Motion of system of particles and rigid body

The angular velocity of a wheel increases from 100 rps to 300 rps in 10 seconds. The number of revolutions made during that time is

The moment of inertia of a thin circular disc about an axis passing through its centre and perpendicular to its plane is I. Then the moment of Inertia of the disc about an axis parallel to its diameter and touching the edge of the rim is

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

A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity ω. Four objects, each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The annular velocity of the ring will be

A circular disc X of radius R is made from an iron plate of thickness t and another disc Y of radius 4R is made from an iron plate of thickness t/4. Then the relation between the moments of inertia Ix and Iʏ is

One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moments of inertia about their diameters are respectively Iᴀ and Iʙ such that

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

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 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 cockroach is moving with a velocity v in anticlockwise direction on the rim of a radius R of mass m. The moment of inertia of the disc about the axis is I and it is rotating in clockwise direction with an angular velocity ω. If the cockroach stops, the angular velocity of the disc will be

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

A coin of mass m and radius r having moment of inertia I about the axis passes through its centre and perpendicular to its plane. It is beaten uniformly to form a disc of radius 2r. What will be the moment of inertia about the same axis?

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 ω. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity:

If F⃗ is the force acting on a particle having position vector r⃗ and ? ⃗ be the torque of this force about the origin, then:

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

Two bodies of mass 1 kg and 3 kg have positive vectors i + 2j + k and -3i – 2j + k respectively. The centre of mass of this system has a position vector:

The moment of inertia of a rod about an axis through its centre and perpendicular to it is 1/12 ML² (where M is the mass and L, the length of the rod). The rod is bent in the middle so that the two halves make an angle of 60°. The moment of inertia of the bent rod about the same axis would be

Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be:

Consider a two particle system with particle having masses m₁ and m₂. If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

A gramophone record is revolving with an angular velocity ω. A coin is placed at a distance r from the centre of the record. The static coefficient of friction is µ. The coin will resolve with the record if:

The instantaneous angular position of a point on a rotating wheel is given by the equation θ(t) = 2t³ – 6t². 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 Iₒ. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

A solid sphere of mass M, radius R and having moment of inertia about an axis passing through the centre of mass as I, is recast into a disc of thickness t, whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains I. Then, radius of the disc will be

A disc of moment of inertia (9.8/π²) kg m² is rotating at 600 rpm. If the frequency of rotation changes from 600 rpm to 300 rpm then what is the work done?

If a solid sphere of mass 1 kg and radius 0.1 m rolls without slipping at a uniform velocity of 1 m/s along a straight line on a horizontal floor, the kinetic energy is

Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is:

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 circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α/R from the centre of the bigger disc. The value of α is

A round uniform body of radius R, mass M and moment of inertia I rolls down (without slipping) an inclined plane making an angle θ with the horizontal. Then its acceleration is

Consider a uniform square plate of side ɑ and mass m. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

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

A thin circular ring of mass M and radius R rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity ω. Four small spheres each of mass m (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be

Three identical spheres, each of mass 3 kg are placed touching each other with their centres lying on a straight line. The centres of the spheres are marked as P, Q and R respectively. The distance of centre of mass of the system from P is

Two point objects of masses 1.5 g and 2.5 g respectively are at a distance of 16 cm apart, the centre of gravity is at a distance x from the object of mass 1.5 gm where x is

Thin uniform rod of length L, cross-sectional area A and density ρ is rotated about an axis passing through centre and perpendicular to its length with angular velocity ω. What will be its rotational energy?

A body is rolling down an inclined plane.If KE of rotation is 40% of KE in a translatory state, then their body is a

A solid sphere, disc and solid cylinder all of the same mass and made up of same material are allowed to roll down (from rest) on inclined plane, then

A small object of uniform density rolls up a curved surface with an initial velocity v’.It reaches upto a maximum height of 3v² / 4g with respect to the initial position. The object is

A flywheel rotating about a fixed axis has a kinetic energy of 360J when its angular speed is 30 rads⁻¹.The moment of inertia of the flywheel about the axis of rotation is

A rod of weight W is supported by two parallel knife edge A and B and is in equilibrium, in a horizontal position.The knives are at a distance d from each other.The centre of mass of the rod is at distance x from A.The normal reaction on A is

A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor,the distance of the man above the floor will be:

A solid cylinder of mass 50 kg and radius 0.5 m is, free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to it and other hanging freely. Tensions in the string required to produce an angular acceleration of 2 revolution s⁻² is

The ratio of the acceleration for a solid sphere (mass m and radius R) rolling down an incline of angle θ without slipping and slipping down the incline without rolling is

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?

A round disc of moment of inertia i₂ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia i₁ rotating with an angular velocity of the combination of discs is