Rotational Motion

A car of mass m is moving on a level circular track of radius R. If \(\mu\)s represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through

A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg m2. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the e...

The instantaneous angular position of a point on a rotating wheel is given by the equation \(\theta \left( t \right) = 2{t^3} - 6{t^2}\)
The torque on the wheel becomes zero at

The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is \(I\)0. Its moment of inertia about an axis passing through one of its ends and perpendicular ...

A small mass attached to a string rotates on a frictionless table top as shown. 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 kinetic energy of t...

A gramophone record is revolving with an angular velocity \(\omega\). A coin is placed at a distance r from the centre of the record. The static coefficient of friction is \(\mu\). The coin will revolve with the record if

A circular disk of moment of inertia \({I_t}\) is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed \({\omega _i}\). Another disk of moment of inertia \({I_b}\) is dropped coaxially onto the rotating dis...

A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

From a circular disc of radius R and mass 9M, a small disc of mass M and radius \({R \over 3}\) is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through ...

A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity \(\omega\). Two objects each of msass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with ang...

A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity \(\omega\). If two objects each of mass m be attached gently to the opposite ends of a diame...

Four identical thin rods each of mass M and length \(l\), form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is

If \(\overrightarrow F\) is the force acting on a particle having position vector \(\overrightarrow r\) and \(\overrightarrow \tau\) be the torque of this force about the origin, then

A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90o. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defin...

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is

A uniform rod AB of length \(l\) and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml2/3, the initial angular acceleration of the rod...

A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is LA when it is at A and LB when it is at B, then

A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of

A uniform rod AB of length \(l\) and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml2/3, the initial angular acceleration of the rod...

The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity \(\omega\). The force exerte...

A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle \(\theta\). The frictional force

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be in the ratio

The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is

A wheel having moment of inertia 2 kg m2 about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel's rotation in one minute would be

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axes in the plane of the ring is

Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side \(l\) cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in...

A round disc of moment of inertia \(I\)2 about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia \(I\)1 rotating with an angular velocity \(\omega\) about the same axis. T...

A stone is tied to a string of length \(l\) and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change...

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity \(\omega\). Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular v...

A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R. then the fraction of total energy associated with its rotational energy will be

A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h. What is the speed of its centre of mass when the cylinder reaches its bottom ?

A disc is rotating with angular speed \(\omega\). If a child sits on it, what is conserved

A point P consider at contact point of a wheel on ground which rolls on ground without slipping then value of displacement of point P when wheel completes half of rotation (if radius of wheel is 1 m)

A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct ?

A circular disc is to be made by using iron and aluminium so that it acquired maximum moment of inertia about geometrical axis. It is possible with

As shown in the figure at point O a mass is performing vertical circular motion. The average velocity of the particle is increased, then at which point will the string break

For the adjoining diagram, the correct relation between I1, I2, and I3 is, (I-moment of inertia)

For a hollow cylinder and a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier