List of top Physics Questions on Rotational Motion and Torque

A uniform rod of mass m and length l suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is _______ (g = acceleration due to gravity).

Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is $\frac{x}{12} ML^2$ kg m$^2$. The value of x is ______ .

A capacitor of capacitance 10 Î¼F is connected with a battery of emf 6V. Now the battery is disconnected and another uncharged capacitor of capacitance 20 Î¼F is connected to the capacitor. Find the charge on the 20 Î¼F capacitor.

A disc is performing pure rolling if the speed of the top point is 8 m/s. Find the speed of point B.

A circular disk of radius $ R $ meter and mass $ M $ kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that $ \theta(t) = 5t^2 - 8t $, where $ \theta(t) $ is the angular position of the rotating disk as a function of time $ t $. How much power is delivered by the applied torque, when $ t = 2 $ s?

A solid sphere of mass $ m $ and radius $ r $ is allowed to roll without slipping from the highest point of an inclined plane of length $ L $ and makes an angle of $ 30^\circ $ with the horizontal. The speed of the particle at the bottom of the plane is $ v_1 $. If the angle of inclination is increased to $ 45^\circ $ while keeping $ L $ constant, the new speed of the sphere at the bottom of the plane is $ v_2 $. The ratio of $ v_1^2 : v_2^2 $ is:

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),