# Linear and Angular acceleration- Difference, Relation

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.

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## 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.

## 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: Pratik is a Graduated Mechanical engineer. He enjoys sharing the engineering knowledge learned by him with people.