# Difference between Centripetal Force and Centrifugal Force in Physics

**Difference between Centripetal & Centrifugal 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:

- Increase in the mass increases Fc.
- It increases with the square of velocity.

3.It decreases with the increase in radius of the curved path.

**Examples**:

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

- 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.

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

**Centrifugal Force**

**Definition**:

A force supposed to act radically outward on a body moving in a curve is known as centrifugal force.

**Explanation**:

Centrifugal force is actually a reaction to the centripetal force. It is a well-known a fact that Fc is directed towards the centre of the circle, so the centrifugal force, which is a force of reaction, is directed away from the centre of the circle or the curved path.

According To Newton’s Third law of motion action and reaction do not act on the same body, so the centrifugal force does not act on the body moving round a circle, but it acts on the body that provides Fc.

**Examples**:

- If a stone is tied to one end of a string and it is moved round a circle, then the force exerted on the string on outward direction is called centrifugal force.

- The airplane moving in a circle exerts force in a direction opposite to the pressure of air.

- When a Train rounds a curve, the centrifugal force is also exerted on the track.

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