A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s-^1. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

Derive an expression for MI of a solid cylinder about its axis.

A solid cylinder rolles down an inclined plane. Its mass is 2 kg and radius 0.1 m. If the height of the inclined plane is 4m, what is its rotational kinetic energy when it reaches the bottom.

A 70 kg man stands in contact against the inner wail of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to ' remain stuck to the wall (without falling) when the floor is suddenly removed?

A body of mass 10 kg is rotating on a circular path of radius 1 m with time period 3.14S. Calculate its angular momentum and rotational kinetic energy.

When a mass is rotating in a plane about a fixed point its angular momentum is directed along

A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 m s^-1 to 3.5 m s^-1 in 25 s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force?

A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m s-1, what is the recoil speed of the gun?

A rope of negligible mass is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rops is pulled with a force of 30 N? What is the linear acceleration of the rope?

A solid cylinder of radius 5 cm and mass 0.5 kg rolls down an inclined plane (1 in 10). Calculate the acceleration and total energy of the cylinder after 10 S.

A trolley of mass 200 kg moves with a uniform speed of 36 km/ h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 m s^-1 relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?