What is a rigid body?

$A$ ring has inner radius $R_1$ and outer radius $R_2$. It rolls without slipping with a constant angular velocity $\omega$. What is the ratio of the forces $F_1/F_2$ experienced by two particles located on the inner and outer surfaces of the ring?

$A$ solid sphere of radius $R$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at a height $h$ from the lowest point. For the maximum acceleration of the centre of mass,which is correct?

In the figure shown,a mass $m$ is attached to a light string which is wrapped around a solid cylinder of mass $M$ and radius $R$. The system starts from rest at $t = 0$. If friction is negligible,what will be the angular velocity at time $t$?

$A$ wheel of radius $1.5 \ m$ rotates with a constant angular acceleration of $10 \ rad/s^2$. Its initial angular speed is $(\frac{60}{\pi}) \ rpm$. What will be its angular speed and angular displacement at $t = 2.0 \ s$?

The velocity of the centre of mass of a rigid rod with respect to an observer $O$ is $\vec v_{cm} = (2\hat i + 3\hat j) \text{ m/s}$. The rod has an angular velocity about its centre of mass given by $\vec \omega = (3\hat j + 4\hat k) \text{ rad/s}$. Let $A$ be a point on the rod with position vector $\vec r = 2(\hat i + \hat k) \text{ m}$ with respect to the centre of mass. The velocity of the point $A$ with respect to $O$ is: