A rotor starts from rest and reaches 32 rad s⁻¹ in 5.2 s with constant angular acceleration. A motor supplies constant torque 0.42 N m and a constant resistive torque 0.052 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 = 6.154 rad s⁻²; I = 0.0598 kg m²; motor work 34.94 J; dissipated energy 4.326 J; final kinetic energy 30.62 J. Constant angular acceleration gives α = Δω/Δt = 6.154 rad s⁻². The relevant dynamical torque is the motor torque minus the opposing resistive torque. Using τ_net = Iα gives I = (0.42 − 0.052)/6.154 = 0.0598 kg m². Ignoring resistance would overestimate this inertia. The angle turned is θ = ½ω_final t = 83.2 rad. Motor work is τ_motor θ = 34.94 J and dissipated energy is τ_resistive θ = 4.326 J. Their difference is 30.62 J, equal to ½Iω_final² = 30.62 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 6

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