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