Project ForgeThe turning moment diagram of a flywheel fitted to an engine shows moment 1500 N·m from θ=0 to π/2, 3000 N·m from π/2 to π, 1000 N·m from π to 3π/2, and 2500 N·m from 3π/2 to 2π (angle in radians). The mean turning moment is 2000 N·m. The average engine speed is 1000 rpm. For fluctuation in speed to be within ±2% of the average speed, the mass moment of inertia of the flywheel is __________ kg.m².
Explanation
Tracking cumulative energy above/below the mean (2000 N·m) through each π/2 segment: at θ=π/2, cumulative=−500×(π/2)=−250π; at θ=π, cumulative=−250π+1000×(π/2)=+250π; at θ=3π/2, cumulative=250π−1000×(π/2)=−250π; back to 0 at θ=2π. Max−min swing = 250π−(−250π)=500π≈1570.8 J. Cs=0.04, ωmean=2π×1000/60≈104.72 rad/s. I=ΔE/(ωmean²×Cs)=1570.8/(10967×0.04)≈3.58 kg·m².
Source: GATE ME 2020 Session 2 (ME-2) (2020)
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