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Circular Motion

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V Circular motion: Motion of a body along a circular path is known as circular motion. Uniform circular motion: Motion of a body long a circular path with the constant speed is called uniform circular motion . Circular motion

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r V A body in circular motion is described by two physical quantities, Speed of the body “v” Radius of the circular path “r” Circular motion

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r F V For uniform circular motion body needs a lateral force such that it continuously changes its direction, this force is called centripetal force. Centripetal force: Centripetal force is defined as the radial force directed towards the center acting on a body in circular motion. Centripetal force Circular motion

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r F V Nature of Centripetal force: Magnitude of centripetal force remains constant Always it acts along the radius It is always directed towards the center Hence, centripetal force is a radial force of constant magnitude. Centripetal force Circular motion

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r F V The centripetal force –f acting on a body of mass - m moving in a circular path is given by , Centripetal force Centripetal acceleration: Circular motion

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Circular motion Centripetal Force and Mass: An object swinging in a circle with constant speed requires certain amount of centripetal force If the mass of the body is doubled then required centripetal force is also double. If the mass of the body is tripled then required centripetal force is also tripled. Hence, centripetal force is directly proportional to the mass of the body.

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Circular motion Centripetal Force and Radius Consider an object of mass-m swinging in a circle with a constant speed-v requires certain amount of centripetal force. If the radius of the circle is doubled then required centripetal force is halved. Radius=2r then centripetal force=f/2 3. If the radius of the circle is halved then required centripetal force is doubled. Radius=r/2 then centripetal force=2f Hence, centripetal force is inversely proportional to the radius of the body.

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Circular motion Centripetal Force and speed Consider an object of mass-m swinging in a circle of radius-r with certain speed requires certain amount of centripetal force. If the speed is doubled then required centripetal force is increased by four times. speed=2v then centripetal force=4f 3. If the speed is tripled then required centripetal force is increased by nine times. speed=3v then centripetal force=9f Hence, centripetal force is directly proportional to square of the velocity of the body.

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STOP r o F V Circular motion What happens if the centripetal is stopped when the body is moving in a circular path? If the centripetal force is stopped the body moves along the tangent to the circle.

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r o Circular motion If the centripetal force is stopped the body moves along the tangent to the circle with a velocity-v. WHY????? v This is in accordance with Newton’s first law of motion. When there is no centripetal force then there can not be any change in direction of the body hence it moves in a straight line along the tangent to the circle.

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