List of top Physics Questions on Rotational Motion and Torque asked in IIT JAM PH

The angular momentum of a particle relative to the origin varies with time ($t$) as $\vec{L} = (4\hat{i} + \alpha t^2 \hat{j})\, \mathrm{kg \cdot m}^2/\mathrm{s}$, where $\alpha = 1\, \mathrm{kg \cdot m}^2/\mathrm{s}^3$. The angle between $\vec{L}$ and the torque acting on the particle becomes $45^\circ$ after a time of ............ s.

A wheel is rotating at a frequency $f_0$ Hz about a fixed vertical axis. The wheel stops in $t_0$ seconds, with constant angular deceleration. The number of turns covered by the wheel before it comes to rest is given by:

If the diameter of the Earth is increased by 4% without changing the mass, then the length of the day is ...... hours.
(Take the length of the day before the increment as 24 hours. Assume the Earth to be a sphere with uniform density.)

Consider an object moving with a velocity $ \vec{v} $ in a frame which rotates with a constant angular velocity $ \vec{\omega} $. The Coriolis force experienced by the object is

The mass per unit length of a rod (length 2 m) varies as $ \rho = 3 \, \text{kg/m} $. The moment of inertia (in kg m$^2$) of the rod about a perpendicular-axis passing through the tip of the rod (at $ x = 0 $) is

A disc of radius $R_1$ having uniform surface density has a concentric hole of radius $R_2<R_1$. If its mass is $M$, the principal moments of inertia are

A pendulum is made of a massless string of length $ L $ and a small bob of negligible size and mass $ m $. It is released making an angle $ \theta_0 $ (<< 1 rad) from the vertical. When passing through the vertical, the string slips a bit from the pivot so that its length increases by a small amount $ \delta $ ($ \delta \ll L $) in negligible time. If it swings up to angle $ \theta_1 $ on the other side before starting to swing back, then to a good approximation, which of the following expressions is correct?

A uniform rigid meter-scale is held horizontally with one of its end at the edge of a table and the other supported by hand. Some coins of negligible mass are kept on the meter scale as shown in the figure. As the hand supporting the scale is removed, the scale starts rotating about its edge on the table and the coins start moving. If a photograph of the rotating scale is taken soon after, it will look closest to:

A particle of mass $ m $ fixed in space is observed from a frame rotating about its $ z $-axis with angular speed $ \omega $. The particle is in the frame’s $ xy $-plane at a distance $ R $ from its origin. If the Coriolis and centrifugal forces on the particle are $ F_{\text{COR}} $ and $ F_{\text{CF}} $, respectively, then (all the symbols have their standard meaning and refer to the rotating frame),

A uniform rigid meter-scale is held horizontally with one of its end at the edge of a table and the other supported by hand. Some coins of negligible mass are kept on the meter scale as shown in the figure. As the hand supporting the scale is removed, the scale starts rotating about its edge on the table and the coins start moving. If a photograph of the rotating scale is taken soon after, it will look closest to:

A particle of mass $ m $ fixed in space is observed from a frame rotating about its $ z $-axis with angular speed $ \omega $. The particle is in the frame’s $ xy $-plane at a distance $ R $ from its origin. If the Coriolis and centrifugal forces on the particle are $ F_{\text{COR}} $ and $ F_{\text{CF}} $, respectively, then (all the symbols have their standard meaning and refer to the rotating frame),