The instantaneous angular position of a point on a rotating wheel is given by the equation $$\theta \left( t \right) = 2{t^3} - 6{t^2}$$

The torque on the wheel becomes zero at

The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is $$I$$₀. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

From a circular disc of radius R and mass 9M, a small disc of mass M and radius $${R \over 3}$$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is

A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity $$\omega $$. Two objects each of msass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by