Question

A 500g uniform sphere of 7cm radiud ppins at 30 rev/sec on an axis through its center

Find it's kinetic energy rotational

Answer 1

$$KE_r=\dfrac{1}{2}I\omega^2,$$ $$KE_r=\dfrac{1}{2}\dfrac{2}{5}mr^2\omega^2=\dfrac{1}{5}mr^2\omega^2.$$ $$KE_r=\dfrac{1}{5}\cdot0.5\ kg\cdot(0.07\ m)^2\cdot(30\ \dfrac{rev}{s}\cdot2\pi\ rad)^2=17.41\ J.$$