# Centripetal and Centrifugal Force

Force is required to make an object move, and force acts differently on objects depending on the type of motion it exhibits. In the case of curvilinear motion, a special force comes into the picture, i.e., centripetal force – literally meaning “centre seeking.” Centripetal force is the force acting towards the centre of the circular path. In this article, let us discuss what centripetal force is and how it is different from centrifugal force.

## Defining Centripetal Force

According to the centripetal force definition,

Centripetal force is the force acting on an object in curvilinear motion directed towards the axis of rotation or centre of curvature.

The unit of centripetal force is newton.

The centripetal force is always directed perpendicular to the direction of the object’s displacement. Using Newton’s second law of motion, it is found that the centripetal force of an object moving in a circular path always acts towards the centre of the circle.

### Calculating Centripetal Force

The Centripetal Force Formula is given as the product of mass (in kg) and tangential velocity (in meters per second) squared, divided by the radius (in meters) that implies that on doubling the tangential velocity, the centripetal force will be quadrupled. Mathematically it is written as:

 $$\begin{array}{l}F=\frac{mv^{2}}{r}\end{array}$$

Where, F is the Centripetal force, m is the mass of the object, v is the speed or velocity of the object and r is the radius.

### Centripetal Force Examples in Daily Life

The centripetal force pulls or pushes an object towards the centre of a circle as it travels, causing angular or circular motion.

• When spinning a ball on a string or twirling a lasso, the force of tension on the rope pulls the object towards the centre.
• The centripetal force is provided by the frictional force between the ground and the wheels when turning a car.
• When going through a loop on a roller coaster, the force is provided by the normal force as the seat or wall pushes you towards the centre.
• For the planets orbiting around the Sun, the centripetal force is provided by Gravity.

## What Is Centrifugal Force?

Centrifugal force is a pseudo force in a circular motion which acts along the radius and is directed away from the centre of the circle. The force does not exist when measurements are made in an inertial frame of reference. It only comes into play when changing our reference frame from a ground/inertial to a rotating reference frame.

The centrifugal force’s unit is newton.

### Calculating Centrifugal Force

A centrifugal force basically uses the centripetal force formula (which describes a real phenomenon) and reverses the direction of the force, to describe the fictitious centrifugal force.

 $$\begin{array}{l}F=-\frac{mv^{2}}{r}\end{array}$$

Where, F is the Centrifugal force, m is the mass of the object, v is the speed or velocity of the object and r is the radius.

### Centrifugal Force Examples in Daily Life

Centrifugal Force acts on every object moving in a circular path when viewed from a rotating frame of reference. Some examples of Centrifugal Force are given below.

• Weight of an object at the poles and on the equator
• A bike making a turn.
• Vehicle driving around a curve
• Equatorial railway

## Centripetal Force vs Centrifugal Force

Check the table below to learn the detailed comparison between Centripetal and Centrifugal Force

Differences Between Centripetal And Centrifugal Force
Centripetal Force
Centrifugal Force
Centripetal force is the component of force acting on an object in curvilinear motion which is directed towards the axis of rotation or centre of curvature. Centrifugal force is a pseudo force in a circular motion which acts along the radius and is directed away from the centre of the circle.
It is observed from an inertial frame of reference. It is observed from a non-inertial frame of reference.
If a car is travelling through a curve on a circular horizontal road, the centripetal force provided by the force of friction between the tyres of the vehicle and the road surface allows the car to negotiate the turn. When a car in motion takes a sudden turn towards the left, passengers in a car experience an outward push. This is due to the centrifugal force acting on passengers.

## Frequently Asked Questions – FAQs

Q1

### What is centripetal force?

Centripetal force is the component of force acting on an object in curvilinear motion which is directed towards the axis of rotation or centre of curvature.
Q2

### Give examples of centripetal force.

The revolution of the moon around the earth and the spinning of the top are some examples of centripetal force.
Q3

### Does centripetal force increase with speed?

Yes! The expression for centripetal force is given by mv2/R. This suggests as the speed of the particle increases, so does the centripetal force experienced by it.
Q4

### Does centripetal force increase with radius?

No! The expression for centripetal force is given by mv2/R. This suggests as the radius of the turn of the particle increases, the centripetal force experienced by it decreases.
Q5

### Compare centrifugal force and centripetal force.

Centripetal force is observed from an inertial frame of reference, while centrifugal force is observed from a non-inertial frame of reference. Centripetal force is directed towards the axis of rotation or centre of curvature, and centrifugal force is directed away from the centre of the circle.

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Test Your Knowledge On Centripetal And Centrifugal Force!

1. What force applies to the planets that are revolving around sun. Centrifugal or centripetal ?

• The centripetal force keeps the planets in orbit around the sun.

The sun’s gravity pulls on the planets just as Earth’s gravity that pulls down anything that is not held by up by some other force. All the planets would like to move in a straight line with constant speed, however, the sun’s gravity prevents it from doing so. Heavier object exerts stronger gravitational pull than the lighter ones, so the heavyweight in our solar system, the sun, exerts the stronger gravitational pull.

Now you might think if the sun is pulling the planet then why don’t they just fall into the sun and burn? Well, in addition to falling towards the sun, the planets are moving sideways too. Without the sideways motion, the planets would fall to the centre of the sun and without the pull toward the centre, it would go flying off in a straight line.

• centripetal force

2. Cycle wheel rotation is example for centrifugal or centripetal force ?

• Neither in itself. But an object attached to the rim of the wheel will experience a centripetal force preventing it being thrown off as the wheel rotates. Centripetal and centrifugal force is equal and opposite but the latter does not actually exist unless a centripetal force is being applied by a retaining cord or gravity or containing rim outside the object.