Moment of Inertia and kinetic energy question

[kpengin]

Homework Statement

The flywheel of a gasoline engine is required to give up 550 of kinetic energy while its angular speed decreases from 720 to 400 .
What moment of inertia is required?

Homework Equations

K=(1/2)Iw^2

The Attempt at a Solution

K=550J
I'm not sure how to get the w value since the velocity is changing.
I tried:
550=(1/2)I(320)^2
then solving for I
I=0.0107
but this is not correct.

 

[Doc Al]

I tried:
550=(1/2)I(320)^2

The right hand side is incorrect. You want Δ((1/2)Iw^2), not (1/2)I(Δw)^2.