What is centripetal force?

A centripetal force is any force that makes an object follow a circular path. In fact, the meaning of the word centripetal is " center seeking " or " toward the center "

There are many real life examples of this force. Take a look at the following examples.


Whirling ball

Centripetal force

Imagine using a string to spin the green ball you see above. According to Newton's first law of motion, the ball should have stayed in a straight path. However, this is not the case. The ball follows instead a circular path because the string is pulling the ball back toward the center or toward the black dot. Without this force, the ball will not revolve. Instead, it would just move along a straight line.


Gravitational force

A gravitational force is directed toward the center of the earth. This force is also a centripetal force keeping the moon in almost circular orbit around the earth.


Car driving around a curve

When a car drives around a curve, there must be sufficient frictional force in place between the tires and the road to provide the required centripetal force. Otherwise, the car will skid instead of going around the curve.  

Is there a formula for the centripetal force?

To find this force, you can use Newton's second law of motion.

F = m × a

m is the mass of the object

a is the centripetal acceleration given by the following formula. We will prove the formula for centripetal acceleration in another lesson.

Centripetal acceleration =
v2 / r

Centripetal force formula

Centripetal force = F =
m × v2 / r

  • The unit of centripetal force is Newton or N.
  • The unit of mass is kilogram or kg.
  • The unit of speed or v is meter per second or m/s
  • The unit of the radius or r is meter or m

An example showing how to use the centripetal force formula

A car with a weight of 1000 kg is going around a circular path that has a radius of 400 meters with a speed of 20 m/s. What is the centripetal force exerted on the car?

F = mv2 / r

F = [1000(20)2] / 400

F = [1000(400)] / 400

F = 400000 / 400

F = 1000

The centripetal force exerted on the car is 1000 Newtons.

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