Centripetal Force Formula

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Centripetal force is developed by the centripetal acceleration towards the center of the circular path. 


Consider an object of mass m is tied to a string of radius r and rotated with velocity of v. The string would follow a circular path
which is against the Newton’s law of motion that tells the natural tendency of any object is to follow a straight path. The radial
force developed is forcing the object to take the circular path. Centripetal acceleration of the object is
ac = v2 /r

According to Newton’s second law

Force = mass x acceleration

As the centripetal force is directed along the same direction as the centripetal acceleration therefore,

Force = mass x v2 /r

Or, Force = m x v2 /r

Fr = mv2 /r

Fr represents radial or centripetal acceleration.

Example 1: A wooden ball of mass 5 kg is rotating with velocity of 4 m/s around a circle of radius 0.4 m. What is the centripetal
force?

Explanation: Centripetal force is given as

Fr = mv2 /r ----------- (1)

Mass of the ball = 5 kg, radius of the circle = 0.4 m and velocity of the rotation = 4 m/s.

Placing the values in equation 1 we get

Fr = (5 x 42)/ 0.4

Fr = 80/ 0.4

Fr = 200 N

Example 2: How much force would be required to keep a stone of mass 0.01 kg whirling around a circle of radius 0.1 m with
velocity of 4 m/s?

Solution: Centripetal force provides the minimum force that is required to keep a stone whirling around a circle. Centripetal
force is given as
Fr = mv2 /r ---------- (1)

Mass of the stone = 0.01 kg, radius of the circle = 0.1 m and velocity of the stone = 4 m/s.

Placing the values in equation 1we get

Fr = (0.01 x 42)/ 0.1

Fr = 0.16/ 0.1

Fr = 1.6 N

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