A wheel turns through \(12\,\mathrm{rad}\) in \(4.0\,\mathrm{s}\). Find its average angular velocity.

A rotor has period \(T=0.20\,\mathrm{s}\). Find its angular speed in \(\mathrm{rad\,s^{-1}}\).

Convert \(90\,\mathrm{rev\,min^{-1}}\) to angular speed in \(\mathrm{rad\,s^{-1}}\).

A wheel starts at \(\theta_0=1.0\,\mathrm{rad}\) and rotates with constant \(\omega=5.0\,\mathrm{rad\,s^{-1}}\) for \(8.0\,\mathrm{s}\). Find \(\theta\).

For \(\theta(t)=4t^2-3t\), find \(\omega\) at \(t=2.0\,\mathrm{s}\).

Counterclockwise is positive. A wheel completes \(3.0\) clockwise revolutions in \(2.0\,\mathrm{s}\). Find average angular velocity.

For \(\theta(t)=2t^2-8t\), over \(0\le t\le5\,\mathrm{s}\), find the net angular displacement and average angular velocity.

For \(\theta(t)=2t^2-8t\), over \(0\le t\le5\,\mathrm{s}\), find the total angle swept as well as the net angular displacement.

A motor's angular velocity changes linearly from \(+6.0\,\mathrm{rad\,s^{-1}}\) to \(-2.0\,\mathrm{rad\,s^{-1}}\) over \(4.0\,\mathrm{s}\). Find when it stops, the net angular displacement, and the total angle swept. State how you handled the reversal.

Let \(\omega(t)=\omega_0-\beta t\) with \(\omega_0>0\) and \(\beta>0\). Derive the net angular displacement and total angle swept over \(0\le t\le T\), including the two cases set by the stopping time.