# How to calculate if a motor is fast AND strong (torque) enough?

I’m working on a prototype and I’m having trouble picking out a motor for that job. I need it to be able to move a rope that is about 2-4 mm thick outward (like a winch in reverse almost) and I also need it to be quick. Quick being about 0.025 mm per second. How would I determine this exactly? Unfortunately, math has never been my strong suit and while I have been looking over datasheets I’m not understanding them too well. What I’m asking is how do you determine if a motor has enough torque AND enough speed for an application.

• There is not enough data here to do the calculations. You would need to know the frictions to determine the maximum speed. 0.025mm per second seems very very slow. Are you sure your unit is right – joojaa Jun 27 '17 at 18:13
• Apart from the data for the calculations, what are you trying to accomplish? I am having trouble visualizing what you mean by a winch in reverse since without something pulling on the rope, you would basically be spewing it all over the place out of the reel/pulley. – Secundus Jun 28 '17 at 20:53

You can get some mileage out of the standard formula for mechanical power, which is $P=\tau\omega$. In other words, for a constant power motor, you can have high torque & low velocity, or low torque & high velocity. So, you can start by calculating the torque required to drive your load. Then, the angular velocity to move the rope at your desired rate of 250 microns/sec. It's straightforward to compute power from that, but don't forget to add a safety factor.