A solid sphere of radius R rotates about a diameter with an angular speed $\omega$. The sphere then collapses under the action of internal forces to a final radius R/2. What is the final angular speed of the sphere?
A)$\omega$/4
B)$\omega$/2
C)$\omega$
D)2$\omega$
E)4$\omega$

Question

Quizplus · Accepted Answer

The moment of inertia of a solid sphere about a diameter is $I = \frac{2}{5}mR^2$. When the sphere collapses to a radius of R/2, its new moment of inertia becomes $I' = \frac{2}{5}m(R/2)^2 = \frac{1}{4} \times \frac{2}{5}mR^2$. By conservation of angular momentum, $I\omega = I'\omega'$. Solving for $\omega'$, we get $\omega' = 4\omega$.

A Solid Sphere of Radius R Rotates About a Diameter ω\omegaω

A Solid Sphere of Radius R Rotates About a Diameter $\omega$