An energy storage system based on a flywheel a rotating disk

An energy storage system based on a flywheel (a rotating disk) can store a maximum of 5.0 MJ when the flywheel is rotating at 19000 revolutions per minute. What is the moment of inertia of the flywheel? Express your answer using two significant figures.

Solution

Angular velocity

W=19000 rpm =19000*2pi/60

W=1989.7 rad/s

Rotational Kinetic energy

KE=(1/2)IW²

(5*10⁶)=(1/2)*I*(1989.7)²

I=2.5 Kg-m²