Past exam of the physics B course of the University of Cambridge / 2018 / Paper 1 / Section C / C12 / c

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- Solution c

Solution

For the uniform solid cylinder, the axial moment of inertia is

I_{z} = \int r^{2} d m = ρ L J_{p} = (8000) (3.0) (4.021 \times 1 0^{- 6}) ≃ 0.0965 kg m^{2} .

The rotational kinetic energy at

Ω = 300 rad s^{- 1}

is

K = \frac{1}{2} I_{z} Ω^{2} ≃ 4.34 \times 1 0^{3} J .

This includes the shaft's bulk steady rotation; the small twist does not appreciably alter its mass moment at this order.

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