E = mc^2 explained (from PBS)

Ten top Physicists talk about the meaning of E = mc^2.
Each recording is about 1.5 minutes...  Go to: http://www.pbs.org/wgbh/nova/einstein/experts.html

Graphing the sin(theta) and cos(theta) using the Unit Circle

The Unit Circle is a circle with a radius of 1, and which is centered at the origin (0,0).
Its equation is: x² + y² = 1.
Its equation is also: x = cos(theta), y = sin(theta).
HOMEWORK part one: PROVE  to yourself that x² + y² = 1
for every point  in the following diagram. 

For example,

(1,0) ==> x = 1 and y = 0 ==>
          x^2 = 1 and y^2 = 0 ==> 1 + 0 = 1    check

(√3/2, 1/2) ==> x = √3/2 and y = 1/2 ==>
          x^2 = 3/4 and y^2 = 1/4 ==> 3/4 + 1/4 = 1   check

(√2/2, √2/2) ==> x = √2/2 and y = √2/2 ==>
          x^2 = 2/4 and y^2 = 2/4 ==> 2/4 + 2/4 = 1  check

and so on for all the points around the circle.

HOMEWORK part two: PLAY with the following applets
for the sin(theta) http://www.ies.co.jp/math/java/trig/graphSinX/graphSinX.html
and cos(theta) http://www.ies.co.jp/math/java/trig/graphCosX/graphCosX.html

and PROVE that sin(theta) = y and cos(theta) = x, for all the points
in the unit circle. Note, Don't forget to rotate the cos(theta) applet
after you have drawn it !

Ten minute TRIG from Victoria University (Australia)

Review the following formulas, write them out, and solve the problems on the following link:
http://www.staff.vu.edu.au/mcaonline/units/trig/ratios.html

Review the Pythagorean theorem again, and solve the problems on the following website: http://www.worsleyschool.net/science/files/pythagoras/pythagoreantheorem2.html

Decomposing vectors using TRIG

How can you decompose vectors into their components?
See this website to find out more:
http://www.sparknotes.com/testprep/books/sat2/physics/chapter4section5.rhtml

Solve the problems on this website for homework:
http://www.physics247.com/physics-homework-help/vector-components.php

stoichiometry -- balancing chemical equations using moles from the Chem Collective from Carnegie Mellon University

The following video gives the "big picture" of the mole and its applications.
The big picture of the mole from the Chem Collective from Carnegie Mellon University

Information on how to use the mole in balancing chemical equations is found here:
Stoichiometry: using the mole to balance chemical equations from The Chem Collective from Carnegie Mellon University

How far is Avogadro's number in meters? (6.023 x 10^23 m)

Avogadro's number...How big is it?
Can a person count to this number in their lifetime (counting once per second)?

How far away from the Earth would you be if you traveled this number of meters? See this video on youtube for an excellent, 9 minute description!
http://www.youtube.com/watch?v=A2cmlhfdxuY  Listen carefully to the video, and fill out this worksheet on google docs and answer the following questions: http://docs.google.com/Doc?docid=0ARNbGsVH1evCZGQ5MjluM2dfNzBkMzMydDNmdA&hl=en

Adding similar sine waves causes "BEATS"

What happens when you add similar sine waves together? Any musician can tell you: as you tune an instrument closer and closer to the correct tone, you start to hear "beats", when the tone sounds louder and softer and louder and softer and ... You get the idea.

What does it look like? Take a look.

 Ok, ok. I get it. What's the homework? Your job is to reproduce this sound, and draw it, using the following link: http://www.falstad.com/fourier/e-logsound.html
 and write a summary of what Beats are using the following article: http://en.wikipedia.org/wiki/Beat_%28acoustics%29

Making the (almost) perfect square wave. Can it be done?

Continue adding up sine waves until you get an almost perfect square wave.
Try changing the number of terms that make up the sum. Move the mouse over the sines/cosines to see each frequency's contribution to the sum.
Try also changing the playing frequency (with your computer's sound ON)
Go to this site: http://www.falstad.com/fourier/e-square.html

Adding sines together to make a square wave

See this site to see how to add sine waves to make a square wave:
http://www.absorblearning.com/media/attachment.action?quick=qh&att=1897

Trig functions: SINE

Waves can be built up from a sum of sine functions, of the form: y = A*sin B(x-C).
What does the graph of A*sin B(x-C) look like? See this website to find out:
http://www.ies.co.jp/math/products/trig/applets/ABCsinX/ABCsinX.html

What in the world is SIGMA notation?!

This notation is used all the time in Physics and Math to represent the sum of a series of numbers.
The numbers can be as simple as 1 + 2 + 3 + 4 + 5 + ... + n,
or, in the case below, a little more complicated: 1 + 4 + 9 + 15 + ... + n^2

Write the following in Sigma notation, then write the VPython code to calculate the sum, then run the code to get the result.

(The first one is done for you..................................)

(1) Write the sum:  1 + 2 + 3 + ... + 10

IDLE 2.6.2

>>> count = 0

>>> for j in range(1,11):

        count += j

>>> print "the sum is: ", count

the sum is: 55

(Now, it's your turn....................)
(2) Write the sum:  1 + 2 + 3 + ... + 100
(3) Write the sum:  1 + 3 + 5 + ... + 99
(4) Write the sum:  1 + 2 + 4 + 16 + ... + 512
(5) Write the sum:  1 + (1/2) + (1/4) + ... + (1/1024)

Questions? send them to Dr. McCarthy ASAP.  Good luck.