Understanding the concept of rotational motion

A wheel of angular acceleration of and an initial angular speed of 2.0 rad/s. in a time of 2 sec, it has rotated through an angle of ___ radians.

The instantaneous angular position of a point on a rotating wheel is given by the equation, . The torque on the wheel becomes zero at t= __

A uniform circular disc of radius 50cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its center. It is subjected to a torque which produces a constant angular acceleration of . Its net acceleration at the end of 2secs is approximately__

An automobile moves on a road with a speed of 54 km/h. The radius of its wheels is 0.45 m and the MOI of the wheel about its axis of rotation is . If the vehicle is brought to rest in 15s, the magnitude of average torque transmitted by its brakes is__  

The MOI of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through_

A solid cylinder of mass 50kg and radius 0.5m is free to rotate about the horizontal axis. A massless string is wound around the cylinder with one end attached to it and the other hanging freely. Tension in the sting required to produce an angular acceleration of is__

Two rotating bodies A and B of masses m and 2m with moments of inertia and have equal KE of rotation. If and be their angular momenta respectively, then__

Two persons of masses 55kg and 65kg respectively are at the opposite ends of a boat. The length of the boat is 3m and weighs 100kg. The 55kg man walks up to the 65kg man and sits with him. If the boat is in still water the center of mass of the system shifts by__

A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity ω. Two objects each of mass m are attached gently to the opposite ends of the diameter of the ring. The ring now rotates with angular velocity given by,

A small mass is attached to a string that rotates on a frictionless tabletop. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the KE of the mass will__

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

Two bodies have their MOI I and 2I respectively about their axis of rotation. If their KE of rotation are equal, their angular velocity will be in the ratio of__

A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their KE of rotation will be__

A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q. When the string is cut, the initial angular acceleration of the rod is__

A disc and a sphere of the same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?