## Introduction

In this post, I will help you to understand how to calculate centripetal acceleration. I will solve a few problems that will help you understand the topic. When you go to the children’s park, you will see many spinning toys for kids like merry-go-rounds.

When you enter a merry-go-round, it will go around a circular path about an axis. its continuous movement would affect you by making you feel like you are being pushed outside. You are experiencing this outward push because the merry-go-round keeps changing direction in a circular path while your body wants to continue moving in a straight line.

Therefore, as the object keeps rotating. Centripetal force provides sufficient force to help your body continue moving around the circular path. Additionally, centripetal acceleration is directed toward the center of the circular path.

## What is Centripetal Acceleration?

**Definition of centripetal acceleration:** Centripetal acceleration is the type of acceleration that is directed toward the center of a circular path. The symbol for centripetal acceleration is a and is measured in meters per second square (ms^{-2}).

The formula for calculating centripetal acceleration is

a=v^{2}/r [where a = centripetal acceleration, v = speed, and r=radius of the circular path]

## Examples of How to Calculate Centripetal Acceleration

Here are a few solved examples that will help you understand Examples of how to calculate centripetal acceleration:

### Example 1

A mass of 15 kilograms is moving in a circular path of radius 3 meters with a uniform speed of 30 meters per second. Find the centripetal acceleration of the object.

**Solution**

**Data:**

Mass, m = 15 kg,

Radius, r = 3 m, and

Uniform speed, v = 30 m/s

Centripetal accelaration, a =?

We can apply the formula for centripetal acceleration that says a=v^{2}/r

Therefore, we can now substitute our data into the above formula

a=v^{2}/r = 30^{2}/3 = 900/3 = 300ms^{-2}

**Therefore, the centripetal acceleration of the body is 300 meters per second square (a=300ms ^{-2}).**

### Example 2

A bus is traveling at a speed of 70 meters per second and is making a turn with a radius of 100 meters. What is the magnitude of the bus’ centripetal acceleration?

**Solution**

**Data:**

Speed, v = 70 m/s,

Radius, r = 100 m,

Centripetal acceleration, a =?

Since the formula for centripetal acceleration says a=v^{2}/r

We can now say that

a=70^{2}/100 = 4,900/100 = 49ms^{-2}

**Hence, the centripetal acceleration of the bus is 49 meters per second square (a=49ms ^{-2})**

### Example 3

An airplane is flying in a circular path at a speed of 400 meters per second and a radius of 1000 meters. Find the centripetal acceleration of the airplane.

**Solution**

**Data:**

Speed, v = 400 m

Radius, r = 1000 m

Centripetal acceleration a=?

We can apply the formula a=v^{2}/r to solve the problem

Hence, substitute our data into the above formula

a=v^{2}/r = 400^{2}/1000

Thus

a = 160,000/1000 = 160ms^{-2}

**Therefore, the centripetal acceleration of the airplane is 160 meters per second square (160ms ^{-2})**

### Example 4

A roller coaster makes a turn of 40 meters and a speed of 20 meters per second. Determine the centripetal acceleration of the roller coaster.

**Solution**

**Data**

The radius of the roller coaster, r = 40 m

Speed, v = 20 m/s

Centripetal acceleration, a =?

and the formula for centripetal acceleration is a=v^{2}/r

After plugin our data into the above formula, we will get

a=v^{2}/r = 20^{2}/60 = 400/40 = 10 ms^{-2}

**Therefore, the centripetal acceleration of the roller coaster is 10 meters per second square (10 ms ^{-2}).**

**Reference**