Homework Set # 1 - Due September 3

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     1)  a) Prove that A=(A_x²+A_y²+A_z²)^1/2_.   Use Pythagoras theorem.
           b) Using a) prove that cos²alpha+cos²beta+cos²gamma=1.

• Solution (pdf file)

     2)  1.7.6

• Solution (pdf file)   

     3)  1.7.8

• Solution (pdf file)

     4)  3.2.1

• Solution (pdf file)

     5)  3.2.4

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     6)  The orbital angular momentum L is given by L=r x p=mr x v, where p is the linear momentum. With linear and angular velocity related by v=w x r, show that

L=mr²[w-r(r . w)].

Here r is a unit vector in the r-direction. For r . w=0 this reduces to L=Iw, with the moment of inertia I given by mr².

• Solution (pdf file)

     7)  3.2.10

•    Solution (pdf file)