How Can A High-Torque Motor Have Low a low RPM

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Torque is the rotational force that influences a motor's performance, with high torque allowing for acceleration but potentially resulting in lower RPMs. A denser coil in a DC motor increases torque while decreasing RPM, whereas a looser coil enhances RPM but reduces torque. The motor's speed stabilizes due to losses that increase with speed, which are related to the mass being spun and the torque applied. Additionally, back electromotive force (emf) rises at higher RPMs, counteracting torque. Ultimately, the relationship between RPM and torque is heavily influenced by the load connected to the motor.
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Torque is the rotational force.
If there is more force, how can the motor be slow?

I'm building a DC motor and read that given a constant amount of coil, creating a very dense coil will increase torque but lower RPMs.
Conversely, making it looser (bigger radius) increases RPM but lowers torque.
 
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The torque gives you acceleration - but it is possible to accelerate to any speed... however slow.

For your motor - it will accelerate to a constant speed due to losses that are proportional to speed. This will be proportional to the amount of mass that has to be spun - and so is the torque.
 
The increase in torque at lower rpm is offset by increase in back emf at higher rpm, which decreases the torque at higher rpm.
 
Motors are connected to loads. The load determines the ratio between RPM and torque. If a "high torque" motor is not connected to a load and is just allowed to freewheel, it does not produce any torque.
 
I built a device designed to brake angular velocity which seems to work based on below, i used a flexible shaft that could bow up and down so i could visually see what was happening for the prototypes. If you spin two wheels in opposite directions each with a magnitude of angular momentum L on a rigid shaft (equal magnitude opposite directions), then rotate the shaft at 90 degrees to the momentum vectors at constant angular velocity omega, then the resulting torques oppose each other...

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