# Rotational kinetic energy of a bike wheel

## Homework Statement

A bicycle has wheels of radius 0.29 m. Each wheel has a rotational inertia of 0.091 kg·m^2 about its axle. The total mass of the bicycle including the wheels and the rider is 79 kg. When coasting at constant speed, what fraction of the total kinetic energy of the bicycle (including rider) is the rotational kinetic energy of the wheels?

## Homework Equations

translational KE = 1/2 mv^2

rotational KE = 1/2 I (omega)^2 = 1/2 I (v/r)^2

rotational KE / total KE

= (I/r^2) / (I/r^2 + m)

## The Attempt at a Solution

Moment of inertia (I) is given: 0.091 kg·m^2

Radius of the wheel is .29 meters

Mass is 79kg

so:

rotational KE / total KE

= (I/r^2) / (I/r^2 + m)

=(0.091kg·m^2/0.29^2m) / (0.091kg·m^2/0.29^2m + 79kg)
=.0135 which is not the right answer.

Anyone know where I messed up?

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rl.bhat
Homework Helper
Rotational motion

Your formula is true when the axis of rotation passes through CM. In this case it is not true.
Using moment of inertia and radius of the wheel and total mass, find the mass of the wheel(Mw) and the rest of the mass (Mr)
Now the total energy = 1/2*(Mr)*v^2 + 2x[1/2{(Mw)*(r^2)/2}(v/r)^2 + 1/2(Mw)*v^2]

Last edited:
Thanks for your reply. I tried to get the velocities (v) to cancel algebraically but I could not. I think it is beyond my ability to derive a speed. Any hints on how to handle to velocity?

Dick
Homework Helper
The answer is a lot simpler than that. There are two wheels.

The answer is a lot simpler than that. There are two wheels.
I am intrigued. Are you implying that the answer could be something such simple as .5 or 1.2?

Dick
Homework Helper
Not with an odd number for the rotational inertia. But it's still pretty simple. In your original calculation you only put in the kinetic energy for one wheel. Double it.

I am a bit confused. Would I double the answer or would I double just rotational or total kinetic energy?

= 2((I/r^2) / (I/r^2 + m))
or
= (I/r^2) / 2(I/r^2 + m)

I am not sure what to do.

Dick
Homework Helper
Think. You did it correctly for a monocycle. Linear KE doesn't change. Just rotational.

Thanks for your help. That gave me just enough information to finally figure that one out.

Dick