Question

A uniform disk of mass M and radius R is initially rotating freely about its central axis with an angular speed of w, and a piece of clay of mass m is thrown toward the rim of the disk with a velocity v, tangent to the rim of the disk as shown. The clay sticks to the rim of the disk, and the disk stops rotating.

What is the magnitude of the total angular momentum of the clay-disk system before the clay sticks to the disk?

What is w in terms of the other variables given?

If the disk is replaced by a hoop of mass M and radius R with the same initial conditions, does the hoop rotate clockwise, counterclockwise, or stop rotating after the collision?

Answer 1

since net external torque on the disc & clay system. so Angular momentum will remain conserved.

Final Angular Momontum = initial angular momentum = 0 as the disk stops rotating after collision so final angular momentum =0.

figure for part b is posted below and for part c is above of that. so first look at the bottom most diagram. to find out

w=2mv/MR

from the diagram for part c, it's clear that wfinal is negative. so if initially disc was rotating clockwise, finally hoop will rotate anticlockwise. but if initially disc was rotating anticlockwise, finally hoop will rotate clockwise.

b.) please note that in the diagram below, it should be"since initial angular momentum=0, not moment of inertia =0