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 acc

Question

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.
How long does it take the flywheel to reach top angular speed of 1200 rpm?

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Thiên Ân 5 years 2021-08-13T13:47:37+00:00 1 Answers 65 views 0

Answers ( )

  1. giabao
    0
    2021-08-13T13:49:07+00:00
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    Answer:

    t = 2.95 min

    Explanation:

    Given that,

    The diameter of flywheeel, d = 1.5 m

    Mass of flywheel, m = 250 kg

    Initial angular velocity is 0

    Final angular velocity, \omega_f=1200\ rpm = 126\ rad/s

    We need to find the time taken by the flywheel to each a speed of 1200 rpm if it starts from rest.

    Firstly, we will find the angular acceleration of the flywheel.

    The moment of inertia of the flywheel,

    I=\dfrac{1}{2}mr^2\\\\I=\dfrac{1}{2}\times 250\times (0.75)^2\\\\I=70.31\ kg-m^2

    Now,

    Let the torque is 50 N-m. So,

    \alpha =\dfrac{\tau}{I}\\\\\alpha =\dfrac{50}{70.31}\\\\\alpha =0.711\ rad/s^2

    So,

    t=\dfrac{\omega_f-\omega_i}{\alpha }\\\\t=\dfrac{126-0}{0.711}\\\\t=177.21\ s

    or

    t = 2.95 min

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