Rotational Kinetic Energy

1. The problem statement, all variables and given/known data

An energy storage system based on a flywheel (a rotating disk) can store a maximum of 4.4 MJ when the flywheel is rotating at 21,300 revolutions per minute. What is the moment of inertia of the flywheel?

2. Relevant equations

K= Ktranslational + Krotational
Krot= (1/2)Iω^2

3. The attempt at a solution

I solved 21,300 rev/min to be equal to 2.23E3 rad/s
I then tried to use this as angular acceleration in the Krot equation to solve for moment of inertia and got 1.77E-3 kgm^2, which was incorrect. I’m wondering if I need to set 4400J= Ktrans + Krot, to solve for I (moment of inertia) but if so I can’t figure out how to solve for velocity in the Ktrans equation.

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