• WHAT ARE THE DERIVATIONS FOR :-
• w+w_o+alpha*t
• thita=w_o*t+1/2 alpha*t²
• w²-w_o ²=2 alpha*theta

Suppose a rigid body is rotating about a given axis with a uniform angular acceleration α.

At t = 0, ω = ω₀

At t= t, ω = ω

Integrating (i) within proper limits, we obtain

This is first rotational kinetic equation.

If ω is angular velocity of the rigid body at any time t, then

At t = 0, θ = 0

At t= t, θ= θ

∴ Integrating (ii) within proper limits, we obtain

This is second rotational kinematic equation.

We know that,

And,

Therefore,

=> ω dω = α dθ …. (iv)

When, θ = 0, ω = ω₀ and when θ = θ, ω = ω

∴ Integrating (iv) within proper limits, we obtain

This is third rotational kinetic equation.