NCERT Class 11 Physics Solutions: Chapter 7 – System of Particles and Rotation Motion-Part 13

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Question 7.29:

Explain why friction is necessary to make the disc in Figure roll in the direction indicated.

(a) Give the direction of frictional force at , and the sense of frictional torque, before perfect rolling begins.

(b) What is the force of friction after perfect rolling begins?

Answer:

disc and it's direction is shown in figure.

Figure Shown the Disc and It's Direction

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A torque is required to roll the given disc. As per the definition of torque, the rotating force should be tangential to the disc. Since the frictional force at point is along the tangential force at point , a frictional force is required for making the disc roll.

Force of friction acts opposite to the direction of velocity at point . The direction of linear velocity at point is tangentially leftward. Hence, frictional force will act tangentially rightward. The sense of frictional torque before the start of perfect rolling is perpendicular to the plane of the disc in the outward direction.

Since frictional force acts opposite to the direction of velocity at point B, perfect rolling will begin when the velocity at that point becomes equal to zero. This will make the frictional force acting on the disc zero.

Question 7.30:

A solid disc and a ring, both of radiuses are placed on a horizontal table simultaneously, with initial angular speed equal to . Which of the two will start to roll earlier? The co-efficient of kinetic friction is

Answer: Disc

Explanation:

Radii of the ring and the disc,

Initial angular speed,

Coefficient of kinetic friction,

Initial velocity of both the objects,

Motion of the two objects is caused by frictional force. As per Newton’s second law of motion,

we have frictional force,

Acceleration produced in the objects

Mass

As per the first equation of motion, the final velocity of the objects can be obtained as:

The torque applied by the frictional force will act in perpendicularly outward direction and cause reduction in the initial angular speed.

Torque,

Angular acceleration

Using the first equation of rotational motion to obtain the final angular speed:

Rolling starts when linear velocity,

Equating equations we get:

For the ring:

For disc

Since the disc will start rolling before the ring.