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# Centripetal Force- Introduction, Explanation & Application

### Key Concepts

• Centripetal force
• Tangential velocity
• Centripetal acceleration

## Introduction:

In this session we are going to read more about centripetal force, which is one of the forces of uniform circular motion and deduce the relation between centripetal force and acceleration.

### Explanation:

#### Centripetal force:

A force is required to maintain circular motion. Any force that causes an object to follow a circular path is called a centripetal force. Centripetal means “center-seeking.”

Newton’s Second Law says that if an object is accelerating, there must be a net force on it. For an object moving in a circle, this is called the centripetal force. The centripetal force points toward the center of the circular path.

Its unit is Newton (N).

Velocity vector is tangential to the direction of the motion of the object and the centripetal force is directed inwards as it is a “center-seeking” force.

#### Centripetal force:

It depends on the:

1. Object’s mass
1. Object’s speed
1. Distance between the object and the axis point

Such that:

#### Centripetal Acceleration

It depends on the:

1. The speed of the object.

It is denoted by ‘ac’ and its unit is m/s2.

The relation between acceleration, radius and speed are:

#### Application of Centripetal force:

A few of the application of centripetal force are:

1. Gravitational force that holds the moon in its orbit is a centripetal force.

b. Electrical forces holding the electrons in orbit around the nucleus are centripetal forces.

c. When a car takes a turn, the force that keeps it in its curved path is centripetal force.

d. When a ball is swirled around a string, the force that keeps it swirling in the circular path is called a centripetal force.

e. When going through a loop on a giant wheel the force experienced is called as a centripetal force.

Question 1: Draw the direction of motion if the object is released from its orbit at point 1 and 2.

For object 1 it will go in horizontal direction towards the right.

For object 2 it will go vertically down.

Question 2: The motion of a boy of weight 40 Kg in a merry-go-round of the radius 20 m and the speed of the boy around the merry go round is 40 m/s. What is the centripetal force and centripetal acceleration experienced by the system?

Velocity = 40m/s

ac  =

v2rv2r

=

4022040220 =

40 × 402040 × 4020 = 80m/s2

Mass of boy = 40kg

Fc =

mv2rmv2r

= 40(80)

= 3200N

### Summary

• Any force that causes an object to follow a circular path is called a centripetal force.
• It is pointed inwards.
• Centripetal force depends upon mass, velocity and radius.

Fc = Mv2/R

• Centripetal acceleration depends upon velocity and radius.

ac=v2/r

• A few of the applications where this is used is:
• When a car takes a turn on a curved path
• Gravitational force that holds the celestial bodies in its orbit ·
• When a ball is swirled around a string
• Electrical forces holding the electrons in its path

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