Circular Motion - Laws Of Motion ,Class 11, Physics - JEE PDF Download

An object is said to be in motion if it changes its position with time. A body which does not move is said to be at rest, motionless, or stationary. Circular motion is a movement of an object along a circular path or a circular orbit. The object in circular motion moves along the circumference of a circle. Motion along a circular with constant speed is called uniform circular motion.

Examples of circular motion include: a stone tied to one end of a string and is revolved uniformly. Moon revolves around the earth and the earth revolves around the sun.

Formulas

The circumference of a circle path of radius r is 2πr. If the period for one rotation is T, the angular velocity ω (omega) is:

ω = 2π/T

The speed of the object in the circular path is:

v = 2πr/T = πr

The angle swept out in time t is give as:

Θ = 2πt/T = ωt

The acceleration due to change in direction is:

a = v²/r

Centripetal force and Centrifugal force

There is a continuous change in direction in uniform circular motion due to which there is acceleration that is perpendicular to the path because of uniform speed. This acceleration is directed towards the center. This acceleration is called the centripetal acceleration or radial acceleration. The force which causes this acceleration is called the centripetal force. Therefore, centripetal force acting on a body in circular motion may be defined as the radial force directed towards the center. The direction of the force changes continuously.

The force acting on a body of mass m moving with a constant speed v along a circular path of radius r is given as:

f = mv²/r

In the stone tied to a string and whirl around the tension in the string provides the centripetal force.

According to Newton’s third law of motion, the agent which exerts centripetal force is subjected to centrifugal reaction which is equal and opposite to centripetal force and directed away from the center of the circular path. While whirling stone tied with a string the stone exerts the outward force, centrifugal reaction, on the hand.

Centrifugal force is a fictitious force due to inertia of rotational motion. There is a misconception that an object moving in a circle has an outward force acting on it called centrifugal force. If a centrifugal force were acting the stone would fly away while whirling. The centrifugal force cannot be created. It is only experience in the context of circular motion.