A flywheel has moment of inertia 0.800 kg m² and rotates at 30.0 rad s⁻¹. A brake pad applies a constant tangential force of 12.0 N at radius 0.250 m until it stops. Determine torque, angular deceleration, stopping time, angle turned and thermal energy produced. If the measured stopping time is 9.0 s instead, infer the average additional resisting torque and discuss whether constant total torque is justified by one timing measurement.

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Brake torque = 3.00 N m; α = −3.75 rad s⁻²; stop time = 8.00 s; angle = 120 rad; thermal energy = 360 J. A 9.0 s stop implies total torque 2.67 N m, so another effect averages +0.333 N m in the direction of rotation. The brake torque magnitude is τ = rF = (0.250)(12.0) = 3.00 N m, opposite the angular velocity. Using τ = Iα gives α = −3.00/0.800 = −3.75 rad s⁻². Constant α gives stopping time t = (0−30.0)/(−3.75) = 8.00 s. Angular displacement is the average angular speed times time: θ = (30.0+0)t/2 = 120 rad. Initial rotational energy ½Iω² = ½(0.800)(30.0)² = 360 J becomes thermal energy. It also equals τθ = (3.00)(120) J. A 9.0 s stop corresponds to α_avg = −3.33 rad s⁻² and τ_total,avg = −2.67 N m, 0.333 N m less opposing than the nominal pad torque. One elapsed time determines only an average; angular-speed data throughout the stop are needed to test torque constancy.

Brake a rotating flywheel

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