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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. Its maximum angular velocity is 1200 rpm.

Q: A motor spins up the flywheel with a constant torque of 50 {\rm N \cdot m}. How long does it take the flywheel to reach top speed? In units of seconds.

  • Physics -

    Torque = (moment of inertia) x (angular acceleration) = 50 N*m

    The moment of inertia is
    I = (1/2) M*R^2 = 281.25 kg*m^2

    The maximum angular velocity you want to achieve is
    w = 1200 rev/min * (2 pi/60) = 125.66 rad/s

    The angular acceleration rate is
    alpha = 125.66 rad/s / t
    where t is the time required.

    alpha = 50/281.25 rad/s^2 = 125.66/t

    Solve for t in seconds

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