A solid wooden door 1 m wide and 2 m high is hinged along one side and has a total mass of 50 kg . Initially open and at rest , the door is struck at its centre by a handful of sticky and mud of mass `0.5` kg travelling at 12 m/s just before impact . Find the final angular velocity of the door .
`"["(72)/(403)` rad/s]

A 10 kg mass travelling 2m /s meets and collides elastically with a 2 kg mass travelling 4 / m s in the opposite direction. Find the final velocities of both objects .

A ring of radius 0.5 m and mass 10 kg is rotating about its diameter with angular velocity of 20 rad/s. Its KE is :-

A body of mass 10 kg is moving in a circle of radian 1 m with an angular velocity of 2 rad//s the centripetal force is

A bullet of mass 10 g and speed 500 m//s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weight 12 kg . It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it.(Hint. The moment of inertia of the door about the vertical axis at one end is ML^(2)//3)

An object of mass 1kg travelling in a straight line with a velocity of 10m//s collides with, and sticks to, a stationary wooden block of mass 5kg . Then, they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object.

A body of mass 2 kg is rotating on a circular path of radius 0.5 m, with an angular velocity of 20 rad/s. If the radius of the path is doubled, then the new angular velocity will be