<p>Flywheels are large, massive wheels used to store energy. They can be spun up

Question

<p>Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 kg. A motor spins up the flywheel with a constant torque of 50 N . m. How long does it take the flywheel to reach top angular speed of 1200 rpm?</p>

Explanation / Answer

First, find the angular acceleration of the disk: t = Ia a = t / I The moment of inertia for a solid disk is mr²/2, so: a = t / mr²/2 = 2t / mr² = 2(50N•m) / (250kg)(0.75m)² = 0.71rad/s² Then, the time may be found from the rotational kinematics: ? = ?0 + at-------------------->?0 = 0 t = ?/a The units between angular velocity and angular acceleration need to be the same, so change 1200rpm to rad/s: 1200rpm = 1200rev/min(2prad/1.0rev)(1.0min/60s) = 130rad/s Therefore: t = 130rad/s / 0.71rad/s² = 180s (3.0min)

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