# Centripetal Acceleration and Centrifugal Acceleration: 5 Facts

In this article, the topic, “centripetal acceleration and centrifugal acceleration” with 5 important several matters will be summarize in a brief manner.

Centripetal acceleration can be explain as, it is a property of a body which is moved by a path in a circular way while centrifugal acceleration can be explain as, a property of a matter which is moved by a circular way and it is straight externally the path of the circle.

### Formula:-

The formula for the centrifugal acceleration is same as the centripetal acceleration. The formula for the centripetal acceleration and centrifugal acceleration is the product of tangential velocity squared and mass, which is divided by the radius that signifies that on doubling that tangential velocity, the centripetal acceleration and centrifugal acceleration will be quadrupled. Image – A body experiencing uniform circular motion requires a centripetal force, towards the axis as shown, to maintain its circular path; Image Credit – Wikipedia

Mathematically the expression for the centripetal acceleration and centrifugal acceleration can be written as,

F = mv2/r

Where,

F represents as, Centrifugal acceleration and unit use to measure is meters per second square.

m represents as, Mass of the matter and unit use to measure is kilogram.

v represents as, Speed or velocity of the product and unit use to measure is meters per second square.

r represents as, radius and unit use to measure is radians.

### Similarities in between the centripetal acceleration and centrifugal acceleration:-

The common things in between the centripetal acceleration and centrifugal acceleration are listed below,

• The both property of the centripetal acceleration and centrifugal acceleration are depend on the moving objects which are rotate in a circular path.
• When force is applied on an object from externally at that time centripetal acceleration and centrifugal acceleration is generated.

## Is centripetal acceleration and centrifugal acceleration same?

No, centripetal acceleration and centrifugal acceleration not the same term. Centripetal acceleration always points towards the center of the circle and centripetal acceleration is straight externally the path of the circle.

## When centripetal acceleration and centrifugal acceleration are same?

Centripetal acceleration and centrifugal acceleration are able to act at same time because to generate the centripetal acceleration centripetal force is required at the same time to generate the centrifugal acceleration centrifugal force is required, the both forces never can be acted at the same time on a moving object.

### Characteristics of Centripetal acceleration:-

The characteristics of the centripetal or radial acceleration are listed below,

1. The characteristics of the motion of the pendulum traversing a path in circular way, and centripetal acceleration always notified according to the center of the path in circular way.
2. The magnitude of the centripetal or radial acceleration can be express as,
1. The direction for the radial or centripetal acceleration is all time changes.
2. For, U.C.M. the magnitude of the centripetal or radial acceleration is unchanged.
3. The centripetal or radial acceleration is identified as a letter. S.I. unit to measure the centripetal or radial acceleration is meter per seconds square.
4. The centripetal or radial acceleration is always conducted towards the spot of the circular way along the radius.

## What is the relation between centripetal acceleration and centrifugal acceleration?

Centripetal acceleration constantly spotted along the spot of the circle, in this case the direction for the moving body all time changes and the velocity or speed constantly tangent to the circle while the centrifugal force is a imaginary force which is the matter is fell when it is rotate in a motion through a circular path.

Mathematically the expression for the centripetal acceleration and centrifugal acceleration can be written as,

ar = mv2/r

Where,

F represents as, Centrifugal acceleration and unit use to measure is meters per second square.

m represents as, Mass of the matter and unit use to measure is kilogram.

v represents as, Speed or velocity of the product and unit use to measure is meters per second square.

r represents as, radius and unit use to measure is radians.

### Formula derivation for the centripetal acceleration and radial acceleration:-

A substance name M is attached with a string and create to spin round about a particular permanent spot O which is denoted as centre of the spot. When the substance start to spin round fast the string that time it almost like radius of the circle. This signifies that a force is acted on the substance from the spot of the circle. For this reason an acceleration a0 is together with the direction of the radial. (Together with the radius of the circle nears the spot of the circle).

To determine this force, tension is generated towards the string in the direction of the opposite. This force for the tension is derive as, centripetal force.

For this reason the acceleration developed on the substance is called centripetal acceleration or radial acceleration and denoted as, ar . Performing the property for the similar triangles and we can write,

A and B both are almost close so we can derive this AB to the length of arc AB and the expression can be write as,

AB = v *dt

The figure (3) we can observe A and B almost same and the expression we can write as,

v + dv≅ dv

v *dt/r= dv/v

On rearranging,

dv/dt = v2/r

Thus,

dv/dt

Under the uniform circular motions the centripetal acceleration or radial acceleration is generated and we can write the formula for the centripetal acceleration or radial acceleration,

ar = v2/r Image – The velocity vectors at time t and time t + dt are moved from the orbit on the left to new positions where their tails coincide, on the right. Because the velocity is fixed in magnitude at v = r ω, the velocity vectors also sweep out a circular path at angular rate ω. As dt → 0, the acceleration vector a becomes perpendicular to v, which means it points toward the center of the orbit in the circle on the left. Angle ω dt is the very small angle between the two velocities and tends to zero as dt → 0; Image Credit – Wikipedia

## What is the difference between centripetal acceleration and centrifugal acceleration?

The major difference in between the centripetal acceleration and centrifugal acceleration are listed below,

## Problem:1

A ball which is made with iron material have mass 2 kilogram. The iron ball is connected with a string. When the external force is applied into the ball, in that case the ball start to move in circular motion which follows a circular way. The radius of the circle is 70 centimeter.

Now

Determine the centripetal acceleration if force is applied in every round for 4 seconds.

Determine the amount of force which is applied to the ball to generate centripetal acceleration.

Solution:-

Given data are,

Mass of the ball (m) = 2 kilogram

Radius (r) = 70 centimetre = 0.7 meter

So, the velocity for the path in which the ball is rate,

v = 1.09 meter per second

Now, we know the formula for centrifugal acceleration,

m/s2

When the centripetal acceleration is generated in that case centripetal force is applied.

The formula for the centripetal force is,

kilogram meter per second square

A ball which is made with iron material have mass 2 kilogram. The iron ball is connected with a string. When the external force is applied into the ball, in that case the ball start to move in circular motion which follows a circular way. The radius of the circle is 70 centimetre. Now

The centripetal acceleration if force is applied in every round for 4 seconds is 1.697 meter per second.

The amount of force which is applied to the ball to generate centripetal acceleration is 3.394 kilogram meter per seconds square.

## Problem:2

A toy which mass is 5 kilogram is attached with a string and spinning round in a circular way continuously. The height of the string with which the toy is connected is 2.2 meter and when the toy is spinning around 300 revolutions per minute.

Determine,

A. linear velocity of the toy.

B. Acceleration of the toy.

C. The force is applied upon the toy.

Solution:-

Given data are,

m = 5 kilogram

r = 2.2 meter

N = 300 revolutions per minute

We know that,

v = 69.08 meter per second

a = v2/r

a = 69.082/2.2

a = 2169 meter per second square.

Centripetal force,

F = ma

F = 5*2169

F = 10845 Newton

A toy which mass is 5 kilogram is attached with a string and spinning round in a circular way continuously. The height of the string with which the toy is connected is 2.2 meter and when the toy is spinning around 300 revolutions per minute.

A. linear velocity of the toy is 69.08 meter per second.

B. Acceleration of the toy is 2169 meter per seconds square.

C. The force is applied upon the toy is 10845 Newton.

#### Conclusion:

Centripetal is real and goes towards the spot of the circle. In the other hand centrifugal is imaginary and goes away from the enter.

Indrani Banerjee

Hi..I am Indrani Banerjee. I completed my bachelor's degree in mechanical engineering. I am an enthusiastic person and I am a person who is positive about every aspect of life. I like to read Books and listen to music. Let's connect through LinkedIn-https://www.linkedin.com/in/indrani-banerjee-2487b4214