Physics Book - User contributions [en]

Superposition principle

2017-04-09T19:12:19Z

Ryany715:

'''Claimed by Ryan Yeung: April 8, 2017'''

This topic covers the Superposition Principle. This was the first and original article on this topic (also the best). However it's now being edited, and therefore has become ever better than the best.

==The Main Idea==

The superposition principle essentially states that in a given closed system, the 'reaction' of an object to outside forces is the sum of the outside force acting on it. These forces can act along multiple dimensions, therefore meaning that vector notation will be needed. More simply stated the principle states that the sum of a systems responses is the same as the net result of the forces taken as individuals. In order for the superposition principle to apply, the system must be linear. This means the reaction of the system follows a linear predictable pattern.

===A Mathematical Model===

The net electric field due to two or more charges is the vector sum of each field due to each individual charge. This not only applies to Electric Fields, but Magnetic Fields as well. It is important to note that in the superposition principle, the electric field caused by a charge is not affected by the presence of other charges. It is important to note that this principle applies to all linear systems, note just those of fields. It has the same net result for mechanics as well. Below are the 2 predominate mathematical models for the principle.

:<math>F(x_1+x_2)=F(x_1)+F(x_2) \,</math>

:<math>F(a x)=a F(x) \,</math> 

===A Computational Model===

Here is a python program that calculates and displays the electric as well as magnetic field at a specific observation location for a '''moving dipole'''. The dipole is a negative and positive charge ''q'' and distance ''s''. Write a porgram that will use the given constants to do this.

# GlowScript 2.0 VPython

magconstant = 1e-7
oofpez = 9e9
q=1.6e-19
s = 1e-9
pluscharge = sphere(pos=vector(-5*s, 0,-s/2), radius=1e-10, color=color.red)
minuscharge = sphere(pos=vector(-5*s, 0, s/2), radius=1e-10, color=color.blue)
velocity = vector(4e4,0,0) # The dipoles cm velocity
robs = vector(0,s,0)

# Initializes two arrows (E and B) at the observation location
E = arrow(pos = robs, axis=vector(0,0,0), color = color.cyan)
B = arrow(pos = robs, axis=vector(0,0,0), color = color.magenta)

# Loop that updates dipole position as well as electric and magnetic field
dt = 1e-18

while pluscharge.pos.x < 10*s:

rate(100)

rplus = robs - pluscharge.pos
rplusmag = mag(rplus)
rplushat = norm(rplus)

Eplus = ((oofpez * q) / (rplusmag ** 2))
Bplus = magconstant * q * cross(velocity, rplushat) / rplusmag ** 2

rminus = robs - minuscharge.pos
rminusmag = mag(rminus)
rminushat = norm(rminus)

Eminus = (oofpez * (-q) / (rminus ** 2)) * rminus
Bminus = (magconstant * (-q) * cross(velocity, rminushat)) / (rminushat ** 2)

#Calculates the new E and B net fields
Enet = Eplus + Eminus
Bnet = Bplus + Bminus

# Updates the E and B fields arrows
E.axis = Enet
B.axis = Bnet
from visual import * #import the visual module

rod = cylinder(pos=(0,2,1), axis=(5,0,0), radius=1)

Notice that this uses the principle of superposition. The magnetic and electric fields of the two particles in the dipole are added. This determines the net field at the observation location and is therefore a perfect example of superposition. This is a very elegant and simple example of the principle. It is essentially stated here as the net force as the sum of all other forces. When using the principle in this way it is very important to note the direction of the forces, as they greatly effect the outcome of the answer.

==Examples==
<gallery widths="300px">
File:Superposition Principle.JPG| This picture shows the electric field at the location of q3. Note that the Electric Fields of both q1 and q2 were both calculated individually (but do not react because of one another) and summed up to get the net electric field. Notice the importance of the signs.
File:1111.PNG| Even by adding more source charges, the individual electric fields created by each source charge are unaffected by subsequent charges.
</gallery>

===Simple===

[[File:Electric_Forces_Fields_P1.JPG]]

Say that we have two positive particles at the above locations. Ignore the charges and distance provided for now. The electric field at the location of the negative charge is <math>\vec{E_1} = <2\hat{i}+0\hat{j}+0\hat{k}> </math>N/C and <math>\vec{E_2} = <0\hat{i}+2\hat{j}+0\hat{k}> </math>N/C. What is the net electric field at the location of the electron? Use the principle of superposition.

''Answer:''

Since we know the electric fields from both particles at the point, the superposition principle tells us that we must add the fields together to find the net field. Doing this gives us:
<math>\vec{E_1} + \vec{E_2} = <2\hat{i}+0\hat{j}+0\hat{k}> </math>N/C + <math><0\hat{i}+2\hat{j}+0\hat{k}> </math>N/C
<math> = <2\hat{i}+2\hat{j}+0\hat{k}> </math>

Therefore, the net electric field at the electron's location is <math><2\hat{i}+2\hat{j}+0\hat{k}> </math>N/C. Again it is important to note the effect of the signs. Since both components have positive notation, the net result is positive. However if any of the components had a negative direction, it would have been important to note this throughout the answer.

=== Difficult ===

[[File:1234556.JPG]]

If <math>Q_1</math> and <math>Q_2</math> are positive and negative charges with charges of 6 nC and -5 nC respectively, what is the net electric field at point A located at (0,0,0)? Charge <math>Q_1</math> is located at (2,-2,0). Charge <math>Q_2</math> is located at (5,0,0).
To begin this problem, the first step is to find <math>r_1</math> <math>r_2</math>, the vectors from the charges to point A as well as their magnitudes:

<math>\vec{r_1} = 0\hat{i}+0\hat{j}-(2\hat{i}+-2\hat{j})\Rightarrow\vec{r_1} = -2\hat{i}+2\hat{j}</math>

<math>||\vec{r_1}|| = \sqrt{2^2 + 2^2} =\sqrt{8}</math>

<math>\vec{r_2} = 0\hat{i}+0\hat{j}-(5\hat{i}+0\hat{j})\Rightarrow\vec{r_2} = -2\hat{i}+0\hat{j}</math>

<math>||\vec{r_2}|| = \sqrt{-5^2 + 0^2} =\sqrt{25}</math>

Again, sign notation is very important. Note how the unit vector defines the direction of the fields in this equation and example. It is easiest to define the unit vector first. Then proceed to multiply this my the magnitude of the field, as this allows you to account for direction before the calculation of field.

Using Coloumb's Law, you get:

<math>\vec{E_1} = \frac{1}{4 \pi \epsilon_0}\frac{Q_1}{||r_1||^2}\hat{r_1}=\frac{1}{4 \pi \epsilon_0}\frac{e}{8}<\frac{-2}{\sqrt{8}}\hat{i}+\frac{-2}{\sqrt{8}}\hat{j}> = <-4.77\hat{i}+4.77\hat{j}> </math>N/C

<math>\vec{E_2} = \frac{1}{4 \pi \epsilon_0}\frac{Q_2}{||r_2||^2}\hat{r_2}=\frac{1}{4 \pi \epsilon_0}\frac{e}{5}<\frac{-5}{\sqrt{25}}\hat{i}+\frac{0}{\sqrt{25}}\hat{j}> = <1.8\hat{i}+0\hat{j}> </math>N/C

Next, you need to add the two electric fields together. Because of the superposition principle, the electric field caused by Q1, does not effect the electric field created by Q2, but both can be summed together to create the net electric field at point A.

<math>\vec{E}=\vec{E_1}+\vec{E_2} = <-2.97\hat{i}+0\hat{j}></math>

==Connectedness==
How is this topic connected to something that you are interested in?
* The Superposition Principle is important because it makes your life easier in Physics. You can make assumptions based on the fact that the net field at any location is equal to the sum of all the individual fields. You don't know one of the individual fields, but know the net field? Simple subtraction can help you calculate each individual field. Imagine if all Electric Fields influenced each other? It'd be really difficult to calculate net electric fields without a complicated equation that takes into account one field as a function of another. yuck. Thank the Physics Gods for the Superposition Principle. Its very important to keep this idea in mind any time a net field comes up. Always remember that the independent fields are not individually effected by each other.

How is it connected to your major?
* Since the Superposition Principle can be applied to circuits, and since Biomedical Engineering sometimes create medical device that require circuity, knowing how to create a circuit and calculate the electric field with the superposition principle is an important tool to have. Or if you're a significantly better major like ME, this can be extremely useful in statics problems. If a system is statically determinant like this one:

[[File:determinate-structures-18-638.jpeg]]

In a system such as this, the superposition principle is especially useful for finding the individual reactions at each point on the beam as it is known that the net reaction for the entire system is 0.

Is there an interesting industrial application?
* In [http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1479978 this] study, the Superposition Principle was used to analyze Solar Cells.

==History==
Daniel Bernouilli, in 1753, first proposed the idea of the Superposition Principle. He stated that "The general motion of a vibrating system is given by a superposition of its proper vibrations." His claim was rejected by mathematicians Leonhard Euler, and Joseph Lagrange. However they were eventually proved wrong by Joseph Fourier and it is now the concept you see today.

== See also ==

*[[Coulomb's Law]]
*[[Electric Field]]
*[[Electric Dipole]]
*[[Electric Force]]
*[[Magnetic Force]]
*[[Magnetic Field]]

===Further reading===
*[https://www.boundless.com/physics/textbooks/boundless-physics-textbook/electric-charge-and-field-17/coulomb-s-law-135/superposition-of-forces-483-853/ Additional Textbook Explanation]

*[http://www.sparknotes.com/testprep/books/sat2/physics/chapter17section4.rhtml Sparknotes Explanation]

*[http://www.physicsbook.gatech.edu/Superposition_Principle This guy who made a Superposition principle on this wiki even though I already made one]

===External links===

[https://www.youtube.com/watch?v=S1TXN1M9t18 Instructional video on how to calculate the net electric field using the superposition principle]

[https://www.youtube.com/watch?v=_8fcT95JV34 Video detailing the general use of the principle]

==References==

Chabay, Ruth W.; Sherwood, Bruce A. (2014-12-23). Matter and Interactions, 4th Edition: 1-2 (Page 522). Wiley. Kindle Edition.

https://www.slideshare.net/tarungehlot1/determinate-structures

[[Fields]]

File:Determinate-structures-18-638.jpeg

2017-04-09T19:08:57Z

Ryany715:

SI Units

2016-11-28T03:41:01Z

Ryany715:

This page is about SI Units. This page is created by Jinyoung Lee. Claimed by Ryan Yeung.
==The Main Idea==

SI unit stands for the 'International System of Units'. It is the modern form of the metric system, and is the most widely used system of measurement. It is used among almost all of the larger countries, with the major exception being the United States. It is used whenever scientific observations or measurements are made. It is made up of 7 standard units. It justifies twenty-two named units, and includes many more unnamed coherent derived units. The system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units.

===A Mathematical Model===

There are some mathematical operations required to translate a non-SI unit to SI unit. For example <math>{\frac{lb}{2.2}} = kg</math> Since 1 kg(SI unit) is equal to 2.2 lb, to change lb to SI unit, or kg, lb has to be divided by 2.2.

Another example can be length. <math>{\frac{inch}{0.394}} = cm</math> Same method used to change lb to kg. Since 1cm is equal to 0.394inch, inch has to be divided by 0.394 to become SI unit, cm.

These transformations can be done throughout all of the recorded units in the world. In order to preform these simply find the accepted transformation values, and preform a simple division or multiplication operation.

==Base SI units==

[[File:SIbase.jpg]]

This image above shows the base SI units. These units include length, mass, time, electric current, temperature, substance amount, and light intensity. There also exist a variety of other units that are not as commonplace as these other 7.

==Prefix==

Mass, length or any numbers in physics can be very small or very large. Electrons can be a great example. The mass of electron is 0.0000000000000000000000910938356g or 9.10938356 E-31. In SI, prefixes are available to adjust the size of a unit so as to keep the number of those units reasonable. It is kind of difficult to read that number in word. However with the prefix it can be. Image below shows the list of prefixes.

[[File:prefix1.jpg]]

These prefixes are incredibly useful for clarity purposes. The prefixes listed are incredibly useful for a speaker or writer in order to help ease their use.

==Derived SI units==

[[File:Relationdiagram.jpg]]

This image above shows the relationships between many units used in physics based on base SI units. As we can see, most of the units in physics is related to the SI units. It is because there are many quantities that cannot be expressed by a single base SI unit. For example, when talking about the density, it is volume/mass. Mass has it's own SI unit which is a gram. However volume doesn't. Volume is expressed with derived SI unit, meters cubed. As a result, unit for density is <math>\mathrm{m}^3/\mathrm{g}</math> . Those units are called derived SI units. Units can be combined to create new unit. Some frequently-used combinations have their units named. Here are some examples:

*Watt (W), the unit of power.
**<math>\mathrm{W} = \mathrm{J}/\mathrm{s} \ </math>

*Pascal (Pa), the unit of pressure.
**<math>\mathrm{Pa} = \mathrm{N}/\mathrm{m}^2 \ </math>

*Hertz (Hz), the unit of frequency.
**<math>\mathrm{Hz} = 1/\mathrm{s} = \mathrm{s}^{-1} \ </math>

*Newton (N), the unit of force.
**<math>\mathrm{N} = \mathrm{kg} \cdot \mathrm{m}/\mathrm{s}^2 </math>

*Joule (J), the unit of energy.
**<math>\mathrm{J} = \mathrm{N} \cdot \mathrm{m} = \mathrm{kg} \cdot \mathrm{m}^2/\mathrm{s}^2 </math>

*Coulomb (C), the unit of electric charge.
**<math>\mathrm{C} = \mathrm{A} \cdot \mathrm{s} </math>

*Volt (V), the unit of electric potential or voltage.
**<math>\mathrm{V} = \mathrm{J}/\mathrm{C} = \mathrm{W}/\mathrm{A} \ </math>

The list is incredibly useful for measuring quantities that dont have a standard SI unit already in place.

==Connectedness==
This topic can be applied to every aspect of science. When solving the problem, or even when doing a research, every equation and theory is based on SI units. It is a promise between scientists to use the certain units to reduce the errors or misunderstanding. Therefore, it is very important to know the concept of SI units. This topic is connected to not only physics but also every other scientific subjects. In addition, it might not be familiar in United States, but in the most of the countries they use SI units in ordinary life. SI units create a form of standardization throughout the scientific community. It's through the use of these units that the community of scientists as a whole that error can be reduced to a minimum and calculations and findings can be standardized across the globe. Si units also allow scientists to reproduce experiments, and record their results in the same form. This allows for more credibility among findings as well. SI units are also very useful for the use of dimensional analysis. Dimensional analysis is the mathematical problem solving method that essentially means that any number expression can be multiplied by another and its inherent value won't be changed. This vital problem solving idea is only possible due to the fact that SI units can be converted to non SI units with incredible ease. SI units create an incredible amount of standardization throughout the scientific community and have been essential for the production of viable and credible scientific results.

==History==

The Metric System was created around the time of the French Revolution and the subsequent deposition of two platinum standards representing the meter and the kilogram, on 22 June 1799, in the Archives de la Republic in Paris can be seen as the first step in the development of the present International System of Units. Each of the base units has root within the physical world. For example the unit of metre is derived from dimensions of the Earth, the kilogram was derived the volume of of one liter of water. These 2 units are the baseline for the remainder of the SI system. The new metric system was originally abandoned by France. In 1837, the metric system was readopted by France, and slowly then became adopted by the scientific community. After this a man named James Clerk Maxwell presented the idea of a number of base units, time, mass, and length. This 3 base units could then be used to derive a series of other measurements throughout the scientific world. However it was quickly discovered that these units cannot describe non-mechanical properties. Most importantly they couldn't properly describe the electrical properties of the world. A man named Giovanni Giorgi, an Italian physicist and electrical engineer, proposed a fourth base unit should be added to the original 3 in order to properly describe the electrical systems of the world. This unit was later decided, in 1935, to be the ampere thus allowing the world to aptly describe electrical systems as well. As the years passed these units began to become more and more commonplace among the world, with many other countries beginning to use the SI system as their main form of measurement. The SI system quickly became the accepted scientific measuring system as well. The use of this system has helped to advance and drive scientific advancement throughout the years.

===Further reading===

SI Units for Clinical Measurement 1st Edition by Donald S. Young

Matter & Interactions, Vol. I: Modern Mechanics, 4nd Edition by R. Chabay & B. Sherwood (John Wiley & Sons 2015)

==References==

http://physics.nist.gov/ National institute of standards and Technology.

http://wps.prenhall.com/wps/media/objects/165/169061/blb9ch0104.html Pearson educational site.

Matter & Interactions, Vol. I: Modern Mechanics, 4nd Edition by R. Chabay & B. Sherwood (John Wiley & Sons 2015)

Tutorial & Drill Problems for General Chemistry (and Intro) By Walter S. Hamilton, Ph.D.

SI Units

2016-11-28T03:20:32Z

Ryany715:

This page is about SI Units. This page is created by Jinyoung Lee. Claimed by Ryan Yeung.
==The Main Idea==

SI unit stands for the 'International System of Units'. It is the modern form of the metric system, and is the most widely used system of measurement. It is used among almost all of the larger countries, with the major exception being the United States. It is used whenever scientific observations or measurements are made. It is made up of 7 standard units. It justifies twenty-two named units, and includes many more unnamed coherent derived units. The system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units.

===A Mathematical Model===

There are some mathematical operations required to translate a non-SI unit to SI unit. For example <math>{\frac{lb}{2.2}} = kg</math> Since 1 kg(SI unit) is equal to 2.2 lb, to change lb to SI unit, or kg, lb has to be divided by 2.2.

Another example can be length. <math>{\frac{inch}{0.394}} = cm</math> Same method used to change lb to kg. Since 1cm is equal to 0.394inch, inch has to be divided by 0.394 to become SI unit, cm.

These transformations can be done throughout all of the recorded units in the world. In order to preform these simply find the accepted transformation values, and preform a simple division or multiplication operation.

==Base SI units==

[[File:SIbase.jpg]]

This image above shows the base SI units. These units include length, mass, time, electric current, temperature, substance amount, and light intensity. There also exist a variety of other units that are not as commonplace as these other 7.

==Prefix==

Mass, length or any numbers in physics can be very small or very large. Electrons can be a great example. The mass of electron is 0.0000000000000000000000910938356g or 9.10938356 E-31. In SI, prefixes are available to adjust the size of a unit so as to keep the number of those units reasonable. It is kind of difficult to read that number in word. However with the prefix it can be. Image below shows the list of prefixes.

[[File:prefix1.jpg]]

These prefixes are incredibly useful for clarity purposes. The prefixes listed are incredibly useful for a speaker or writer in order to help ease their use.

==Derived SI units==

[[File:Relationdiagram.jpg]]

This image above shows the relationships between many units used in physics based on base SI units. As we can see, most of the units in physics is related to the SI units. It is because there are many quantities that cannot be expressed by a single base SI unit. For example, when talking about the density, it is volume/mass. Mass has it's own SI unit which is a gram. However volume doesn't. Volume is expressed with derived SI unit, meters cubed. As a result, unit for density is <math>\mathrm{m}^3/\mathrm{g}</math> . Those units are called derived SI units. Units can be combined to create new unit. Some frequently-used combinations have their units named. Here are some examples:

*Watt (W), the unit of power.
**<math>\mathrm{W} = \mathrm{J}/\mathrm{s} \ </math>

*Pascal (Pa), the unit of pressure.
**<math>\mathrm{Pa} = \mathrm{N}/\mathrm{m}^2 \ </math>

*Hertz (Hz), the unit of frequency.
**<math>\mathrm{Hz} = 1/\mathrm{s} = \mathrm{s}^{-1} \ </math>

*Newton (N), the unit of force.
**<math>\mathrm{N} = \mathrm{kg} \cdot \mathrm{m}/\mathrm{s}^2 </math>

*Joule (J), the unit of energy.
**<math>\mathrm{J} = \mathrm{N} \cdot \mathrm{m} = \mathrm{kg} \cdot \mathrm{m}^2/\mathrm{s}^2 </math>

*Coulomb (C), the unit of electric charge.
**<math>\mathrm{C} = \mathrm{A} \cdot \mathrm{s} </math>

*Volt (V), the unit of electric potential or voltage.
**<math>\mathrm{V} = \mathrm{J}/\mathrm{C} = \mathrm{W}/\mathrm{A} \ </math>

The list is incredibly useful for measuring quantities that dont have a standard SI unit already in place.

==Connectedness==
This topic can be applied to every aspect of science. When solving the problem, or even when doing a research, every equation and theory is based on SI units. It is a promise between scientists to use the certain units to reduce the errors or misunderstanding. Therefore, it is very important to know the concept of SI units. This topic is connected to not only physics but also every other scientific subjects. In addition, it might not be familiar in United States, but in the most of the countries they use SI units in ordinary life. SI units create a form of standardization throughout the scientific community. It's through the use of these units that the community of scientists as a whole that error can be reduced to a minimum and calculations and findings can be standardized across the globe. Si units also allow scientists to reproduce experiments, and record their results in the same form. This allows for more credibility among findings as well. SI units are also very useful for the use of dimensional analysis. Dimensional analysis is the mathematical problem solving method that essentially means that any number expression can be multiplied by another and its inherent value won't be changed. This vital problem solving idea is only possible due to the fact that SI units can be converted to non SI units with incredible ease. SI units create an incredible amount of standardization throughout the scientific community and have been essential for the production of viable and credible scientific results.

==History==

The Metric System was created around the time of the French Revolution and the subsequent deposition of two platinum standards representing the meter and the kilogram, on 22 June 1799, in the Archives de la Republic in Paris can be seen as the first step in the development of the present International System of Units. Each of the base units has root within the physical world. For example the unit of metre is derived from dimensions of the Earth, the kilogram was derived the volume of of one liter of water. These 2 units are the baseline for the remainder of the SI system. The new metric system was originally abandoned by France. In 1837, the metric system was readopted by France, and slowly then became adopted by the scientific community. After this a man named James Clerk Maxwell presented the idea of a number of base units, time, mass, and length. This 3 base units could then be used to derive a series of other measurements throughout the scientific world. However it was quickly discovered that these units cannot describe non-mechanical properties. Most importantly they couldn't properly describe the electrical properties of the world. A man named Giovanni Giorgi, an Italian physicist and electrical engineer, proposed a fourth base unit should be added to the original 3 in order to properly describe the electrical systems of the world. This unit was later decided, in 1935, to be the ampere thus allowing the world to aptly describe electrical systems as well.

===Further reading===

SI Units for Clinical Measurement 1st Edition by Donald S. Young

Matter & Interactions, Vol. I: Modern Mechanics, 4nd Edition by R. Chabay & B. Sherwood (John Wiley & Sons 2015)

==References==

http://physics.nist.gov/ National institute of standards and Technology.

http://wps.prenhall.com/wps/media/objects/165/169061/blb9ch0104.html Pearson educational site.

Matter & Interactions, Vol. I: Modern Mechanics, 4nd Edition by R. Chabay & B. Sherwood (John Wiley & Sons 2015)

Tutorial & Drill Problems for General Chemistry (and Intro) By Walter S. Hamilton, Ph.D.

SI Units

2016-11-28T02:00:38Z

Ryany715:

This page is about SI Units. This page is created by Jinyoung Lee. Claimed by Ryan Yeung.
==The Main Idea==

SI unit stands for the 'International System of Units'. It is the modern form of the metric system, and is the most widely used system of measurement. It is used among almost all of the larger countries, with the major exception being the United States. It is used whenever scientific observations or measurements are made. It is made up of 7 standard units. It justifies twenty-two named units, and includes many more unnamed coherent derived units. The system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units.

===A Mathematical Model===

There are some mathematical operations required to translate a non-SI unit to SI unit. For example <math>{\frac{lb}{2.2}} = kg</math> Since 1 kg(SI unit) is equal to 2.2 lb, to change lb to SI unit, or kg, lb has to be divided by 2.2.

Another example can be length. <math>{\frac{inch}{0.394}} = cm</math> Same method used to change lb to kg. Since 1cm is equal to 0.394inch, inch has to be divided by 0.394 to become SI unit, cm.

These transformations can be done throughout all of the recorded units in the world. In order to preform these simply find the accepted transformation values, and preform a simple division or multiplication operation.

==Base SI units==

[[File:SIbase.jpg]]

This image above shows the base SI units. These units include length, mass, time, electric current, temperature, substance amount, and light intensity. There also exist a variety of other units that are not as commonplace as these other 7.

==Prefix==

Mass, length or any numbers in physics can be very small or very large. Electrons can be a great example. The mass of electron is 0.0000000000000000000000910938356g or 9.10938356 E-31. In SI, prefixes are available to adjust the size of a unit so as to keep the number of those units reasonable. It is kind of difficult to read that number in word. However with the prefix it can be. Image below shows the list of prefixes.

[[File:prefix1.jpg]]

These prefixes are incredibly useful for clarity purposes. The prefixes listed are incredibly useful for a speaker or writer in order to help ease their use.

==Derived SI units==

[[File:Relationdiagram.jpg]]

This image above shows the relationships between many units used in physics based on base SI units. As we can see, most of the units in physics is related to the SI units. It is because there are many quantities that cannot be expressed by a single base SI unit. For example, when talking about the density, it is volume/mass. Mass has it's own SI unit which is a gram. However volume doesn't. Volume is expressed with derived SI unit, meters cubed. As a result, unit for density is <math>\mathrm{m}^3/\mathrm{g}</math> . Those units are called derived SI units. Units can be combined to create new unit. Some frequently-used combinations have their units named. Here are some examples:

*Watt (W), the unit of power.
**<math>\mathrm{W} = \mathrm{J}/\mathrm{s} \ </math>

*Pascal (Pa), the unit of pressure.
**<math>\mathrm{Pa} = \mathrm{N}/\mathrm{m}^2 \ </math>

*Hertz (Hz), the unit of frequency.
**<math>\mathrm{Hz} = 1/\mathrm{s} = \mathrm{s}^{-1} \ </math>

*Newton (N), the unit of force.
**<math>\mathrm{N} = \mathrm{kg} \cdot \mathrm{m}/\mathrm{s}^2 </math>

*Joule (J), the unit of energy.
**<math>\mathrm{J} = \mathrm{N} \cdot \mathrm{m} = \mathrm{kg} \cdot \mathrm{m}^2/\mathrm{s}^2 </math>

*Coulomb (C), the unit of electric charge.
**<math>\mathrm{C} = \mathrm{A} \cdot \mathrm{s} </math>

*Volt (V), the unit of electric potential or voltage.
**<math>\mathrm{V} = \mathrm{J}/\mathrm{C} = \mathrm{W}/\mathrm{A} \ </math>

The list is incredibly useful for measuring quantities that dont have a standard SI unit already in place.

==Connectedness==
This topic can be applied to every aspect of science. When solving the problem, or even when doing a research, every equation and theory are based on SI units. It is a promise between scientists to use the certain units to reduce the errors or misunderstanding. Therefore, it is very important to know the concept of SI units. This topic is connected to not only physics but also every other scientific subjects. In addition, it might not be familiar in United States, but in the most of the countries they use SI units in ordinary life. SI units create a form of standardization throughout the scientific community. It's through the use of these units that the community of scientists as a whole that error can be reduced to a minimum and calculations and findings can be standardized across the globe. Si units also allow scientists to reproduce experiments, and record their results in the same form. This allows for more credibility among findings as well. SI units are also very useful for the use of dimensional analysis. Dimensional analysis is the mathematical problem solving method that essentially means that any number expression can be multiplied by another and its inherent value won't be changed. This vital problem solving idea is only possible due to the fact that SI units can be converted to non SI units with incredible ease. SI units create an incredible amount of standardization throughout the scientific community and have been essential for the production of viable and credible scientific results.

==History==

The Metric System was created around the time of the French Revolution and the subsequent deposition of two platinum standards representing the meter and the kilogram, on 22 June 1799, in the Archives de la Republic in Paris can be seen as the first step in the development of the present International System of Units. Each of the base units has root within the physical world. For example the unit of metre is derived from dimensions of the Earth, the kilogram was derived the volume of of one liter of water. These 2 units are the baseline for the remainder of the SI system. The new metric system was originally abandoned by France. In 1837, the metric system was readopted by France, and slowly then became adopted by the scientific community. After this a man named James Clerk Maxwell presented the idea of a number of base units, time, mass, and length. This 3 base units could then be used to derive a series of other measurements throughout the scientific world. However it was quickly discovered that these units cannot describe non-mechanical properties. Most importantly they couldn't properly describe the electrical properties of the world. A man named Giovanni Giorgi, an Italian physicist and electrical engineer, proposed a fourth base unit should be added to the original 3 in order to properly describe the electrical systems of the world. This unit was later decided, in 1935, to be the ampere thus allowing the world to aptly describe electrical systems as well.

===Further reading===

SI Units for Clinical Measurement 1st Edition by Donald S. Young

Matter & Interactions, Vol. I: Modern Mechanics, 4nd Edition by R. Chabay & B. Sherwood (John Wiley & Sons 2015)

==References==

http://physics.nist.gov/ National institute of standards and Technology.

http://wps.prenhall.com/wps/media/objects/165/169061/blb9ch0104.html Pearson educational site.

Matter & Interactions, Vol. I: Modern Mechanics, 4nd Edition by R. Chabay & B. Sherwood (John Wiley & Sons 2015)

Tutorial & Drill Problems for General Chemistry (and Intro) By Walter S. Hamilton, Ph.D.

SI Units

2016-11-27T23:41:39Z

Ryany715:

SI Units

2016-11-27T16:11:44Z

Ryany715: