physical interaction. In addition, being able to take a large complex interactions whether springs, gravitational potential or rotational energies are involved, you can solve and break down the interactions
How is it connected to your major?

#This topic is not directly connected to my major, but the underlying ideas connect very closely to my major. By first looking at a point particle we have a starting point to looking and breaking down a complex system. As a biochemist there are large complex biological systems that I will encounter in my studies.

[[File:Biochem.png]]

While I may not be able to break everything down to one single point, starting off with the simplest path way to understand and comprehend the largest and most complex systems is a similar method to my topic. Like with real and Point particle systems, you start off with a simple point so that one part of the interaction can be understood, from there the rest of the system can be dissected and other interactions can be solved for. With biochemical system, understanding one path, than moving from their to larger paths will help you understand the whole system.

Is there an interesting industrial application?

#I do not really know if their is a physical industrial application that can be seen from looking at real and Point particle systems. However, the methodology and thought process behind looking at a real system can be applied to many problem solving situations.

===External links===
[http://www.physicsbook.gatech.edu/Point_Particle_Systems]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." <i>Matter & Interactions</i>. N.p.: n.p., n.d. N. pag. Print.

Wiki Commons Picture

--[[User:Nfortingo3|Nfortingo3]]([[User talk:Nfortingo3|talk]]) 19:26, 28 November 2015 (EST)

[[Category:Energy]]

File:Fnetjump.PNG

2016-04-18T02:43:19Z

Mwyatt6:

File:Jumpsteps.PNG

2016-04-18T02:37:32Z

Mwyatt6:

File:Jumpktrans.PNG

2016-04-18T02:32:28Z

Mwyatt6:

Real Systems

2016-04-18T02:16:13Z

Mwyatt6:

This topic has been claimed by mwyatt6

==The Main Idea==
[[File:RealPointParticleDifference.PNG|thumb|left]]
In [[Point Particle Systems]], the only change in energy is from translational kinetic energy because every force is assumed to act on the center of mass. Up until Week 10, we have been measuring change in energy of systems using the Point Particle Method. From what we learned in Week 10 though, we know that translational kinetic energy is not the only type of energy there can be a change in (see: [[Thermal Energy]] and [[Translational, Rotational and Vibrational Energy]]). In a real system, you must consider the point of application of each force when calculating the change in energy. Also in real systems, forces may also occur over a different displacement than the displacement of the center of mass. These two key differences lead to an interesting mathematical model that differs from that used for the Point Particle Method.

===A Mathematical Model===

The mathematical equation used for Real Systems can vary depending on what his happening within and on the system. For the sake of flow with the WikiPhysicsBook, we will be analyzing real systems with the energy principle.

[[File:EnergyPrinEqn.png]]

(We are ignoring Q for the sake of simplicity. It will not be taken into account in the subsequent examples despite the possible transfer of energy from temperature differences).
'''E''' is the total energy of the system and '''W''' is the net work done from the surroundings on system. The major difference of a point particle system versus a real system is in the calculation of Work. In a point particle system, it is calculated by the net force dot product with the change in the position of the center of mass. However, Work in a real system is calculated by:

[[File:Workeq.PNG]]

This means that the summation of the all the external forces dot product with the distance each force was applied amounts to the total change in energy of the real system. The change in the mathematical equation for Work between a point particle system and a real system is important because now different forms of energy may be taken into account. In a real system, the change in energy of a system can be given by:

[[File:Realenergyeq.PNG]]

Where,
total change in internal energy ('''U''') is given by:

[[File:Utotaleq.PNG]]

total change in kinetic energy ('''K''') is given by:

[[File:Ktoteq.PNG]]

and change in Miscellaneous Energy is given by:

[[File:Emisceq.PNG]]

==Examples==

This is an example to differentiate between solving for both the point particle and real system
===The Problem===
[[File:Simple.png]][http://www.example.com link title](Chabay)

===Step 1: Solve for Point Particle System===

[[File:Middling.png]]

[[File:Simple Part Two.png]]

In this part of the problem, when it the point particle is the only thing in the system, the only thing that can be solved for is the translational kinetic energy. Since there is only one thing in the system, there is no potential energy involved and the only thing the particle can do it move or translate. The forces acting on the point particle are equal in '''magnitude''' and '''direction''' to the real system. However, their is one key difference discussed in the next section (Chabay)

===Step Two: Solve for Real System===
[[File:Difficult.png]]

As stated before, the forces acting on the point particle are equal in magnitude and direction to the real system. However, the is one key difference is the displacement of the applied force.(Chabay)

==Connectedness==
How is this topic connected to something that you are interested in?
#This topic interest me because from one single particle you can mathematically determine the other form of energy that can occur in various physical interaction. In addition, being able to take a large complex interactions whether springs, gravitational potential or rotational energies are involved, you can solve and break down the interactions
How is it connected to your major?

#This topic is not directly connected to my major, but the underlying ideas connect very closely to my major. By first looking at a point particle we have a starting point to looking and breaking down a complex system. As a biochemist there are large complex biological systems that I will encounter in my studies.

[[File:Biochem.png]]

While I may not be able to break everything down to one single point, starting off with the simplest path way to understand and comprehend the largest and most complex systems is a similar method to my topic. Like with real and Point particle systems, you start off with a simple point so that one part of the interaction can be understood, from there the rest of the system can be dissected and other interactions can be solved for. With biochemical system, understanding one path, than moving from their to larger paths will help you understand the whole system.

Is there an interesting industrial application?

#I do not really know if their is a physical industrial application that can be seen from looking at real and Point particle systems. However, the methodology and thought process behind looking at a real system can be applied to many problem solving situations.

===External links===
[http://www.physicsbook.gatech.edu/Point_Particle_Systems]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." <i>Matter & Interactions</i>. N.p.: n.p., n.d. N. pag. Print.

Wiki Commons Picture

--[[User:Nfortingo3|Nfortingo3]]([[User talk:Nfortingo3|talk]]) 19:26, 28 November 2015 (EST)

[[Category:Energy]]

File:Emisceq.PNG

2016-04-18T02:15:21Z

Mwyatt6:

File:Ktoteq.PNG

2016-04-18T02:12:48Z

Mwyatt6: K total equation for real systems

K total equation for real systems

File:Utotaleq.PNG

2016-04-18T02:10:51Z

Mwyatt6: U total equation for real systems

U total equation for real systems

File:Realenergyeq.PNG

2016-04-18T02:03:21Z

Mwyatt6: Energy equation of a real system

Energy equation of a real system

File:Workeq.PNG

2016-04-18T01:31:03Z

Mwyatt6: Real Systems Work Equation

Real Systems Work Equation

Real Systems

2016-04-18T01:08:52Z

Mwyatt6: /* The Main Idea */

Real Systems

2016-04-18T00:34:25Z

Mwyatt6:

This topic has been claimed by mwyatt6

==The Main Idea==
[[File:RealPointParticleDifference.png]]
In [[Point Particle Systems]], the only change in energy is from translational kinetic energy. Up until Week 10, we have been measuring change in energy of systems using the Point Particle Method. From what we learned in Week 10 though, we know that translational kinetic energy is not the only energy there can be a change in (see: [[Thermal Energy]] and [[Translational, Rotational, and Vibrational Energy]]).

===A Mathematical Model===

The mathematical equations for these types of systems can vary, depending on what his happening within and on the system. However, typically there will always be some form of tranlational kinetic energy becasue the objects, or objects involved will move in some way displacing and conserving energy. The principle that will be used in real systems is the energy principle :

[[File:EnergyPrinEqn.png]]

where '''E''' is the total energy of the system and '''W''' is the net work done from the surroundings. The sum of all the total energies in the system is the sum of the all the external forces(F) over a certain distance(d) within the system(Work). This is know as the Work done on the system. So the energy principles demonstrates that the energy of the system is equal to the work done by the system.

==Examples==

This is an example to differentiate between solving for both the point particle and real system
===The Problem===
[[File:Simple.png]][http://www.example.com link title](Chabay)

===Step 1: Solve for Point Particle System===

[[File:Middling.png]]

[[File:Simple Part Two.png]]

In this part of the problem, when it the point particle is the only thing in the system, the only thing that can be solved for is the translational kinetic energy. Since there is only one thing in the system, there is no potential energy involved and the only thing the particle can do it move or translate. The forces acting on the point particle are equal in '''magnitude''' and '''direction''' to the real system. However, their is one key difference discussed in the next section (Chabay)

===Step Two: Solve for Real System===
[[File:Difficult.png]]

As stated before, the forces acting on the point particle are equal in magnitude and direction to the real system. However, the is one key difference is the displacement of the applied force.(Chabay)

==Connectedness==
How is this topic connected to something that you are interested in?
#This topic interest me because from one single particle you can mathematically determine the other form of energy that can occur in various physical interaction. In addition, being able to take a large complex interactions whether springs, gravitational potential or rotational energies are involved, you can solve and break down the interactions
How is it connected to your major?

#This topic is not directly connected to my major, but the underlying ideas connect very closely to my major. By first looking at a point particle we have a starting point to looking and breaking down a complex system. As a biochemist there are large complex biological systems that I will encounter in my studies.

[[File:Biochem.png]]

While I may not be able to break everything down to one single point, starting off with the simplest path way to understand and comprehend the largest and most complex systems is a similar method to my topic. Like with real and Point particle systems, you start off with a simple point so that one part of the interaction can be understood, from there the rest of the system can be dissected and other interactions can be solved for. With biochemical system, understanding one path, than moving from their to larger paths will help you understand the whole system.

Is there an interesting industrial application?

#I do not really know if their is a physical industrial application that can be seen from looking at real and Point particle systems. However, the methodology and thought process behind looking at a real system can be applied to many problem solving situations.

===External links===
[http://www.physicsbook.gatech.edu/Point_Particle_Systems]

==References==

Chabay, Ruth W., and Bruce A. Sherwood. "9." <i>Matter & Interactions</i>. N.p.: n.p., n.d. N. pag. Print.

Wiki Commons Picture

--[[User:Nfortingo3|Nfortingo3]]([[User talk:Nfortingo3|talk]]) 19:26, 28 November 2015 (EST)

[[Category:Energy]]

File:RealPointParticleDifference.PNG

2016-04-18T00:13:15Z

Mwyatt6: Photo showing difference between forces all acting on center of mass versus forces acting on the actual locations

Photo showing difference between forces all acting on center of mass versus forces acting on the actual locations

Main Page

2016-04-17T23:45:44Z

Mwyatt6: /* Different Models of a System */

__NOTOC__
Welcome to the Georgia Tech Wiki for Introductory Physics. This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in three semester of introductory physics. You can add subcategories as needed but a single topic should direct readers to a page in one of these categories.

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A page for review of [[Vectors]] and vector operations
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">
==Physics 1==
===Week 1===

====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Help with VPython=====
<div class=“mw-collapsible-content”>
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Vectors and Units=====
<div class=“mw-collapsible-content”>
*[[Vectors]]
*[[SI units]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>

=====Interactions=====
<div class=“mw-collapsible-content”>
</div>
</div>
*[[Types of Interactions and How to Detect Them]]

<div class=“toccolours mw-collapsible mw-collapsed”>

=====Velocity and Momentum=====
<div class=“mw-collapsible-content”>
*[[Newton’s First Law of Motion]]
*[[Velocity]]
*[[Mass]]
*[[Speed and Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:vpython_resources Software for Projects]

</div>

===Week 2===
====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Momentum and the Momentum Principle=====
<div class=“mw-collapsible-content”>
*[[Momentum Principle]]
*[[Inertia]]
*[[Net Force]]
*[[Derivation of the Momentum Principle]]
*[[Impulse Momentum]]
*[[Acceleration]]
*[[Momentum with respect to external Forces]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Constant Force=====
<div class=“mw-collapsible-content”>
*[[Newton’s Second Law of Motion]]
*[[Iterative Prediction]]
*[[Kinematics]]
*[[Newton’s Laws and Linear Momentum]]
*[[Projectile Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:scalars_and_vectors Scalars and Vectors]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:displacement_and_velocity Displacement and Velocity]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:modeling_with_vpython Modeling Motion with VPython]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:relative_motion Relative Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:graphing_motion Graphing Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum_principle The Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:acceleration Acceleration & The Change in Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:motionPredict Applying the Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:constantF Constant Force Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:iterativePredict Iterative Prediction of Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>

===Week 3===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Analytic Prediction with a Constant Force=====
<div \
class=“mw-collapsible-content”>
*[[Analytical Prediction]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Varying Force=====
<div \
class=“mw-collapsible-content”>
*[[Predicting Change in multiple dimensions]]
*[[Spring Force]]
*[[Hooke’s Law]]
*[[Simple Harmonic Motion]]
*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Determinism]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:drag Drag]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:impulseGraphs Impulse Graphs]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:springMotion Non-constant Force: Springs & Spring-like Interactions]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:friction Contact Interactions: The Normal Force & Friction]

</div>

===Week 4===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Fundamental Interactions=====
<div class=“mw-collapsible-content”>
*[[Gravitational Force]]
*[[Electric Force]]
*[[Reciprocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]

</div>

===Week 5===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Conservation of Momentum=====
<div class=“mw-collapsible-content”>
*[[Conservation of Momentum]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Properties of Matter=====
<div class=“mw-collapsible-content”>
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young’s Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:model_of_a_wire Modeling a Solid Wire: springs in series and parallel]

</div>

===Week 6===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Identifying Forces=====
<div class=“mw-collapsible-content”>
*[[Free Body Diagram]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Curving Motion=====
<div class=“mw-collapsible-content”>
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_accel Gravitational Acceleration]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:freebodydiagrams Free Body Diagrams]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:curving_motion Curved Motion]

</div>

===Week 7===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Energy Principle=====
<div class=“mw-collapsible-content”>
*[[The Energy Principle]]
*[[Conservation of Energy]]
*[[Kinetic Energy]]
*[[Work]]
*[[Power (Mechanical)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:define_energy What is Energy?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:point_particle The Simplest System: A Single Particle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work Work: Mechanical Energy Transfer]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_cons Conservation of Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]

</div>

===Week 8===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Work by Non-Constant Forces=====
<div \
class=“mw-collapsible-content”>
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Potential Energy=====
<div class=“mw-collapsible-content”>
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work_by_nc_forces Work Done by Non-Constant Forces]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:power Power: The Rate of Energy Change]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 9===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Multiparticle Systems=====
<div class=“mw-collapsible-content”>
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Momentum with respect to external Forces]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_sep Separating Energy in Multi-Particle Systems]

</div>

===Week 10===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Choice of System=====
<div class=“mw-collapsible-content”>
*[[System & Surroundings]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Thermal Energy, Dissipation and Transfer of Energy=====
<div \
class=“mw-collapsible-content”>
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Heat Capacity]]
*[[Specific Heat Capacity]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Predicting Change]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Rotational and Vibrational Energy=====
<div \
class=“mw-collapsible-content”>
*[[Translational, Rotational and Vibrational Energy]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:escape_speed Escape Speed]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:internal_energy Internal Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 11===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Different Models of a System=====
<div \
class=“mw-collapsible-content”>
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Models of Friction=====
<div class=“mw-collapsible-content”>
*[[Friction]]
*[[Static Friction]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 12===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Collisions=====
<div class=“mw-collapsible-content”>
*[[Newton’s Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:collisions Colliding Objects]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real Point Particle and Real Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:colliding_systems Collisions]

</div>

===Week 13===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Rotations=====
<div class=“mw-collapsible-content”>
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Angular Momentum=====
<div class=“mw-collapsible-content”>
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Momentum Compared to Linear Momentum]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[Angular Momentum of Multiparticle Systems]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
*[[Right Hand Rule]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>
===Week 14===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Analyzing Motion with and without Torque=====
<div \
class=“mw-collapsible-content”>
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:torque Torques Cause Changes in Rotation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]

</div>

===Week 15===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Introduction to Quantum Concepts=====
<div \class=“mw-collapsible-content”>
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]

</div>

<div style=“float:left; width:30%; padding:1%;”>

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

<div class="mw-collapsible-content">
*[[Electric field]]
</div>
'''CLAIMED BY DIPRO CHAKRABORTY'''

<div class="toccolours mw-collapsible mw-collapsed">

====Electric force====
<div class="mw-collapsible-content">

*[[Electric Force]] Claimed by Amarachi Eze
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field of a point particle====

<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

'''Bold text'''====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Sign of Potential Difference====
<div class="mw-collapsible-content">
*[[Sign of Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">

====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Node rule====
<div class="mw-collapsible-content">
*[[Node Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Series circuit]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel CIrcuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]] *CLAIMED BY MARK RUSSELL SPRING 2016
*[[R Circuit]]
*[[AC and DC]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===

====Student Content====

<div class=“toccolours mw-collapsible mw-collapsed”>
==== Hall Effect ====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]

</div>
</div>

===Week 13===
<div class=“toccolours mw-collapsible mw-collapsed”>
==== Changing Field Patterns ====
<div class="mw-collapsible-content">
*[[Faraday's Law - claimed by duql1030]]

</div>
</div>

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[Frame of Reference]]
*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>