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Prove that ki...

Question

Prove that kinetic energy = $1 / 2 I_{P} ω^{2}$

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Solution

If $m$ is the mass of the disc.
Then,
Kinetic Energy $= \frac{1}{2} {m v}^{2} = \frac{1}{2} {m w}^{2} R^{2} = \frac{1}{2} {m R}^{2} \times w^{2} = \frac{1}{2} I_{p} w^{2} [M . I . I_{p} = {m R}^{2}]$

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