A flywheel rotating about a fixed axis has a kinetic energy of 360J when its angular speed is 30 rad/s. The moment of inertia of the wheel about the axis of rotation is _______.

A thin circular ring of mass M  and radius r is rotating about its axis with a constant angular velocity ω.  Two objects  each of mass m are attached gently to the opposite ends of diameter of  the ring.  They will now rotate with an angular velocity.

O is the centre of an equilateral triangle ABC. F₁, F₂ and F₃ are three forces acting along the side AB, BC and AC as shown in figure. What should be the magnitude of F₃. So that the total torque about O is zero ?
                            

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity ω. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be

A solid sphere, disc and solid cylinder, all of the same mass and made of same material are allowed to roll down ( from rest ) on the inclined plane, then :

A circular disc is to be made using iron and aluminium. To keep its moment of inertia maximum about a geometrical axis, it should be so prepared that

If a sphere is rolling, the ratio of the translational energy to total kinetic energy is given by  _____.

Angular momentum  :

A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is k. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be

The amount of inertia of uniform circular disc of radius r  and  mass M about an axis passing from the edge of the disc and normal to the disc