Angular Momentum and the Moment of Inertia Tensor
I want to explain this cool problem, but I want to sort of give a rough outline of how to get there. It’s useful to see where things start and where they end up.
Point Masses
When you start off in your physics course, you use point masses. Oh, you don’t necessarily call them point masses — but that’s what they are. When you model a block sliding down a plane, it’s a point. When you toss a ball — yup, that’s a point.
For a point mass, we treat all the forces as acting at the same point on the object (usually the center of mass).
Two Point Masses
What’s better than one point mass? Obviously two masses are better. Let’s imagine that I have two masses connected by a spring (with no other forces acting on them).
It’s possible to model this situation by calculating the force on each mass (due to the spring) and then use the momentum principle:
Of course if both masses are moving, the vector spring force will keep changing such that’s not completely trivial to find a solution. OK, it is indeed possible if you assume an equivalent 1 body problem —…
