## Category: Systems of Particles and Rotational Motion

## Read each statement below carefully, and state, with reasons, if it is true or false; During rolling, the force of friction acts in the same direction as the direction of motion of the CM of the body. The instantaneous speed of the point of contact during rolling is zero. The instantaneous acceleration of the point of contact during rolling is zero.For perfect rolling motion, work done against friction is zero. A wheel moving down a perfectly frictionless inclined plane will undergo sli ping (not rolling) motion

Read each statement below carefully, and state, with reasons, if it is true or false; During rolling, the force of friction acts in the same direction as the direction of motion of the CM of the body. The instantaneous speed of the Read More …

## A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination 30°. The coefficient of static friction μs =0.25. How much is the force of friction acting on the cylinder? What is the work done against friction during rolling? If the inclination θ of the plane is increased, at what value of θ does the cylinder begin to skid, and not roll perfectly?

A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination 30°. The coefficient of static friction μs =0.25. How much is the force of friction acting on the cylinder? What is the work done against Read More …

## A solid disc and a ring, both of radius 10 cm are placed on a horizontal table simultaneously, with initial angular speed equal to 10 ð rad s-1. Which of the two will start to roll earlier? The co-efficient of kinetic friction is μk =0.2

A solid disc and a ring, both of radius 10 cm are placed on a horizontal table simultaneously, with initial angular speed equal to 10 ð rad s-1. Which of the two will start to roll earlier? The co-efficient of kinetic friction Read More …

## Explain why friction is necessary to make the disc in Fig. 7.41 roll in the direction indicated. Give the direction of frictional force at B, and the sense of frictional torque, before perfect rolling begins. What is the force of friction after perfect rolling begins?

Explain why friction is necessary to make the disc in Fig. 7.41 roll in the direction indicated. Give the direction of frictional force at B, and the sense of frictional torque, before perfect rolling begins. What is the force of friction after Read More …

## A disc rotating about its axis with angular speed ωo is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is R. What are the linear velocities of the points A, B and C on the disc shown in Fig. 7.41? Will the disc roll in the direction indicated?

A disc rotating about its axis with angular speed ωo is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is R. What are the linear velocities of the points A, B and C on the Read More …

## Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by

Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by [latex]v^{2}=\frac{2gh}{\left ( 1+\frac{k^{2}}{R^{2}} \right )}[/latex] Using dynamical Read More …

## Prove the theorem of perpendicular axes. (Hint: Square of the distance of a point (x, y) in the x–y plane from an axis through the origin perpendicular to the plane is x2 + y2 ). Prove the theorem of parallel axes. (Hint: If the centre of mass is chosen to be the origin ∑ mi ri =0)

Prove the theorem of perpendicular axes. (Hint: Square of the distance of a point (x, y) in the x–y plane from an axis through the origin perpendicular to the plane is x2 + y2 ). Prove the theorem of parallel Read More …

## Two discs of moments of inertia I1 and I2 about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds ω1 and ω2 are brought into contact face to face with their axes of rotation coincident. (a) What is the angular speed of the two-disc system? (b) Show that the kinetic energy of the combined system is less than the sum of the initial kinetic energies of the two discs. How do you account for this loss in energy? Take ω1 ≠ ω2

Two discs of moments of inertia I1 and I2 about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds ω1 and ω2 are brought into contact face to face with their axes of rotation coincident. (a) What Read More …

## A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it. (Hint: The moment of inertia of the door about the vertical axis at one end is ML2 / 3 .)

A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end Read More …

## A man stands on a rotating platform, with his arms stretched horizontally holding a 5 kg weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then brings his arms close to his body with the distance of each weight from the axis changing from 90cm to 20 cm. The moment of inertia of the man together with the platform may be taken to be constant and equal to 7.6 kg m2 . What is his new angular speed? (Neglect friction.) Is kinetic energy conserved in the process? If not, from where does the change come about?

A man stands on a rotating platform, with his arms stretched horizontally holding a 5 kg weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then brings his arms close to his body with Read More …