Systems of Part...

A solid sphere of mass 2 kg and radius 5 cm is rotating at the rate of 300 rpm. The torque required to stop it in 2 π revolutions is

The moment of inertia of a solid cylinder about its axis is I. It is allowed to roll down an incline without slipping. If its angular velocity at the bottom be ω, then KE of the cylinder will be

A gramophone record has radius r and mass M. It is rotating with a speed ω. Two drops of wax of mass m fall on it at a distance r/2 on opposite sides. The new angular speed is

A body rolls down an inclined plane. If its K.E. of rotational motion is 40% of its K.E. of translation, then the body is

Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes ∠θ with AB. The moment of inertia of the plate about axis CD is then equal to

A small sphere is attached to a cord and rotates in a vertical circle about a pt. O. If the average speed of the sphere is increased, the cord is most likely to break at the orientation when the mass is at

One quarter sector is cut from a uniform circular disc of mass M and radius R. It is made to rotate about a line perpendicular to its plane and passing through the center of the original disc. Its moment of inertia about the axis of rotation is

A constant torque of 31.4 N–m is exerted on a pivoted wheel. If angular acceleration of wheel is 4 π rad/s², then the moment of inertia of the wheel is