Rolling Motion

A uniform disc of mass 2 kg and radius 3 cm is rolling down on a rough inclined plane of inclination 0 = 37°. The acceleration of its centre is (g = 10 m/s²)

A semi-Cylindrical wedge $A$ of mass $M$ and radius $R$ is placed on a horizontal smooth surface. A solid cylinder of mass $m$ and radius $r$ is placed at the top of the wedge as shown in the figure, and released with a gentle rightward push. There is no friction between the curved surface of semi cylinder and solid cylinder. Find the velocity of the wedge when the line $CO$ makes an angle of $60°$ with the vertical. (given $R=3\mathrm{r}$ and $M=3\mathrm{m}$)

Choose the correct formula for the rotational kinetic energy from the following options.

A ring and a disc have the same mass and roll without slipping with the same linear velocity $v$. If the total $KE$ of the ring is $8 \mathrm{J}$, the $KE$ of the disc must be

If a thin ring is subjected to a force $F$ as shown in the figure. Find the force of friction required to make sure that the ring does pure rolling on the rough surface.
 

Two balls of masses $2 \mathrm{g}$ and $6 \mathrm{g}$ are moving with a kinetic energy in the ratio $3:1$. What is the ratio of their linear momentum?

The kinetic energy of a body of moment of inertia $I$ and angular momentum $L$ is

A ring of radius $r$ and mass $m$ rotates about its central axis. The kinetic energy is 

A uniform solid ball of mass '$m$' rolls without sliding on a fixed horizontal surface. The velocity of the lowest point of the ball with respect to the center of the ball is $v$. The total kinetic energy of the ball is:

A couple produces

The speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height h is

A couple produces,

The rotational $KE$ of a body is $E$ and its moment of inertia is $I$. The angular momentum is

A uniform sphere of mass $\mathrm{m}=2.5 \mathrm{kg}$ and radius $R=10 \mathrm{cm}$ rotates with an angular velocity, $\omega =200 \mathrm{rad} {\mathrm{s}}^{-1}$ about its diameter. Find its kinetic energy.

If the rotational kinetic energy of a body is increased by $300 \%$ then the percentage increase in its angular momentum :-

Since the two bodies have same mass and collide head-on elastically, the linear momentum gets interchanged. Hence just after the collision$\text{'}B\text{'}$will move with velocity ' $v_0^{\text{'}}$ and $\text{'}A\text{'}$ becomes stationary but continues to rotate at the same initial angular velocity $\left(\frac{v_0}{R}\right)$ Hence, after collision.

What is the work done against friction during rolling, if length of the incline is $1$ meter?

A body is in pure rolling motion on a horizontal surface. For which body the rotational kinetic energy is not less than translational kinetic energy

A ring of mass $m$ and radius $R$ is acted upon by a force $F$ as shown in the figure. There is sufficient friction between the ring and the ground. The force of friction necessary for pure rolling is

The fraction of total energy of spherical shell in translational motion is.