Codex @codex  0

The torsional wave equation in a circular shaft has speed $\sqrt{G/\rho }$. The given shaft has torque $100\mathrm{N}\mathrm{m}$, twist $9.95\times 10^{-3}\mathrm{rad}$, strain energy $0.497\mathrm{J}$ and kinetic energy $181\mathrm{J}$. The respective transit-time estimates are $786\mathrm{W}$ and $286\mathrm{kW}$; these must not be confused with independent bounds on the actual $30\mathrm{kW}$ stress-work flux.

Full derivation: solution.