A particle moves in a circle of radius \(3\,\mathrm{m}\) at speed \(6\,\mathrm{m\,s^{-1}}\). Find centripetal acceleration.

A wheel has radius \(0.50\,\mathrm{m}\) and angular velocity \(8\,\mathrm{rad\,s^{-1}}\). Find rim speed.

A wheel turns through \(6\,\mathrm{rad}\) in \(3\,\mathrm{s}\) at constant angular speed. Find \(\omega\).

Using \(r=0.50\,\mathrm{m}\) and \(\omega=8\,\mathrm{rad\,s^{-1}}\), find centripetal acceleration.

A particle completes one circle of radius \(2\,\mathrm{m}\). Find distance traveled.

If speed doubles while radius stays fixed, what happens to \(a_c\)?

A particle completes one revolution in \(5\,\mathrm{s}\). Find angular velocity.

A particle moves with \(r=4\,\mathrm{m}\) and period \(T=2\,\mathrm{s}\). Find speed.

A wheel starts from rest with \(\alpha=2\,\mathrm{rad\,s^{-2}}\). Find \(\omega\) after \(4\,\mathrm{s}\).

If radius doubles while speed stays fixed, what happens to \(a_c\)?

Does uniform circular motion have acceleration?

What direction is centripetal acceleration?

Using \(r=0.30\,\mathrm{m}\) and \(\omega=8\,\mathrm{rad\,s^{-1}}\), find speed.

A particle has \(r=2\,\mathrm{m}\), \(\omega=3\,\mathrm{rad\,s^{-1}}\), and \(\alpha=4\,\mathrm{rad\,s^{-2}}\). Find \(a_c\) and \(a_t\).

A wheel has angular acceleration \(\alpha=3\,\mathrm{rad\,s^{-2}}\) and radius \(0.20\,\mathrm{m}\). Find tangential acceleration.

A point rotates through \(\theta=2.5\,\mathrm{rad}\) on a circle of radius \(6\,\mathrm{m}\). Find arc length.

A particle moves in a circle with \(r=5\,\mathrm{m}\) and \(\omega=2\,\mathrm{rad\,s^{-1}}\). Find \(a_c\).

A wheel rotates with \(\omega(t)=4+0.50t\,\mathrm{rad\,s^{-1}}\). Find angular displacement from \(t=0\) to \(t=6\,\mathrm s\).

A particle has \(v=10\,\mathrm{m\,s^{-1}}\) and \(a_c=20\,\mathrm{m\,s^{-2}}\). Find radius, period, and angular speed.

At an instant, \(r=1.5\,\mathrm m\), \(\omega=5\,\mathrm{rad\,s^{-1}}\), and \(\alpha=-3\,\mathrm{rad\,s^{-2}}\). Find total acceleration magnitude and its angle from inward radial direction.

A particle moves in a circle of radius \(r\) with angular position \(\theta(t)=\theta_0+\omega_0t+\frac{1}{2}\alpha t^2\). Derive \(v(t)\), \(a_t(t)\), \(a_c(t)\), and the time when total acceleration is minimum (assuming \(\omega_0>0,\alpha>0\)).

A point on a rotating disk starts from rest with constant angular acceleration \(\alpha\). It must not exceed total acceleration \(a_{\max}\) at radius \(r\). Derive the maximum allowable time interval of acceleration in terms of \(r,\alpha,a_{\max}\).