$A$ uniform non-deformable cylinder of mass $m$ and radius $R$ is rolling without slipping on a horizontal rough surface. The force of friction is

$A$ 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 $= 5 \ m$)

$A$ sphere rolls without slipping on a fixed horizontal surface. In the figure,$A$ is the point of contact,$B$ is the center,and $C$ is the topmost point. Then...

$A$ wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is $8 \ m/s$. The speed of the particle on the rim of the wheel at the same level as the centre of the wheel will be

$A$ 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:

$A$ ring and a disc roll on a horizontal surface without slipping with the same linear velocity. If both have the same mass and the total kinetic energy of the ring is $6 \ J$,then the total kinetic energy of the disc is: (in $/2 \ J$)