Question

Derive an expression for the centripetal acceleration for uniform circular motion.

Answer 1

The acceleration acting towards the centre in case of the circular motion is called as the Centripetal acceleration.

The direction of the centripetal acceleration is always towards the centre and along the Radius.

Answer 2

Answer:

The formula of centripetal acceleration is a = $\frac{v^{2} }{r}$

Explanation:

The rate at which tangential velocity changes is known as centripetal acceleration. Centripetal force is defined as the total force that accelerates an item in a circular motion.

A body is perpetually kept travelling along a curved path at the same speed by the centripetal force.

The centripetal force points in the direction of the centre and is parallel to the body's motion.

The force of a moving object can be written as

F = ma

Derivation:

From the below diagram

PQ + QS = PS

$-v_{1} + v_{2} =$Δ v

Δ v = $v_{2} - v_{1}$

Triangle PQS and AOB are similar.

Therefore,

Δ v/AB = $\frac{v}{r}$

AB = arc AB = Δ v t

Δ v/vΔ t = $\frac{v}{r}$

Δ v/Δ t = $\frac{v^{2} }{r}$

a = $\frac{v^{2} }{r}$

This is the formula of centripetal acceleration.

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