Predicting top speed of a flywheel 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?
EDIT:
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?
 A: 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.
https://electronics.stackexchange.com/questions/110557/calculating-back-emf-from-torque-constant
https://electronics.stackexchange.com/questions/43066/how-to-improve-torque-and-rpm-of-a-dc-motor/43099#43099
http://www.gearseds.com/files/Lesson3_Mathematical%20Models%20of%20Motors.pdf
