Homework Set # 1 - Due September 2

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     1)  a) Prove that A=(Ax2+Ay2+Az2)1/2.   Use Pythagoras theorem.
           b) Using a) prove that cos2alpha+cos2beta+cos2gamma=1.


     2)  1.7.6


     3)  1.7.8


     4)  3.2.1


     5)  3.2.4


     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.


     7)  3.2.10