A \(2.0\,\mathrm{kg}\) particle moves at \(6.0\,\mathrm{m\,s^{-1}}\) in a circle of radius \(3.0\,\mathrm{m}\). Find the required inward net force.

A particle has centripetal acceleration \(9.0\,\mathrm{m\,s^{-2}}\) on a circle of radius \(4.0\,\mathrm{m}\). Find its speed.

A \(1000\,\mathrm{kg}\) car takes a flat curve of radius \(50\,\mathrm{m}\) at \(10\,\mathrm{m\,s^{-1}}\). Find the static friction force required.

In uniform circular motion, what direction is the net force?

A car takes a flat curve of radius \(60\,\mathrm{m}\) at \(15\,\mathrm{m\,s^{-1}}\). Find the minimum coefficient of static friction.

A \(70\,\mathrm{kg}\) rider crosses the top of a circular hill with \(r=40\,\mathrm{m}\) and \(v=12\,\mathrm{m\,s^{-1}}\). Find the normal force.

The same \(70\,\mathrm{kg}\) rider passes through the bottom of a circular dip with \(r=40\,\mathrm{m}\) and \(v=12\,\mathrm{m\,s^{-1}}\). Find the normal force.

A \(0.50\,\mathrm{kg}\) object moves in a horizontal circle of radius \(1.2\,\mathrm{m}\) at \(3.0\,\mathrm{m\,s^{-1}}\). Find the required horizontal component of the tension.

A frictionless banked curve has radius \(80\,\mathrm{m}\) and bank angle \(15^\circ\). Find the speed for which no friction is needed.

A ball on a string moves in a vertical circle of radius \(2.0\,\mathrm{m}\). Find the minimum speed at the top for the string to remain taut, and the corresponding speed at the bottom if mechanical energy is conserved.

A coin sits \(0.25\,\mathrm{m}\) from the center of a turntable. If \(\mu_s=0.60\), find the maximum angular speed before slipping and the corresponding maximum period of rotation frequency \(f_{\max}\).

A \(0.20\,\mathrm{kg}\) ball forms a conical pendulum with string length \(1.0\,\mathrm{m}\) and angle \(30^\circ\) from vertical. Find tension, speed, and period of revolution.