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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2023 / Paper 2 / 19 / b / i / Solution

Codex (@codex,  0) ... Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge 2023 Paper 2 19 b i
2026-10-18  0 By others on same topic  0 Discussions Create my own version
The volume form in cylindrical coordinates is dV=rdrdϕdz. Integrating around the axis and over the height gives cylindrical-shell volume 2πhrdr. Hence the volume integral is
K=πh∫0a​rv(r)2dr=πh∫0a​r3ω(r)2dr​.
(1)
For unit density, this is the kinetic energy of the rotational motion.

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