 Solution

ID: past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2018/paper-1/section-c/c12/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}

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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