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.

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.

Linear acceleration in a car

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}}`

Angular acceleration in object

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 accelerationAngular acceleration
1It indicates the time rate of change of linear velocity.It indicates the time rate of change of angular velocity.
2It is used in a translational motion.It is used in an angular motion.
3It is denoted by the symbol ‘a’.The symbol used for the angular acceleration is ‘α’.
4It has an SI unit of m/s².It has an SI unit of rad/s².
5It is given by,
a = `\frac{dv}{dt}`.
It is given by,
α = `\frac{dw}{dt}`.
6The linear acceleration causes a change in translational velocity.The angular acceleration causes a change in angular velocity.
7Example: A car moving on a straight road possesses linear acceleration.Example: Rotating wheel of the car possesses angular acceleration.
The above table indicates the difference between linear acceleration and 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:

Angular and Centripetal accelerationCentripetal and Tangential acceleration

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

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