Dynamics of Rotational Motion — MCQ Practice

A solid cylinder of mass $M$ and radius $R$ rolls without slipping on a horizontal surface with a linear velocity $v$. What is its total kinetic energy?

A uniform rod of mass $M$ and length $L$ is pivoted at one end and allowed to swing freely. If it is released from rest in a horizontal position, what is its angular speed when it reaches the vertical position?

A disc of moment of inertia $I_1$ is rotating with angular velocity $\omega_1$ about an axis perpendicular to its plane and passing through its center. Another disc of moment of inertia $I_2$ (initially at rest) is gently placed on the first disc coaxially. What is the final angular velocity of the combined system?

A force $\vec{F} = (2\hat{i} + 3\hat{j} - \hat{k})\,\text{N}$ acts on a particle whose position vector is $\vec{r} = (\hat{i} - \hat{j} + 2\hat{k})\,\text{m}$ relative to the origin. What is the torque acting on the particle about the origin?

A uniform rod of mass $m$ and length $L$ is hinged at one end. A horizontal force $F$ is applied at the free end perpendicular to the rod. What is the angular acceleration of the rod?

A solid sphere and a hollow sphere of the same mass and radius are released from rest at the top of an inclined plane. Which one will reach the bottom first, assuming they roll without slipping?

A particle of mass $m$ is moving in a circular path of radius $r$ with a constant speed $v$. What is its angular momentum about the center of the circle?