What is Rolling Motion?
The rolling motion is the combination of translatory and rotatory motion, which can happen with or without slipping. The wheels of a plane landing on a runway or a car moving along the highway are some examples of rolling motion. All these examples, including circular wheels, possess rolling motion.
Pure and Impure Rolling
Pure rolling is a condition in which there is no sliding or slipping during rolling. The point of contact of the body with the ground is always at rest. However, in impure rolling, the body slips as it rolls.
Important Questions on Rolling Motion
1) If the radius of the wheel is R, then what will be the displacement of the centre of the wheel in one rotation?
a) 4R
b) 3Ï€R
c) 2Ï€R
d) 0
Correct Option: (c)
Explanation: Let ‘T’ be the time taken for one rotation, and ‘w’ be the angular speed of the wheel: Hence, w = 2π/T.
At the centre, the velocity is given by: Rw = R x 2Ï€/T.
Therefore, the distance moved by it = R x 2Ï€/T x T = 2Ï€R.
2) On a smooth inclined surface, a sphere can roll purely. Is it True or False?
a) True
b) False
Correct Option: (b)
Explanation: The above statement is false because the condition for pure rolling is (V = Rw) at every instant of time, where the speed of the centre of the sphere is denoted by V, and angular speed is denoted by w. A component of gravity on an inclined surface converts its potential energy to kinetic energy, and therefore ‘V’ increases, due to which ‘w’ should also increase. And for this, the presence of torque is needed, which is to be provided by friction. Hence, the surface should be rough for pure rolling on an inclined plane.
3) To decrease the angular velocity, a ballet dancer folds her arms and brings the stretched leg close to the other leg. Is it true or false?
a) True
b) False
Correct Option: (b)
Explanation: The above statement is false because a ballet dancer folds her arms and brings the legs closer to increase the angular velocity. When the dancer stretches her hands outward, angular speed decreases to conserve angular momentum because her moment of inertia increases.
4) If two cars are moving at such speeds that each of them makes a complete circle at the same time t, then what will be the ratio of angular speeds of the first car to the second car, if the mass of the first car is m1 and mass of the second car is m2, and both cars are moving in circles of radii r1 and r2, respectively?
a) 1:1
b) r1:r2
c) m1:m2
d) 2:2
Correct Option: (a)
Explanation: As we know that ω=v/r=2π/T
Since the same time is taken by both cars for one revolution, ω is the same for both cars.
5) A flywheel is attached to an engine to _____.
a) Decrease its energy
b) Increase its speed
c) Help in overcoming the dead point
d) None of these
Correct Option: (c)
Explanation: A flywheel helps the engine to overcome the dead points due to its large inertia of motion, and this is why they are attached to an engine.
6) Which among the following conditions is correct for the maximum acceleration of the centre of mass, if a solid sphere of radius (R) is placed on a smooth horizontal surface, and at height (h) from the lowest point, a horizontal force (F) is applied?
a) h=2R
b) 3h=2R
c) h=1
d) There will be no relation between h and R
Correct Option: (d)
Explanation: The sphere does not roll because the smooth horizontal surface does not provide any friction. Hence, the acceleration of the centre of mass of the sphere does not depend on the position of the applied force. So, there will be no relation between h and R.
7) _____ is the force that keeps the body moving in a circular motion.
a) Centripetal force
b) Tangential force
c) Gravitational force
d) Reaction forces
Correct Option: (a)
Explanation: For keeping bodies moving in a circular motion, centripetal force is responsible. The centripetal force and the square of the tangential velocity are proportional to each other, while the centripetal force is inversely proportional to the radius of the circle.
8) The centrifugal force always acts _____.
a) In the centre
b) Away from the centre
c) In the tangential direction
d) On the plane of motion
Correct Option: (b)
Explanation: When a body is in a circular motion, the centrifugal force always acts away from the centre of the circle. On the other hand, keeping the body moving in the circle, the centripetal force always acts towards the centre of the circle.
9) What is the difference between pure and impure rolling?
Pure rolling is a condition in which there is no sliding or slipping during rolling. The point of contact of the body with the ground is always at rest. However, in impure rolling, the body slips as it rolls.
10) What is the condition for pure rolling?
Pure rolling is a condition in which there is no sliding during rolling. This can only happen when the contact point of the rolling object with the surface has zero velocity. It happens when the velocity of rotation motion precisely cancels out with the velocity of translation motion. This will happen if V = rω, where V denotes the linear velocity and ω denotes the angular velocity.
Practice Questions
1) What is pure rolling?
2) What is impure rolling?
3) Define friction.
4) What is centrifugal force?
5) What are the conditions for pure rolling?
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