Derivation of Centripetal Acceleration: Overview, Questions, Preparation

Centripetal acceleration has the path of motion in a circular form. An object that has acceleration and is moving in a circular motion is known as centripetal acceleration. We all see examples of centripetal acceleration in our daily routine. For example, the car and satellite orbiting around the earth. Both examples have centripetal acceleration.

The mathematical formula of centripetal acceleration was first discovered and written by the Physicist Christian Huygens in 1659. He stated that the object’s velocity changes every second, due to which the acceleration is measured in m/s. I can write the equation of the centripetal acceleration as:

Here, the centripetal acceleration is denoted as Ac,

Velocity is denoted as v,

Radius as r.

Centripetal force

The force directing the object’s tangential acceleration to the orbit’s center to move the object in a circular motion is the centripetal force.

Derivation of Centripetal Acceleration

We all know that the force of an object is written as:

F = ma

Let us consider a triangle PQS, sides of the triangle being -V1, V2, and Δv, respectively.

We can say that.

PQ + QS = PS

-v1 + v2 = Δv

We can write it as Δv = v2 -v1

Let us assume that the triangle PQS and AOB are similar to each other,

Δv / AB = v / r

AB = arc AB = V Δt

Δv / vΔt = v / r

Δv / Δt = v2 / r

This is the derivation of centripetal acceleration.

As per the new guidelines and pattern of 2021, the chapter of 'Rotational Motion' holds a significant weightage of 7 marks in total. However, it only includes 2 questions. It consists of one short question of 2 marks and one long question of 5 marks.

Example 1) Illustrate the formula of the centripetal acceleration.

Answer – The derivation of the centripetal acceleration can be written as a = v2 / r

Example 2) Write the equation of the force of a moving object.

Answer – the force of a moving object is F = ma, where F is the force of a moving object, m is the mass of the moving object, and a is the acceleration of the moving object.

Example 3) Write down the different forces that act on a moving car.

Answer – There are different types of forces that act on an accelerated car. But primarily, there are two frictional forces, kinetic frictional force and static frictional force.

Question 1) What do you mean by centripetal force?

Answer – The force directing the object’s tangential acceleration to the orbit’s center to move the object in a circular motion is the centripetal force.

Question 2) What is the reason behind centripetal force being equal to the weight?

Answer – The centripetal is universally equal to the weight. There is no specific reason, but it could be due to the tension of the string attached to the ball, which makes it strong.

Question 3) What is the cause of centripetal acceleration?

Answer – the primary cause of centripetal acceleration is the gravitational force between the objects attracting each other.

Question 4) What is the name of the force that causes centripetal acceleration?

Answer – The frictional force is responsible for the centripetal acceleration.

Question 5) What is centripetal acceleration?

Answer - Centripetal acceleration is the path of motion in a circular form. An object that has acceleration and is moving in a circular motion is known as centripetal acceleration.