I connect a DC motor to a flywheel with a given moment of inertia. I then supply that motor with a constant voltage and current for an infinite time interval. What do I need to know about my motor to predict the top angular speed of my flywheel? How do I calculate the top angular speed of the flywheel?


I read here that an unloaded motor will reach a terminal angular velocity when the back EMF rises to the same value as the applied voltage. This concept makes sense to me, but where in a motor's specifications can I find the constants in the equation for back EMF? $$E_b = \omega \phi k_b$$ Moreover, can that calculation be used to find the terminal angular velocity of a loaded motor?

  • $\begingroup$ Welcome to Physics Stack Exchange, Kevin. Please note that this is a site for students and researchers of physics. Users are expected to show some effort to work through the problem they are asking about. Please state what thoughts you have about the problem, or what you have found out eg using internet search. $\endgroup$ – sammy gerbil Jul 5 '16 at 6:23
  • $\begingroup$ @sammygerbil thank you for your comment. I added more information about my understanding of the problem. I hope it helps $\endgroup$ – Kevin K. Jul 5 '16 at 6:44
  • $\begingroup$ @JohnRennie I read that question and all of its answers. They seem to be specific to unloaded motors. My motor is loaded with a flywheel. $\endgroup$ – Kevin K. Jul 5 '16 at 6:46
  • $\begingroup$ Hi Kevin. In the absence of friction the flywheel will have no effect. It will slow the rate at which the motor reaches the top speed, but the top speed will be the same. $\endgroup$ – John Rennie Jul 5 '16 at 7:07
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    $\begingroup$ @JohnRennie Assuming a spherical flywheel in a vacuum. $\endgroup$ – Aron Jul 5 '16 at 7:30

Apart from friction in the load (which cannot be predicted), the flywheel does not make any difference to the maximum rotation speed reached by the motor. If there is no friction, then given sufficient time the motor can accelerate the flywheel up to its own maximum unloaded speed, however small the torque supplied by the motor. An even higher speed can be achieved for the flywheel if gears are used. It is not limited by the speed of the motor.

The above is the ideal case. In practice there will be some friction, which will increase with the size of the flywheel, and depends on how it is mounted. This can be measured but would be very difficult to predict. You can measure it by accelerating the flywheel using a dropped weight and timing how long it takes to stop.

$k_b$ is the back-emf constant of the motor. It is (I think) approximately equal to the torque constant $k_t$ for brushless dc motors. One or both should be in the specification.


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  • $\begingroup$ "the flywheel does not make any difference to the maximum rotation speed" I assume you mean that, after the flywheel reaches its tensile strength and explodes, the flywheel will no longer be a load on the motor. $\endgroup$ – Aron Jul 5 '16 at 7:29
  • $\begingroup$ Thank you for your answer. It sounds logical that a load may not effect top speed. Tomorrow, I will test this with an experiment. $\endgroup$ – Kevin K. Jul 5 '16 at 7:40
  • $\begingroup$ @Aron : No, I mean that when the flywheel is rotating at constant speed without friction, then it provides no load, since no torque is required to keep it rotating at constant speed. $\endgroup$ – sammy gerbil Jul 5 '16 at 7:42
  • $\begingroup$ @Aron Are you arguing that the flywheel's load does have an effect on the top speed? $\endgroup$ – Kevin K. Jul 5 '16 at 7:43
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    $\begingroup$ @Aron that's assuming the motor is even capable of reaching a speed where the flywheel could break. $\endgroup$ – LLlAMnYP Jul 5 '16 at 9:41

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