List of top Physics Questions on Rotational motion

A thin spherical shell of radius $ 0.5 \, \text{m} $ and mass $ 2 \, \text{kg} $ is rotating about its axis of symmetry with an angular velocity of $ 10 \, \text{rad/s} $. What is its moment of inertia?

A metal rod of length $ L = 0.8 \, \text{m} $ is rotating about its center with an angular velocity $ \omega = 10 \, \text{rad/s} $. What is the linear velocity of a point on the rod at a distance $ r = 0.4 \, \text{m} $ from the center?

A disc of moment of inertia $ I $ is rotating with angular velocity $ \omega $. A ring of the same mass and radius, initially at rest, is gently placed coaxially on top of the disc. What is the final angular velocity of the system?

A solid sphere of mass 2 kg and radius 0.5 m rolls without slipping down an inclined plane of height 3 m. What is its speed at the bottom? (Take $ g = 9.8\, \text{m/s}^2 $)

A uniform rod AB of length 1 m and mass 4 kg is sliding along two mutually perpendicular frictionless walls OX and OY. The velocity of the two ends of the rod A and Bare 3 m/s and 4 m/s respectively, as shown in the figure. Then which of the following statement(s) is/are correct?

A small ball of mass m is suspended from the ceiling of a floor by a string of length L. The ball moves along a horizontal circle with constant angular velocity ω, as shown in the figure. The torque about the center (O) of the horizontal circle is:

The position vector of a particle of mass $m$ moving with a constant velocity $\mathbf{u}$ is given by $\mathbf{r} = x(t)\hat{i} + b\hat{j}$, where $b$ is a constant. At an instant, $\mathbf{r}$ makes an angle $\theta$ with the x-axis as shown in the figure. The variation of the angular momentum of the particle about the origin with $\theta$ will be:

Rate of cooling of a body is $0.2^\circ \text{C/min}$ when excess temperature is $20^\circ \text{C}$. The proportionality constant $ k $ is: