IIT Jee Problem: A stationary horizontal disc is free to rotate about its axis, when a torque is applied on it.

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it its, kinetic energy as a function of theta , where theta is the angle by which it has rotated, is given as k theta . If its moment of inertia is I then the angular acceleration of the disc is :

On account of the earth rotating about its axis

A block hangs from a string wrapped on a disc of radius 20 cm free to rotate about its axis which is fixed in a horizontal position. If the angular speed of the disc is 10 rad/s at some instant, with what speed is the block going down at that instant?

A metal rod of length 'L' and mass 'm' is pivoted at one end. A thin disc of mass 'M' and radius 'R' (ltL) is attached at its center to the free end of the rod. Consider two ways the disc is attached : (case A). The dise is not free to rotate about its centre and (case B) the disc is free to rotate about its centre. The rod disc system perfoms (SHM) in vertical plane after being released from the same displacement position. Which of the following statement (s) is (are) true ? .

A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is

A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is

A flywheel whose moment of inertia about its axis of rotation is 16kg-m^(2) is rotating freely in its own plane about a smooth axis through its centre. Its angular velocity is 9rads^(-1) when a torque is applied to bring it to rest in t_(0) seconds find t_(0) if (a). The torque is constant and of magnitude 4 N-m (b). The magnitude of the torque after t second is given by kt .

A uniform disc of mass M, radius R is attached to a frictionless horizontal axis. Its rim is wound with a light string and a tension T is applied to it, the angular acceleration will be?

Torques of equal magnitude are applied to hollow cylinder and a solid sphere, both having the same mass and same radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. which of the two will acquire a greater angular speed after a given time ?

On a disc of radius R a concentric circle of radius R//2 is drawn. The disc is free to rotate about a frictionless fixed axis through its center and perpendicular to plane of the disc. All three forces ( in plane of the disc ) shown in figure are exerted tangent to their respective circular periphery. The magnitude of the net torque ( about centre of disc ) acting on the disc is :