Pure Rotational Motion

A turbine fan in a jet engine has moment of inertia $2.5 \mathrm{kg} {\mathrm{m}}^2$ about its axis of rotation. Its angular velocity is $40t^2$. The net torque is

A ring and a disc of different masses are rotating with the same kinetic energy. If we apply a retarding torque $\tau$ on the ring, it stops after making $n$ revolutions. After how many revolutions will the disc stop, if the retarding torque on it is also $\tau$?

An automobile engine develops a power of $100 \mathrm{kW}$ when rotating at a speed of $1800$ $\mathrm{rpm}$. The torque delivered by the engine is:

A light rod of length $3l$ is hinged as given in figure with two-point masses $2m$ and $5m$ . Angular acceleration will be:

A uniform thin rod of mass M and length L is standing vertically along y-axis on a smooth horizontal surface, with its lower end at origin (0,0) a slight disturbance at t= 0 causes the lower end to slip on smooth surface along the positive x-axis and the rod starts falling the acceleration vector of centre of mass of the rod during its fall is

If applied torque on a system is zero, i.e., $\tau =0$ , then for that system.

In the diagram shown, a rod of mass $\mathrm{M}$ has been fixed on a ring of the same mass. The whole system has been placed on a perfectly rough surface. The system is gently displaced so that the ring starts rolling. The velocity of the centre of the ring when the rod becomes horizontal is (the length of the rod is equal to the radius of the ring)

A circular disc of radius R is free to rotate about an axis passing through its centre. An external tangential force F is applied on the disc along its edge. If the angular velocity of disc is increased from 0 to w in a time t then the work done by F during same time t is

The intensity of magnetic field is $\mathrm{B}$ and magnetic moment is $\mathrm{M}$. Then, the maximum potential energy will be

A solid sphere of mass $M$ and radius $R$ is lying on a rough horizontal plane. A constant force $F=4 Mg$ acts vertically at point $\mathrm{P}$ such that $\mathrm{O}\mathrm{P}$ makes $600$ with horizontal. Find the minimum value of coefficient of friction $\mathrm{\mu }$ so that sphere starts pure rolling -

Part of the tuning arrangement of a radio consists of a wheel which is acted on by two parallel constant forces as shown in the figure. If, the wheel rotates just once, the work done will be

(Diameter of the wheel $=0.05\mathrm{ }\mathrm{m}$)

A ring and a disc of different masses are rotating with the same KE. If we apply a retarding torque $\tau$ on the ring stops after making $n$ revolutions, then in how many revolutions will the disc stop under the same retarding torque?

A ring and a disc of different masses are rotating with the same KE. If we apply a retarding torque $\tau$ on the ring, it stops after making $n$ revolutions, then the number of revolutions for the disc to stop under the same retarding torque is

A solid sphere of radius $R$ and mass $M$ is rolled by a force $F$ acting at the top of the sphere as shown in the figure. The sphere starts from rest and rolls without slipping, then


            

A homogeneous cylinder of mass $M$ and radius $R$ is pulled on a horizontal plane by a horizontal force $F$ acting through its mass centre. Assuming rolling without slipping the angular acceleration of the cylinder is