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 ωo 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 – ωo
But, angular acceleration = change in angular velocity / change taken
So, α = (ω – ωo)/t
Then, ω = ωo + αt … … … (1)
The total angular displacement = average angular velocity*taken time
θ = ωot + ½ αt2 … … … (2)
Equations (1) and (2) are the equations of rotational motion.