System Of Particles Rotational Motion

For spheres each of mass and radius are placed with their centres on the four comers and of a square of side . The spheres and are hollow and and are solids. The moment of inertia of the system about side of square is

The moment of inertia of a circular ring of mass about an axis passing through its centre and perpendicular to its plane is . The diameter of the ring is

The correct vector relation between linear velocity and angular velocity in rigid body dynamics is ( where is the position vector)

A constant torque of is exerted on a pivoted wheel. If the angular acceleration of the wheel is then the moment of Inertia of the wheel is

A uniform rod of length and mass is held vertical, with its bottom end pivoted to the floor. The rod falls under gravity, freely turning about the pivot. If acceleration due to gravity is , what is the instantaneous angular speed of the rod when it makes an angle with the vertical?

A cheetah, weighing , chases a deer, weighing , in a straight path. The speed of the cheetah is and that of the deer is . The approximate speed of the centre of mass of the pair is

A solid cylinder of mass and radius rolls on a flat surface. Find its moment of inertia about the line of contact.

A body of mass acquires an angular acceleration of by an applied torque of . Find its radius of gyration.

Why there are two propellers in a helicopter ?

A uniform bar of mass and Length is bent in the form of an equilateral triangle. Find the moment of inertia of the triangle about an axis passing through the centre of mass and perpendicular to the plane of the triangle.

Two masses and are connected by a massless string over a fixed pulley. If , will move downward and will move upward. What is the acceleration with which the combination o f two masses will move? ( acceleration due to gravity)