# Kinetic energy of a rotating wheel?

A simple wheel has the form of a solid cylinder of radius r with a mass m uniformly distributed throughout its volume. The wheel is pivoted on a stationary axle through the axis of the cylinder and rotates about the axle at a constant angular speed. The wheel rotates n full revolutions in a time interval .
Express your answer in terms of m, r , n ,t and, pi .

does anyone have any pointers for me?

i do know that this formula, 1/2mr^2 can help me, but i don't know how create the right equation using the other arts given to me.

Nylex
Rotational kinetic energy is given by

$$KE_{rot} = \frac{1}{2}I\omega^2$$.

Just write everything in terms of the variables you've been given.

Last edited:
this is my answer so far, but I am having a problem with the angular of velocity
1/2*m*r^2*((2*PI)/n*t)^2. can anyone point me in the right direction

Nylex
It should have $$\frac{1}{4}$$ at the front, because you have $$\frac{1}{2}\frac{1}{2}mr^2$$.

In your angular velocity, your n should be in the numerator of the fraction.

Homework Helper
this is my answer so far, but I am having a problem with the angular of velocity
1/2*m*r^2*((2*PI)/n*t)^2. can anyone point me in the right direction
$$I = \int_0^m r^2 dm$$
$$\frac{n_- revs}{t_- sec} * \frac{2 \pi_- rad}{1_- rev} = \omega$$