We know that power is Given by
P = τω …(1)
Also we know that,
K.E. = \(\frac{1}{2} Iω^2\) …(2)
As P = rate of change of energy
= rate of change of K.E.
= \(\frac{d}{dt}\)(\(\frac{1}{2} Iω^2\))
= \(\frac{1}{2}\times I \times 2ω\frac{dω}{dt}\)
= Iωα (∵ \(\frac{dω}{dt}\) = α)…(3)
∴ From equation (1) and (3), we get
τω = Iωα
τ = Iα