Definition of Centripetal Force

 

Definition:

 

The force that causes an object to move along a curve (or a curved path) is called centripetal force.

 

 

Mathematical Expression:

 

We know that the magnitude of centripetal acceleration of a body in uniform circular motions is directly proportional to the square of velocity and inversely proportional to the radius of the path Therefore,

 

 

a(c) < v2 (Here <  represents the sign of proportionality do not write this in your examination and 2 represents square of v)

 

a(c) < 1/r

 

Combining both the equations:

 

a(c) < v2/r

 

From Newton’s Second Law of Motion:

 

F = ma

 

=>  F(c) = mv2/r

 

Where,

 

Fc = Centripetal Force

m = Mass of object

v = Velocity of object

 

r = Radius of the curved path

 

Factors on which Fc Depends:

 

Fc depends upon the following factors:

 

1. Increase in the mass increases Fc.
2. It increases with the square of velocity.
3. It decreases with the increase in radius of the curved path.

 

 

Examples:

 

1. The centripetal force required by natural planets To move constantly round a circle is provided by the gravitational force of The sun.

 

2. If a stone tied to a string is whirled in a circle, the required centripetal force is supplied to it by our hand. As a reaction the stone exerts an equal force which is felt by our hand.

 

3. The pilot while turning his airplane tiIts one wing in the upward direction so that the air pressure may provide the required suitable Fc.

 

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