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

$A$ disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in the figure. At any instant,for the lowermost point of the disc -

$A$ particle on the outer surface of a wheel,which is initially at rest,is in contact with the ground at point $P$. Find the displacement of this particle when the wheel completes half a rotation in the forward direction. (Radius of the wheel $= 5 \ m$)

$A$ solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is ................

$A$ spool consists of a cylinder of radius $R_1$ wrapped with thread,and its end caps have radius $R_2$ as shown in the end view illustrated in the figure. The mass of the spool,including the thread,is $m$,and its moment of inertia about an axis through its center is $I$. The spool is placed on a rough horizontal surface so that it rolls without slipping. When a force $\vec{T}$ acting to the right is applied to the free end of the thread,the friction force exerted by the surface on the spool is given by:

$A$ disc of radius $R$ is rotating with an angular velocity $\omega_0$ about a horizontal axis. It is placed on a horizontal table. The coefficient of kinetic friction is $\mu_k$.
$(a)$ What was the velocity of its centre of mass before being brought in contact with the table?
$(b)$ What happens to the linear velocity of a point on its rim when placed in contact with the table?
$(c)$ What happens to the linear speed of the centre of mass when the disc is placed in contact with the table?
$(d)$ Which force is responsible for the effects in $(b)$ and $(c)$?
$(e)$ What condition should be satisfied for rolling to begin?
$(f)$ Calculate the time taken for the rolling to begin.