# Equations of rotational motion and their derivation

We have the equations of motion for a linear(or translational) motion as:

For the rotational motion, we replace by , by , by and by in the above equations of motion. To know more about rotational motion, click here.

The equations of rotational motion become:

Here is the derivation of the rotational motion equation.

## equations of rotational motion

### 1] Proof of the first equation of rotational motion

Consider a rigid body moving with constant angular acceleration ‘‘ such that its angular velocity reaches ‘‘ from ‘‘ in time ‘‘ covering an angular displacement ‘‘.

Integrating the above equation with the corresponding limit.

### 2] Proof of second equation of rotational motion

Integrating the above equation with the corresponding limit.

### 3] Proof of third equation of rotational motion

We know, that angular acceleration is the rate of change of angular velocity. So,

Now,

Integrating within a corresponding limit,

These three equations can define the rotational motion of a rigid body.

Sharing is Caring