A rotor starts from rest and reaches 36 rad s⁻¹ in 5.6 s with constant angular acceleration. A motor supplies constant torque 0.46 N m and a constant resistive torque 0.056 N m opposes rotation. (a) Determine angular acceleration and rotor moment of inertia. (b) Calculate motor work, energy dissipated, and final rotational kinetic energy. (c) Explain how a coast-down measurement with the motor disconnected could independently check the inertia, assuming the same resistive torque.

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α = 6.429 rad s⁻²; I = 0.06284 kg m²; motor work 46.37 J; dissipated energy 5.645 J; final kinetic energy 40.72 J. Constant angular acceleration gives α = Δω/Δt = 6.429 rad s⁻². The relevant dynamical torque is the motor torque minus the opposing resistive torque. Using τ_net = Iα gives I = (0.46 − 0.056)/6.429 = 0.06284 kg m². Ignoring resistance would overestimate this inertia. The angle turned is θ = ½ω_final t = 100.8 rad. Motor work is τ_motor θ = 46.37 J and dissipated energy is τ_resistive θ = 5.645 J. Their difference is 40.72 J, equal to ½Iω_final² = 40.72 J. This independently checks the rotational work-energy calculation. Disconnect the motor and measure the angular deceleration while the rotor coasts. If the resistive torque is unchanged, I = τ_resistive/|α_coast|; compare this estimate with the acceleration result and repeat measurements to assess uncertainty.

Determine a rotor's inertia and energy · set 8

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