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Angular momentum




I'm asking a physics question this time!!!

I'm curious how various people handle a certain topic in the calculus level
intro course for scientist and engineers; (also in an algebra based course).

I just finished dealing with angular momentum.

For rigid body rotation about a fixed axis of rotation:

Its not too hard to show that the z component of angular momentum is equal
to I time omega (where one has chosen the z axis to coincide with the
rotation axis.

What bothers me is what I do next. I more or less simply state that if the
rotation axis is a symmetry axis this generalizes to L = I Omega, but you
can not make this assumption if the rotation axis is not a symmetry axis.

To illustrate this I have a nice transparency from a text that shows two
similar situations, one where it is true and one where it isn't.

a) the rigid body is two point masses rotating on opposite sides of the same
circular path about the z axis and both masses have the same z coordinate.
Here L = I omega.

b) same thing but one of the masses z coordinate is minus the z coordinate
of the other one. Here it isn't true.

Its fairly easy to use the right rule and get the individual angular
momentum vectors and sum them to see that in case (a) the total is parallel
to omega vector and for case (b) it isn't.

I'm rather uncomfortable with all this and want to hear how others handle
this. I have limited time to address this topic (damn it; breadth vs depth
again). I feel something needs to be said, but I obviously don't want to go
into moment of inertial tensors at this level.

so let's hear the thoughts and start a new thread.

Thanks to all

Joel