Moment of Inertia for a Decreasing Angular Velocity

[leehufford]

Homework Statement

You guys might recognize me from a post earlier. Yep, I'm still plugging away at rotation of rigid bodies and have another question.

The flywheel of a gasoline engine is required to give up 500 J of kinetic energy while its angular velocity decreases from 650 rpm to 520 rpm. What moment of inertia is required?

Homework Equations

I = moment of inertia

E = (1/2)I(ω^2)

I = 2E/(ω^2)

The Attempt at a Solution

I converted the rpm's into rad/s. They are 1.13 and 0.91 respectively. Other than that, I sat and thought for a while and couldn't come up with a start. The 500 J obviously needs to be worked in somehow, but this is a change in E not a constant E. Any help would be greatly appreciated.

-Lee

 

[ehild]

I converted the rpm's into rad/s. They are 1.13 and 0.91 respectively.
-Lee

How did you get these values for the angular speeds? Remember, rpm means revolutions per minute.

ehild

 

[leehufford]

How did you get these values for the angular speeds? Remember, rpm means revolutions per minute.

650 rpm (2pi/1 rev)(1 min/60 sec) = whoops that should be 68.07 rad/sec and

520 rpm (2pi/1 rev)(1 min/60 sec) = 54.45 rad/s

Anyone know how to find the moment of inertia?

 

[ehild]

You know the difference between initial and final rotational energy.

ehild

 

[leehufford]

You know the difference between initial and final rotational energy.

ehild

I got it. I did Energy final - Energy initial = -500 J, factored the I out of the 2 terms on the left and got 0.600 kg m^2 for the moment of inertia. Thanks for the hint. I hope I recognize that trick next time I need it!

Thanks,
Lee

 

[ehild]

Good job!

ehild