# Angular velocity of a wheel

If a wheel has a constant velocity $v$, which point on the wheel has the greatest angular velocity?

I was thinking that either every point has the same angular velocity since $\omega = v/r$, but I wasn't sure if the top of the wheel had the greatest velocity since it is positive $v$ rather than at the bottom of the wheel, $-v$.

• What would happen if different parts of the wheel had different velocities? You can choose whatever coordinate system suits you, it won't alter physical laws. – user140606 Jan 30 '17 at 1:01
• – Farcher Jan 31 '17 at 15:09

Well you must consider rotational velocity and translational velocity. Assuming that skidding is not being taken into account we have the following situation:

We can clearly see that for the bottom of the wheel the velocity in the first two pictures for translational and rotational velocity are in opposite directions and hence cancel out. Where the velocity at the top of the wheel for trans and rotational are in the same direction and can be added together.

• The question was about angular velocity and if the wheel is rigid then the answer is that the angular velocity is the same for each point on the wheel. – Farcher Jan 31 '17 at 15:09