Question

a question about angular momentum:
when you calculate angular mom. with respect to a pole, the moment of inertia associated with it must be calculated with respect to an axis which goes through that point, or it not explicitly required that you do that?

Answer 1

for example, let's suppose there's a cilinder with linear velocity Vi, it is not rotating in that instant,
but the force of friction Fd after some time Tf, enforces on it a pure rolling motion, if we choose to calculate torque from the point of contact with the surface, we find that Net Torque = (0,0,0) ,
so we can conclude that angular momentum is conserved, but now i wonder, what axis should i use to calculate the moment of inertia?

Answer 2

We want to calculate the moment of inertia about the axis of rotation.

Take a baseball bat for example. If we drilled a hole through the center of mass of bat and put a rod through, like this and spun it about this rod. The moment of inertia would be much different than if we swung the bat like this.

Identical bat, identical mass, different axis of rotation.