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==Rotational Angular Momentum==


Angular momentum is the quantity of rotation of a system, and in specific, rotational angular momentum is the system's angular momentum relative to its center of mass.
Claimed by: Tiffany Zhou
==Main Idea==


This topics focuses on energy work of a system but it can only deal with a large scale response to heat in a system.  '''Thermodynamics''' is the study of the work, heat and energy of a system. The smaller scale gas interactions can explained using the kinetic theory of gases.  There are three fundamental laws that go along with the topic of thermodynamics.  They are the zeroth law, the first law, and the second law.  These laws help us understand predict the the operation of the physical system.  In order to understand the laws, you must first understand thermal equilibrium.  [[Thermal equilibrium]] is reached when a object that is at a higher temperature is in contact with an object that is at a lower temperature and the first object transfers heat to the latter object until they approach the same temperature and maintain that temperature constantly.  It is also important to note that any thermodynamic system in thermal equilibrium possesses internal energy.
What is Rotational Angular Momentum? In short, rotational angualr momentum is the momentum of an object spinning on its own axis. Therefore if an object does not spin on its own axis, then it does not have a rotational angualr momentum. This page will give you and overall understanding of rotational angular momentum, through a couple practice problems and detailed explanation of rotational angular momentum and its relationship with other physics concept.


===Zeroth Law===
'''Total angualr momentum can be defined as the sum of the translational and  rotational angualr momentum'''. In other words, we can find rotatational angualr momentum without anything more than simple subtration, if we  have both the total angular momentum and translational momentum.


The zeroth law states that if two systems are at thermal equilibrium at the same time as a third system, then all of the systems are at equilibrium with each other.  If systems A and C are in thermal equilibrium with B, then system A and C are also in thermal equilibrium with each other. There are underlying ideas of heat that are also important. The most prominent one is that all heat is of the same kind.  As long as the systems are at thermal equilibrium, every unit of internal energy that passes from one system to the other is balanced by the same amount of energy passing back.  This also applies when the two systems or objects have different atomic masses or material.
In other cases, solving for rotational angular momentum will take more than just subtraction, and require us to use some of the equation listed below.  
===Mathematical Model===
'''There are two equations that can be used to describe rotational angular momentum.'''
The first one is a generalized form that can be described as the sum of cross products of distance and momentum.


====A Mathematical Model====
[[File:rotationalangularmomentum.png]]


If A = B and A = C, then B = C
The next equation summarizes rotational angular momentum as the product of inertia and angular velocity.
A = B = C
(The units of rotational angular momentum are kg*m^2/s.
[[File:rotationalang.jpg]]


====A Computational Model====
To use the above equation, the following equations may be needed.
The first equation is used to calculate the moment inertia.
The moment of inertia can be defined as the tendency to resist changes in their state of motion.
(The units of inertia are kg*m^2.)


How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]
[[File:variousinertia.jpg]]


===First Law===
The next equation angular velocity which is the rate of change of angular position of a rotating object.
(The units of angular velocity are radians per second).


The first law of thermodynamics defines the internal energy (E) as equal to the difference between heat transfer (Q) ''into'' a system and work (W) ''done by'' the system. Heat removed from a system would be given a negative sign and heat applied to the system would be given a positive sign.  Internal energy can be converted into other types of energy because it acts like potential energy.  Heat and work, however, cannot be stored or conserved independently because they depend on the process.  This allows for many different possible states of a system to exist.  There can be a process known as the adiabatic process in which there is no heat transfer.  This occurs when a system is full insulated from the outside environment.  The implementation of this law also brings about another useful state variable, '''enthalpy'''. 
[[File:Equationangvelpng.png]]


====A Mathematical Model====
==Examples==


E2 - E1 = Q - W
Listed below are examples of rotational angular momentum problems.


==Examples==
===Simple===
Below is a conceptual rotational angular momentum problem.


Be sure to show all steps in your solution and include diagrams whenever possible
[[File:ramsample3.png]]
[[File:ramsample4.png]]


===Simple===
===Middling===
===Middling===
These rotational angular momentum problems use both the inertia and angular velocity equations.
Example 1
[[File:ramsample.png]]
Example 2
[[File:ramsample2.png]]
===Difficult===
===Difficult===
Example 1
[[File:ramsample6.png]]
[[File:ramsample5.png]]
[[File:ramsample7.png]]
[[File:ramsample8.png]]
Example 2
[[File:ramsample9.png]]
[[File:ramsample10.png]]
[[File:ramsample11.png]]
[[File:ramsample12.png]]


==Connectedness==
==Connectedness==
#How is this topic connected to something that you are interested in?
Rotational angular momentum can be applied to every day life. Examples include the earth rotating on its axis, a figure skater, a football spinning as it's being thrown, or even a firing bullet. Anything that rotates on its own axis will have rotational angular momentum.
#How is it connected to your major?
[[File:skaterang.png]]
#Is there an interesting industrial application?


==History==
==History==


Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
The idea of rotational angular momentum came from Johannes Kepler, a German scientist and astronomer who lived in the late 1500's through the mid 1600's. Kepler believed that planets orbited in an ellipse, but he also needed a rule to describe the change of velocity over time. He discovered a law of areas. This means that as planets orbit the sun, they sweep out in equal areas over equal amounts of time. However, Isaac Newton, a physicist and mathematician who came after Kepler, realized that the area law was part of a larger theory of motion.
 
Newton's second law particularly covers angular momentum. The second law states that the acceleration is dependent on the net force upon the object and the mass of the object. The vector sum of all torques acting on a particle is equal to the time rate
of change of the angular momentum of that particle.


== See also ==
== See also ==


Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?


===Further reading===
===Further reading===
Matter and Interactions by Ruth W. Chabay and Bruce A. Sherwood


Books, Articles or other print media on this topic
Elementary Theory of Angular Momentum by M.E. Rose
 
Angular Momentum in Quantum Mechanics by A.R. Redmonds


===External links===
===External links===
http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html
https://www.youtube.com/watch?v=MULe4xv3lVk
==References==


Internet resources on this topic
http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law


==References==
https://physics.ucf.edu/~roldan/classes/phy2048-ch10_new.pdf
 
http://www.physicsclassroom.com/mmedia/circmot/ksl.cfm
 
http://farside.ph.utexas.edu/teaching/301/lectures/node122.html
 
https://www.crashwhite.com/apphysics/materials/practicetests/practice_test-6-rotation-angular_momentum.pdf


https://www.grc.nasa.gov/www/k-12/airplane/thermo0.html
http://www.cordonline.net/cci_pic_pdfs/Chap7-2PT.pdf
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html


[[Category:Which Category did you place this in?]]
[[Category:Angular Momentum]]

Latest revision as of 21:09, 26 November 2016

Claimed by: Tiffany Zhou

Main Idea

What is Rotational Angular Momentum? In short, rotational angualr momentum is the momentum of an object spinning on its own axis. Therefore if an object does not spin on its own axis, then it does not have a rotational angualr momentum. This page will give you and overall understanding of rotational angular momentum, through a couple practice problems and detailed explanation of rotational angular momentum and its relationship with other physics concept.

Total angualr momentum can be defined as the sum of the translational and rotational angualr momentum. In other words, we can find rotatational angualr momentum without anything more than simple subtration, if we have both the total angular momentum and translational momentum.

In other cases, solving for rotational angular momentum will take more than just subtraction, and require us to use some of the equation listed below.

Mathematical Model

There are two equations that can be used to describe rotational angular momentum. The first one is a generalized form that can be described as the sum of cross products of distance and momentum.

The next equation summarizes rotational angular momentum as the product of inertia and angular velocity. 

(The units of rotational angular momentum are kg*m^2/s.

To use the above equation, the following equations may be needed. The first equation is used to calculate the moment inertia. The moment of inertia can be defined as the tendency to resist changes in their state of motion. (The units of inertia are kg*m^2.)

The next equation angular velocity which is the rate of change of angular position of a rotating object. (The units of angular velocity are radians per second).

Examples

Listed below are examples of rotational angular momentum problems.

Simple

Below is a conceptual rotational angular momentum problem.

Middling

These rotational angular momentum problems use both the inertia and angular velocity equations.

Example 1

Example 2

Difficult

Example 1

Example 2


Connectedness

Rotational angular momentum can be applied to every day life. Examples include the earth rotating on its axis, a figure skater, a football spinning as it's being thrown, or even a firing bullet. Anything that rotates on its own axis will have rotational angular momentum.

History

The idea of rotational angular momentum came from Johannes Kepler, a German scientist and astronomer who lived in the late 1500's through the mid 1600's. Kepler believed that planets orbited in an ellipse, but he also needed a rule to describe the change of velocity over time. He discovered a law of areas. This means that as planets orbit the sun, they sweep out in equal areas over equal amounts of time. However, Isaac Newton, a physicist and mathematician who came after Kepler, realized that the area law was part of a larger theory of motion.

Newton's second law particularly covers angular momentum. The second law states that the acceleration is dependent on the net force upon the object and the mass of the object. The vector sum of all torques acting on a particle is equal to the time rate of change of the angular momentum of that particle.

See also

Further reading

Matter and Interactions by Ruth W. Chabay and Bruce A. Sherwood

Elementary Theory of Angular Momentum by M.E. Rose

Angular Momentum in Quantum Mechanics by A.R. Redmonds

External links

http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html https://www.youtube.com/watch?v=MULe4xv3lVk

References

http://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law

https://physics.ucf.edu/~roldan/classes/phy2048-ch10_new.pdf

http://www.physicsclassroom.com/mmedia/circmot/ksl.cfm

http://farside.ph.utexas.edu/teaching/301/lectures/node122.html

https://www.crashwhite.com/apphysics/materials/practicetests/practice_test-6-rotation-angular_momentum.pdf

http://www.cordonline.net/cci_pic_pdfs/Chap7-2PT.pdf

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