A flywheel’s mean of maximum/minimum speeds is500 rpm, and maximum energy fluctuation is10000 N m. Other rotary inertias are negligible. Find inertia needed to limit maximum speed fluctuation to30 rpm, in kg m² (one decimal).
Coefficient of fluctuation Cs=(Nmax−Nmin)/Nmean=30/500=0.06. With ω=2π(500)/60, ΔE=Iω²Cs. Therefore I=10000/[ω²(0.06)]≈60.8 kg m². The30 rpm is the full difference, not a half-amplitude.
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