**The main distinction between linear and angular acceleration is that linear acceleration refers to the time rate of change of linear velocity, while angular acceleration refers to the time rate of change of angular velocity.**

## Linear acceleration:

Simply said, the linear acceleration represents variations in the object’s linear velocity with respect to time. Mathematically it is expressed as,

**a =** `\mathbf{\frac{dv}{dt}}`

The linear acceleration is generally denoted by the symbol ‘a’ and expressed as m/s² or ft/s².

The above figure shows the vehicle moving in a straight line, accelerating from `V_{1}` = 11 m/s to `V_{2}` = 17 m/s in a time interval of 10 seconds. Thus, in this case, the average linear acceleration in the car is given by,

a = `\frac{\Delta V}{\Delta t}`

a = `\frac{V_{2}-V_{1}}{t_{12}}`

a = `\frac{17-11}{10}`

**a = 0.6 m/s²**

## Angular acceleration:

In a rotational motion, the angular acceleration indicates the time rate of change of angular velocity (ω). It is generally denoted by the symbol ‘α’ and is given by,

**α = **`\mathbf{\frac{d\omega}{dt}}`

As shown in the above figure, the object translating in a circular path possesses both tangential (linear) acceleration and rotational acceleration. In such a case, the **relation between them is given by**,

**a = r α**

Where ‘r’ indicates the radius of rotation.

## Difference between Linear and Angular acceleration:

Sr. No. | Linear acceleration | Angular acceleration |
---|---|---|

1 | It indicates the time rate of change of linear velocity. | It indicates the time rate of change of angular velocity. |

2 | It is used in a translational motion. | It is used in an angular motion. |

3 | It is denoted by the symbol ‘a’. | The symbol used for the angular acceleration is ‘α’. |

4 | It has an SI unit of m/s². | It has an SI unit of rad/s². |

5 | It is given by, a = `\frac{dv}{dt}`. | It is given by, α = `\frac{dw}{dt}`. |

6 | The linear acceleration causes a change in translational velocity. | The angular acceleration causes a change in angular velocity. |

7 | Example: A car moving on a straight road possesses linear acceleration. | Example: Rotating wheel of the car possesses angular acceleration. |

## FAQ:

How angular acceleration and linear acceleration are related?

The relation between the linear acceleration (a) and the angular acceleration (α) is given by,

a = radius of rotation x α

**Related differences:**