$A$ solid sphere rolls without slipping on a rough surface and the centre of mass has a constant speed $v_0$. If the mass of the sphere is $m$ and its radius is $R$,then find the angular momentum of the sphere about the point of contact $P$.

Given $V_{CM} = 2\; m/s$,$m = 2\; kg$,$R = 4\; m$. Find the angular momentum of the ring about the origin if it is in pure rolling. (in $kg \cdot m^2/s$)

Can the relation $v = r\omega$ be used for an object undergoing rolling motion with slipping? Why?

$A$ solid sphere of mass $2\,kg$ is making pure rolling on a horizontal surface with kinetic energy $2240\,J$. The velocity of the centre of mass of the sphere will be $..........\,m/s$.

$A$ disc is rolling (without slipping) on a horizontal surface. $C$ is its centre and $Q$ and $P$ are two points on the same horizontal line passing through $C$,such that $Q$ is at a distance $r$ from $C$ and $P$ is at a distance $r$ from $C$ on the opposite side. Let $V_P, V_Q$ and $V_C$ be the magnitudes of velocities of points $P, Q$ and $C$ respectively,then:

$A$ disc rotating about its axis with angular speed $\omega_{o}$ is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is $R$. What are the linear velocities of the points $A, B$ and $C$ on the disc shown in Figure? Will the disc roll in the direction indicated?