# what is centripetal acceleration derive an expression for it

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## Define centripetal acceleration. Derive an expression for the centripetal acceleration of a particle moving with uniform speed 'v' along a circular path of radius 'r'. Give the direction of this acceleration.

Click here👆to get an answer to your question ✍️ Define centripetal acceleration. Derive an expression for the centripetal acceleration of a particle moving with uniform speed 'v' along a circular path of radius 'r'. Give the direction of this acceleration.

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## Define centripetal acceleration. Derive an expression for the centripetal acceleration of a particle moving with uniform speed 'v' along a circular path of radius 'r'. Give the direction of this acceleration.

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Updated on : 2022-09-05

rate of change of tangential velocity is called as the centripetal acceleration.Solution Verified by Toppr F= r mv 2

centripetal acceleration is given by,

a c = m F = m r mv 2 ∴a c = r v 2

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## Derivation Of Centripetal Acceleration

The Derivation Of Centripetal Acceleration is provided here. Get the complete Centripetal Acceleration Derivation and learn the concept more efficiently by visiting BYJU'S

PhysicsDerivation of Physics FormulaDerivation Of Centripetal Acceleration

## Derivation of Centripetal Acceleration

Centripetal acceleration is the rate of change of tangential velocity. The net force causing the centripetal acceleration of an object in a circular motion is defined as centripetal force. The derivation of centripetal acceleration is very important for students who want to learn the concept in-depth. The direction of the centripetal force is towards the centre, which is perpendicular to the velocity of the body.

The centripetal acceleration derivation will help students to retain the concept for a longer period of time. The derivation of centripetal acceleration is given in a detailed manner so that students can understand the topic with ease.

The centripetal force keeps a body constantly moving with the same velocity in a curved path. The mathematical explanation of centripetal acceleration was first provided by Christian Huygens in the year 1659. The derivation of centripetal acceleration is provided below.

## Centripetal Acceleration Derivation

The force of a moving object can be written as

F=ma……. (1)

From the diagram given above, we can say that,

PQ→+QS→=PS→ –v1+v2=Δv Δv=v2–v1

The triangle PQS and AOB are similar. Therefore,

ΔvAB=vr AB=arcAB=vΔt ΔvvΔt=vr ΔvΔt=v2r a=v2r

Thus, we derive the formula of centripetal acceleration. Students can follow the steps given above to learn the derivation of centripetal acceleration.

**Read More:**Centripetal Acceleration

## Frequently Asked Questions – FAQs

### What do you mean by centripetal acceleration?

Centripetal acceleration is the rate of change of tangential velocity of a body moving in a circular motion. Its direction is always towards the centre of the circle.

### Give the formula for finding centripetal acceleration.

Let v be the magnitude of the velocity of the body

Let r be the radius of the circular path

Then centripetal acceleration,

a=v2/r

### Which force is responsible for producing centripetal acceleration?

Centripetal force is responsible for producing centripetal acceleration./div>

Is centripetal acceleration a constant or a variable vector?

### Is centripetal acceleration a constant or a variable vector?

Centripetal acceleration has a constant magnitude since both v and r are constant, but since the direction of v keeps on changing at each instant in a circular motion, hence centripetal acceleration’s direction also keeps on changing at each instant, always pointing towards the centre. Hence, centripetal acceleration is a variable vector.

### What is the unit of centripetal acceleration?

The unit of centripetal acceleration is ms-2

## From the video learn the concept of centripetal acceleration in detail

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## What is centripetal acceleration? Derive the expression for centripetal acceleration.

What is centripetal acceleration? Derive the expression for centripetal acceleration.. Ans: Hint: In circular motion centripetal force is perpendicular to velocity. Also if the particles decrease or increase their speeds in circular motion then accel...

## What is centripetal acceleration? Derive the expression for centripetal acceleration.

Last updated date: 13th Mar 2023

• Total views: 255k • Views today: 3.35k Answer Verified 255k+ views 3 likes

**Hint:**In circular motion centripetal force is perpendicular to velocity. Also if the particles decrease or increase their speeds in circular motion then acceleration is generated which deviates the net acceleration from pointing towards the centre.

**Formula used:**

a= v 2 r a=v2r

**Complete answer:**

We know that the motions are two types: one is straight motion and the circular motion. Then we know that circular motion, though the magnitude of velocity is a constant, the direction of velocity is changing. A circle. It is also defined as rotation of an object along a circular path. It can be of two forms, uniform circular motion, with constant angular rate of rotation and constant speed, or non-uniform circular motion with a changing rate of rotation.

Consider a body of mass

m m

moving along the circumference of a circle. the radius of a circle

r r with velocity v v

,as shown in the figure. Then if a small force

F F

is applied on the body, then we know that the force is given as

F=ma F=ma .

Where, a a

is the acceleration and is given as the rate of change of velocity

Δv Δv

with respect to time.

Consider the △OAB △OAB and △PQR △PQR , then Δv AB = v r ΔvAB=vr Clearly, AB=vΔt AB=vΔt ⟹ Δv vΔt = v r ⟹ΔvvΔt=vr ⟹ Δv Δt = v 2 r ⟹ΔvΔt=v2r ⟹a= v 2 r ⟹a=v2r

Thus, the acceleration due to centripetal force is given by,

a= v 2 r a=v2r

. Clearly as the velocity

v v and the radius r r

of the circle are constant, acceleration

a a

will also remain a constant.

**Note:**

Centripetal force is the force that acts on a body moving in a circular path and is directed towards the centre around which the body is moving. If the particles decrease or increase their speeds during the circular motion the net force deviates the particle from its initial path.

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