Formula For Centripetal Force

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If an object is travelling on a circular path, there are different kinds of forces acting on the object due to its position with respect to the center of the circle. Centripetal force is the force which acts on an object moving on a circular path and this force pulls the object towards the center of the circle. Therefore the direction of the centripetal force always acts towards the center of the circle. The centripetal force formula is given as the product of mass and the centripetal acceleration.
 

Example 1: What is the centripetal force of a car of mass 20kg travelling on a circular path of radius 4m, with a velocity of 10m/sec?

Centripetal force, Fc = mass * centripetal acceleration

And, centripetal acceleration, ac = (velocity)2 / (radius) = v2/ r

This implies: Centripetal force, Fc = m * v2/ r

In the given question, mass of the car, m = 20kg

Radius, r = 4m and velocity of the car, v = 10m/sec

Therefore, centripetal force, Fc = 20 * (10)2/ 4 ==> Fc = 500N
 
 
Example 2: What is the centripetal force of an object of mass 15kg travelling on a circular path of radius 10m, with a velocity of 30m/sec?

Centripetal force, Fc = mass * centripetal acceleration

And, centripetal acceleration, ac = v2/ r

So we have, Centripetal force, Fc = m * v2/ r

In the given question, mass of the car, m = 15kg

Radius, r = 10m and velocity of the car, v = 30m/sec

Therefore, centripetal force, Fc = 15 * (30)2/ 10 ==> Fc = 1350N


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