A spherical ball of material is rotating about its center at 35 rad/s.It has a mass of 2.0 kg and a radius of 0.11 m.If it suddenly expands to become a disk of 0.22-m radius,what will be its rate of rotation?
A)51 rad/s
B)7 rad/s
C)87 rad/s
D)29 rad/s
E)14 rad/s

Question

Quizplus · Accepted Answer

The total angular momentum of the system must be conserved. Therefore, 
I1ω1 = I2ω2, 
where I1 and ω1 are the moment of inertia and the angular velocity of the sphere, and I2 and ω2 are the moment of inertia and the angular velocity of the disk. 
The moment of inertia of a sphere is given by I = (2/5)mr², and for a disk is I = (1/2)mr². Substituting the given values, we have 
(2/5)(2.0 kg)(0.11 m)²(35 rad/s) = (1/2)(2.0 kg)(0.22 m)²ω2 
Solving for ω2, we get ω2 = 7 rad/s.

A Spherical Ball of Material Is Rotating About Its Center