Equations of Rotational Motion

As in linear motion, for a body having uniform angular acceleration, here derive the equations of motion.

Let consider a particle start rotating with angular velocity ω_o and angular acceleration α. At any instant t, let ω be the angular velocity of the particle and θ the angular displacement produced by the particle.

Therefore change in angular velocity in time; t = ω – ω_o

But, angular acceleration = change in angular velocity / change taken

So, α = (ω – ω_o)/t

Then, ω = ω_o + αt … … … (1)

The total angular displacement = average angular velocity*taken time

θ = ω_ot + ½ αt² … … … (2)

Equations (1) and (2) are the equations of rotational motion.