A \(0.40\,\mathrm{kg}\) particle moves at \(5.0\,\mathrm{m\,s^{-1}}\) perpendicular to a radius \(0.30\,\mathrm{m}\). Find \(L\) about the origin.

A disk has \(I=0.25\,\mathrm{kg\,m^2}\) and \(\omega=16\,\mathrm{rad\,s^{-1}}\). Find its angular momentum about its axle.

A particle moves directly away from the origin. What is its angular momentum about the origin?

If \(\vec r\) points along \(+\hat\imath\) and \(\vec p\) points along \(+\hat\jmath\), what direction is \(\vec L\)?

A \(2.0\,\mathrm{kg}\) particle is at \(\vec r=3\hat\imath+1\hat\jmath\,\mathrm{m}\) and has velocity \(\vec v=4\hat\jmath\,\mathrm{m\,s^{-1}}\). Find \(L_z\).

A net torque of \(6.0\,\mathrm{N\,m}\) acts for \(2.5\,\mathrm{s}\) along a fixed axis. Find the change in angular momentum.

A particle has \(m=0.20\,\mathrm{kg}\), \(r=0.50\,\mathrm{m}\), \(v=8.0\,\mathrm{m\,s^{-1}}\), and the angle between \(\vec r\) and \(\vec v\) is \(30^\circ\). Find \(L\).

A wheel's angular momentum changes from \(3.0\) to \(11.0\,\mathrm{kg\,m^2\,s^{-1}}\) in \(4.0\,\mathrm{s}\). Find the average external torque.

A particle moves in the plane with \(\vec r(t)=bt\,\hat\imath+c\,\hat\jmath\) and \(\vec v=b\,\hat\imath\), where \(b\) and \(c\) are constants. Find \(\vec L\) about the origin and interpret why it is constant.

A disk with \(I=0.40\,\mathrm{kg\,m^2}\) spins at \(20\,\mathrm{rad\,s^{-1}}\). A constant external torque of \(2.0\,\mathrm{N\,m}\) acts opposite the spin for \(3.0\,\mathrm{s}\). Find the final angular momentum and angular speed.

A particle moves under a central force \(\vec F=f(r)\hat r\). Show that its angular momentum about the force centre is conserved, and state what this implies about the plane of motion.

For a rigid body moving in a plane, derive \(L_O=\vec R_{\mathrm{cm}}\times M\vec V_{\mathrm{cm}}+I_{\mathrm{cm}}\omega\,\hat k\) about an arbitrary origin \(O\). State the condition under which the simpler form \(L_O=I_O\omega\) is valid.