A wheel's angular velocity changes from \(3.0\) to \(15.0\,\mathrm{rad\,s^{-1}}\) in \(4.0\,\mathrm{s}\). Find average angular acceleration.

For \(\omega(t)=5+2t\), find \(\alpha\).

At one instant, \(\omega=-4.0\,\mathrm{rad\,s^{-1}}\) and \(\alpha=+1.0\,\mathrm{rad\,s^{-2}}\). Is the angular speed increasing or decreasing?

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

A point is \(0.50\,\mathrm{m}\) from an axis. If \(\alpha=6.0\,\mathrm{rad\,s^{-2}}\), find its tangential acceleration.

A wheel changes from \(+10\,\mathrm{rad\,s^{-1}}\) to \(-5.0\,\mathrm{rad\,s^{-1}}\) in \(3.0\,\mathrm{s}\). Find average angular acceleration.

For \(\theta(t)=t^3-6t^2\), find when \(\alpha=0\), then state whether the wheel is instantaneously at rest then.

For \(\omega(t)=8-4t+t^2\), determine whether the rotation ever stops for \(t\ge0\). Use the result to interpret the angular speed.

A wheel starts from rest with angular acceleration \(\alpha(t)=6.0-2.0t\) in \(\mathrm{rad\,s^{-2}}\). Find when angular speed is maximum, the maximum angular speed, and the angular displacement up to that instant. State the assumption behind the maximum condition.

For \(\omega(t)=\omega_0+\alpha_0t-\frac{1}{2}\beta t^2\) with \(\beta>0\), derive the condition for real stopping times and give the first positive stopping time when it exists.