What is the moment of inertia of the rotating disk?

Question

An energy storage system based on a flywheel (a rotating disk) can store a maximum of 4.8 MJ when the flywheel is rotating at 19,600 revolutions per minute. What is the moment of inertia of the flywheel?

Answer 1

1/4 MR^2

Answer 2

Rotational energy (E) equals 1/2 I w^2

where I is moment of inertia.

and w is angular velocity

Rearrange the equation to solve for I

E = 1/2 I w^2

2 E/w^2 = I

Convert rpm to rad/sec.  There's 2 pi radians per revolution.  There's 60 sec in a minute

2 ( 4.8 MJ)/(19,600 rpm * 2pi/60) = I

(9.6 MJ)/(2052.5 rad/sec) = I

4677 kg-m^2 = I