# 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.

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