Dynamics of rotational motion about a fixed axis

An automobile engine develops 10⁵ W power when rotating at an angular speed of 900 rad/minute. The instantaneous torque delivered by the engine is

A uniform cylinder of mass 1 kg and radius 2 cm is rotating about its main axis at the rate of 4 rpm. The constant torque required to stop it after $2\pi$ revolution is

A body of moment of inertia 4 kg m² rotating with an angular speed of 4 rad/s has the 4x J of kinetic energy. Determine the value of x.

A solid sphere of diameter 10 cm and mass 5 kg is rolling down an inclined plane with speed of 4 m/s. The total kinetic energy of the sphere is

A uniform circular disc is rolling down an inclined plane of inclination 30° without slipping. Its linear acceleration along the inclined plane is

A solid sphere of mass $M$ and radius $R$ and a hollow sphere of mass $\frac{M}{2}$ and radius $2R$ are spinning with the same angular speed $\omega$ about their own symmetry axes. The ratio of amount of work required to bring them to rest is

A solid sphere of radius 1.26 m rotating with an angular speed of 5 rad/s is placed in a rough horizontal surface. If initial velocity of centre of sphere is zero, then velocity of centre of sphere after it starts pure rolling is

The maximum tension which an inextensible ring of mass 0.4 kg/m can bear is 40 N. The maximum velocity in m/s with which it can be rotated about centre is

If a body has equal amount of rotational kinetic energy and translational kinetic energy while rolling without slipping on a horizontal surface. Then body is a