Question

What is the rotational kinetic energy of a 1.20-kg sphere with a radius of 0.250m rotating about its axis and an angular speed of 0.38 rad/s?

Answer 1

For solid sphere (ball) of radius $r$ and mass $m$:

$I=(2/5)mr^2$ . So,

$KE=\frac{I\omega^2}{2}=\frac{(2/5)mr^2\omega^2}{2}=$

$=\frac{mr^2\omega^2}{5}=\frac{1.2\cdot 0.25^2\cdot 0.38^2}{5}\approx0.0022(J)$