Question

A 500g uniform sphere of 7cm radius spins at 30rev/sec on an axis through its center find its
A, KEr
B, angular momentum
C, radius of gyration

Answer 1

The moment of inertia of a solid uniform sphere is

$$I=\frac{2}{5}mr^2.$$

The kinetic energy of rotation is

$$KE=\frac{1}{2}I\omega^2=\frac{1}{5}mr^2\omega^2=\frac{1}{5}mr^2(2\pi n)^2=\\ =17.4\text{ J}.$$

The angular momentum is

$$L=I\omega=\frac{4\pi}{5}mnr^2=0.185\text{ Js}.$$

The radius of gyration is

$$R_g=\sqrt\frac{I}{m}=r\sqrt\frac{2}{5}=4.43\text{ cm}.$$