What is the angular velocity about 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 (b). The angular momentum of the system relative to the center of mass is 6.82e-03 kg*m^2/s.

I know that you have to use w=L/I i know you find the inertia for both pucks and i sort of know but i'm missing somethign the center mass is confusing me.

i found the center mass by doing(r1+r2)*m1/(m1+m2) but how do i put that in Inertia formula

any help is appreciated thanks in advance

Answer 1

Place the origin of the coordinate system at the center of puck 2, with the pucks at the moment of contact having their centers on the y-axis. The location of the center of mass from the origin is

ym = m1/(m1+m2) * (r1+r2) = 3.71 cm

The angular momentum of the system the instant before contact, measure from the system's center of mass is

m1*v1*(distance from center of m1 to center of mass)=

m1*v1*(r1 + r2 - ym) = 87.6*10^-3*1.53*(5.14/100) = 6.88*10^-3 kg*m^2/s