# Predicting top speed of a flywheel [duplicate]

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?

## marked as duplicate by John Rennie, ACuriousMind♦, user36790, Diracology, CuriousOneJul 6 '16 at 5:13

• 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. – sammy gerbil Jul 5 '16 at 6:23
• @sammygerbil thank you for your comment. I added more information about my understanding of the problem. I hope it helps – Kevin K. Jul 5 '16 at 6:44
• @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. – Kevin K. Jul 5 '16 at 6:46
• 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. – John Rennie Jul 5 '16 at 7:07
• @JohnRennie Assuming a spherical flywheel in a vacuum. – Aron Jul 5 '16 at 7:30

$k_b$ 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.