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Using the expression for power and K.E. of rotation motion, derive the relation τ = Iα.

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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

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