Question

A uniform circular disk (merry-go-round) of radius R=2.19 m and mass M=21.9 kg freely rotates about a vertical axis, which is perpendicular to the ground, with initial angular velocity omegai=3.05 rad/s. A cat of mass m=8.70 kg, climbing in a tree, which hangs over the disk, falls straight down onto the edge of the disk and rides on it. The cat decides to walk inward and sits down R/2 m from the center. What is now the magnitude of the angular velocity of the cat/disk system?

Answer 1

M =21.9 kg , R =2.19 m, w1 =3.05 rad/s

d =R/2m=2.19/2 =1.095 m , m =8.7 m

Moment of inertia of circular disk I1 = MR^2/2 =(21.9*2.19*2.19)/2

I1 = 52.52 kg.m^2

From conservation of angular momentum

I1w1 =I2w2

I1w1 = (I1 +md²)w2

(52.52*3.05) = [52.52+(8.7*1.095*1.095)w2

w2 = 2.545 rad/s