# Rotational Kinetic Energy of Moving Wheel

1. Mar 9, 2010

### easchwen

1. The problem statement, all variables and given/known data
A bicycle has wheels of radius 0.25 m. Each wheel has a rotational inertia of 0.096 kg* m2 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?

2. Relevant equations
KE=1/2 Iw^2 KE=1/2 mv^2

3. The attempt at a solution
I tried using (1/2 Iw^2)*(1/2 mv^2) = total KE, but that didn't seem to work. Help?

2. Mar 9, 2010

### benhou

1. By " * " did you mean multiplying? It shouldn't be multiplying, it should a plus sign.

2. What you are asked for is the fraction of the wheels' energy; meaning $$\frac{E_{wheels}}{E_{total}}$$

3. You have to calculate the sum of the two wheels' energy first. Divide that by the total energy of the whole thing.

3. Mar 9, 2010

### easchwen

yes, I meant a plus sign... my mistake! I still am unsure as to what I should do... I am not given angular velocity or linear velocity so I don't know how to find the energy.

4. Mar 9, 2010

### Staff: Mentor

Since you only are asked to find the ratio, you don't need the actual values for the speed. Call the linear speed V. (Hint: You should be able to express the angular velocity in terms of V.)

5. Mar 9, 2010

### benhou

Well, you don't always have to have all the data. e.g. the mass is a variable but will be canceled out--> $$E_{g}=K$$
$$mgh=\frac{1}{2}mv^{2}$$

Let me give you a hint. What happens in smooth rolling?