Consider a point $P$ at the contact point of a wheel on the ground,which rolls on the ground without slipping. Find the displacement of point $P$ when the wheel completes half of a rotation (given the radius of the wheel is $1 \ m$).

$A$ 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:

$A$ force $F$ is applied at the centre of a disc of mass $M$. The minimum value of the coefficient of friction of the surface for pure rolling is:

$A$ wheel is rolling on the ground with a speed of $2 \ m/s$. What is the velocity of the endpoints of the horizontal diameter of the wheel?

$A$ sphere of mass $50\,g$ and diameter $20\,cm$ rolls without slipping with a velocity of $5\,cm/s$. Its total kinetic energy is

$A$ wheel of radius $R$ rolls on the ground with a uniform velocity $v$. The relative acceleration of the topmost point of the wheel with respect to the bottommost point is