What is the moment of inertia of the flywheel?

[bikeeich]

Homework Statement

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?

Homework Equations

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

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.

 

[Doc Al]

I solved 21,300 rev/min to be equal to 2.23E3 rad/s

OK.

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.

Looks like you're off by a few powers of 10. Do that calculation over.

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.

No, you're on the right track.

 

[bikeeich]

I tried again and got the same answer. I'm sure I have a stupid mistake somewhere
Is it incorrect that 4.4MJ = 4400 J?

 

[slider142]

I tried again and got the same answer. I'm sure I have a stupid mistake somewhere
Is it incorrect that 4.4MJ = 4400 J?

4.4MJ = 4.4x10^6 J. 4400J is 4.4x10^3 J, or 4.4 kJ. :)

 

[bikeeich]

WOW. I might need to take a break. Thank you for the correction help!