Centripetal Force Equation

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Centripetal force is a force that tends to make the body follows either circular or curved path. For a body in a circular motion experience an inward acceleration towards the center known as centripetal acceleration. According to Newton’s second law of motion, if there is an acceleration, then a net force must be acting along with the same direction. Thus, in circular motion inward force directed towards the center of the circle is known as centripetal force.

A body of mass ‘m’ moving in a circular path of radius ‘r’ with velocity ‘v’ has centripetal force of

F = mv2/r

Example: A ball of mass 0.1 kg attached to one end of a string of length 0.3 m. If the tension developed in
the string is 300 N, what is the velocity with which the ball is rotating?

Solution: Tension developed here is nothing but the centripetal force. Centripetal force is responsible to

keep the ball rotating around the circular path. Placing the values of mass (0.1 kg), radius (0.3 m) and force

(300 N) in the expression of centripetal force we get

300 = (0.1 x v2)/ 0.3

90 = 0.1 x v2

v2 = 90/0.1

v2 = 900

v = sqrt (900)

v = 30 m/s

Example: A car taking a turn of 4 m experiences an inward force of 30000 N due to friction. If the car is
moving with velocity of 15 m/s, what is the mass of the car?

Solution: Here centripetal force is developed due to frictional force. Placing the values of force (30000 N),

radius (4 m) and velocity (15 m/s) in the expression of centripetal force we get

30000 = (m x 152)/ 4

120000 = 225m

m = 120000/225

m = 533.33 kg

Example: A jet plane of mass 25000 kg is taking a turn on the ground under a force of 1000000 N. What is
the centripetal acceleration?

Solution: Centripetal force is written as

F = mv2/r

Centripetal acceleration has the expression of

ac = v2/r

Therefore, we can write

F = m x ac

F = 1000000 N and m = 25000 kg therefore,

1000000 = 25000 x ac

ac = 1000000/25000

ac = 40 m/s2

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