What is the angular momentum of the system relative to the center of mass?

Question

A puck of mass 86.7 g and radius 3.73 cm slides along an air table at a speed of v = 1.53 m/s. It makes a glancing collision with a second puck of radius 5.12 cm and mass 120 g (initially at rest) such that their rims just touch. The pucks stick together and spin after the collision

Answer 1

Like linear momentum, angular momentum is conserved. Select the point where the two pucks first touch as the origin and measure the initial angular momenta about that point. The target puck will have none but the incoming puck's center of mass travels on a line that doesn't go through that point, so it has angular momentum of mass times the vector product of velocity and distance:

m ( v x r )

In this particular problem, the cross product of v and r will just be velocity times the radius of the puck.

After the collision, it may be convenient to note that angular momentum can also be expressed as

I w

where I is the moment of inertia of the system and w the angular velocity