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 Incoming links: Tangent-axis inertia of a spherical shell

Past exam of the physics B course of the University of Cambridge / 2013 / Paper 1 / Section A / A5 / Solution 2026-10-20

For the tangent-axis inertia of a spherical shell, subtract the missing solid core from a solid sphere:

M = \frac{4 π ρ}{3} (R_{2}^{3} - R_{1}^{3}), I_{c} = \frac{8 π ρ}{15} (R_{2}^{5} - R_{1}^{5}) .

The parallel axis theorem shifts the axis a distance

R_{2}

:

I_{tangent} = \frac{8 π ρ}{15} (R_{2}^{5} - R_{1}^{5}) + \frac{4 π ρ}{3} (R_{2}^{3} - R_{1}^{3}) R_{2}^{2} .

It tends to

7 M R_{2}^{2} /5

for a solid sphere and

5 M R_{2}^{2} /3

for a thin spherical shell.

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