A circular plate is moving on a table having angular velocity w. If m be the mass and r be the radies of the plate then show that its total kinetic energy will, be k =`3/4mw^2r^2`.

A particle of mass m is revolving along a circular path of radius r with uniform angular velocity omega . What will be the magnitude and direction of the angular momentum of that particle ?

Two particles of masses m_1 and m_2 move on the same plane. If their relative velocity is u, and the velocity of their centre of mass is v, show that the total kinetic energy is 1/2(m_1+m_2)v^2+1/2 ((m_1m_2)/(m_1+m_2))u^2 .

A thin circular ring of mass M and radius R is rotating about its own axis with a constant angular velocity omega . Two object each of mass m are placed gently on the opposite ends of a diameter of the ring. What will be the angular velocity of the ring?

A circular iron-plate of thickness (2)/(3) cm is made by beating an iron-sphere of diameter 4 cm. What will be the radius of the iron-plate?

A circular disc of mass m and radius r is rolling over a horizontal table top with angular velocity omega . Prove that the total energy of the disc , K = (3)/(4) m omega ^(2) r^(2) .

A particle of mass m moves in a circular path of radius r in a horizontal plane with uniform angular velocity vec(omega) about the z- aixs. Write down the position vector of the particle at any instant and hence derive expressions for velocity and acceleration of the particle.

A bullet of mass m, moving with a velocity u hits a wooden block of mass M and gets embedded. Assuming that the wooden block can move freely, show that, the loss of kinetic energy =1/2 (mM)/(m+M) u^2 .

A thin uniform rod of mass M and length L is rotating about a perpendicular axis passing through its centre with a constant angular velocity omega . Two objects each of mass (M)/(3) are attached gently to the two end of the rod. The rod will now rotate with an angular velocity of

A mass 2m is at rest and another mass m is moving with a velocity. An elastic collision takes place between them. Show that the mass m loses 8/9 part of its initial kinetic energy in this collision.

A wheel of mass 5 kg and radius 0.4 m is rolling on a road without sliding with angular velocity 10 rad. s^(-1) . The moment of inertia of the wheel about the axis of rotation is 0.65 kg . m^(2) . What is the percentage of the kinetic energy of rotation in the total kinetic energy of the wheel ?