A round disc of moment of inertia I₂  about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I₁ rotating with an  angular velocity  ω about the same axis.  The final angular velocity of the combination of discs is _____.

A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity

Four identical thin rods each of mass M and length l, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is

Consider a system of two particles having masses m₁ and m₂.  If the particle of mass m₁ is pushed towards the mass centre of particles through a distance  d, by  what distance  would the particles of mass m₂ move so as to keep the mass centre of the particles at the original position?

A disc is rotating with angular velocity ω. If a child sits on it, what is conserved?

A disc is rotating with angular velocity & If a child sits on it, what is conserved ?

A spherical ball rolls on a table without slipping. Then the fraction of its total energy associated with rotation is

A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the centre of mass

In a rectangle ABCD ( BC = 2AB). Through which axis the moment of inertia is minimum
   

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 ?