The object under motion can undergo a change in its speed. The measure of the rate of change in its speed along with direction with respect to time is called acceleration. The motion of the object can be linear or circular. Thus, the acceleration involved in linear motion is called linear acceleration. The acceleration involved in a circular motion is called angular acceleration.

Table of Contents |

## Introduction

If we recall circular motion, here distance covered will be along the curved path (circumference of a circle). The velocity involved is angular velocity and not linear velocity. Similarly, the acceleration involved is centripetal acceleration. Some important terms involved are-

Terms |
Definition |
Symbol |
Formula |
Units |

## Angular displacement |
The angular difference between the initial and final position of an object. | 𝜃 | \(\begin{array}{l}\theta =\frac{s}{r}\end{array} \) |
Radian |

## Angular velocity |
The rate of change of angular displacement with respect to time. | ⍵ | \(\begin{array}{l}\omega =\frac{d\theta }{dt}\end{array} \) |
radian/sec |

## Angular acceleration |
The rate of change of angular velocity with respect to time. | 𝛼 | \(\begin{array}{l}\alpha =\frac{d\omega }{dt}\end{array} \) |
radian/sec^{2} |

In a circular motion, the acceleration experienced by the body towards the centre is called the centripetal acceleration. This can be resolved into two-component. A radial component and a tangential component depend upon the type of motion.

## Radial Acceleration Definition

In a uniform circular motion, “the acceleration of the object is along the radius, directed towards the centre” is called radial acceleration.

## Radial Acceleration Formula

*figure(1) schematic diagram representing an object under rotational motion*

An object A is tied to a string and made to rotate about a fixed point O (centre) (see figure(1)). The object when rotated fast, the string (OA) looks almost like the radius of the circle, which implies that a force is exerted on the object from the centre, thereby an acceleration a_{0} along the radial direction (along the radius of the circle towards the centre). To counter this force, tension is developed along the string in the opposite direction. This force due to tension is called centripetal force, thus the acceleration generated on the object is called centripetal acceleration or radial acceleration a_{r}.

*figure(2) Positions of two objects A and B. They are infinitesimally close. *

*figure(3) The equivalent diagram of the centripetal velocity vector A and B.*

Implementing the property of similar triangles we get-

Since A and B are infinitesimally close, we can approximate AB to the length of arc AB.

From figure(3) since A and B are very close,

On rearranging,

Thus,

\(\begin{array}{l}a_{r}=\frac{v^{2}}{r}\end{array} \) |

## Tangential Component

The tangential component is defined as the component of angular acceleration tangential to the circular path. The unit of measurement is m.s^{-2}. The mathematical representation is given as:

- a
_{t}is the tangential component - t is the time period
- v
_{1}and v_{2}are the respective velocities of the two objects in a circular motion

## Radial Acceleration units

Radial Acceleration has the unit same as that of angular acceleration is radian/sec^{2}

**Physics Related Topics:**

## Understand uniform circular motion with the help of real-life examples.

## Frequently Asked Questions – FAQs

### What is acceleration?

### What are the main types of acceleration?

### What is linear acceleration?

### What is circular acceleration?

### What is radial acceleration?

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IS THERE ANY DIFFERENCE between radial acc. and angular acc. ?

Angular acceleration applies to the whole rigid object. However, centripetal acceleration is for a specific radius.