# Flywheel Angular Velocity Problem

## Homework Statement

A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means of storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 300 mile trip in a typical mid-sized car produces about 1.2x10^9 J of energy. How fast would a 13kg flywheel with a radius of 0.3m have to rotate to store this much energy? Give your answer in rev/min

## Homework Equations

Rotational Kinetic Energy (KEr) = (1/2)Iw^2
where I = mr^2

## The Attempt at a Solution

So doing some basic algebra, and solving for w, I came up with:

w = sqrt(KEr/.5mr^2)

w = sqrt(1.2x10^9J / .5(13kg)(.3m^2)

(45291 rad/s) / 2pi = 7208 rev/s * 60s = 432497 rev/min

The answer that the book is providing is: 6.1x10^5 rev/min

I'm not sure what I'm doing wrong, or If this is even the correct approach I should be taking to solve this problem.

Any help would be greatly appreciated.

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Hootenanny
Staff Emeritus
Gold Member
Welcome to PF cchase88,
where I = mr^2
Are you sure that's the moment of inertia of a disk about an axis passing through it's centre?

tiny-tim
Homework Helper
Welcome to PF!

Hi cchase88! Welcome to PF!

Have you noticed you're out by a factor of √2?

When in doubt, wkikpedia is often helpful: see http://en.wikipedia.org/wiki/Flywheel#Physics

Welcome to PF cchase88,

Are you sure that's the moment of inertia of a disk about an axis passing through it's centre?
Hi cchase88! Welcome to PF!

Have you noticed you're out by a factor of √2?

When in doubt, wkikpedia is often helpful
Thank you both for your help. I forgot about that 1/2. I guess that's what I get for doing a problem at 4 in the morning

tiny-tim
Homework Helper
:zzz: cchase 88 z's ! :zzz:​