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 $1 \ m$).

$A$ spherical ball is rolling on a table without slipping. What fraction of its total kinetic energy is associated with its rotational motion?

$A$ solid sphere is moving on a horizontal plane. The ratio of its translational kinetic energy to its rotational kinetic energy is:

$A$ solid sphere of mass $1 \ kg$ is rolling on a rough table with a linear speed of $1 \ m/s$. Its total kinetic energy is ....... $J$.

$A$ ring of mass $m$ is rolling without slipping with linear velocity $v$ as shown in the figure. $A$ rod of identical mass $m$ is fixed along one of its diameters. The total kinetic energy of the system is:

$A$ uniform disc of mass $0.5\,kg$ and radius $r$ is projected with velocity $18\,m/s$ at $t = 0\,s$ on a rough horizontal surface. It starts off with a purely sliding motion at $t = 0\,s$. After $2\,s$ it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after $2\,s$ will be $..............J$ (given,coefficient of friction is $0.3$ and $g = 10\,m/s^2$).