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I'm trying to make a rock tumbler. The 12V DC motor I have is rated for 1000rpm. Can I run it at lower rpm without harming the motor? I'm planning to use an Arduino and motor controller for the project.

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Running the motor slower is OK. The main limitation of how a motor is run is due to the heat it produces. This heat is from the DC resistance of the windings carrying current.

The heat is therefore proportional to the square of the current. Since the motor torque is proportional to the current, you must be running the motor at a lower current to get the slower speed.

The above assumes that the mechanical load on the motor is no greater at the lower speed than at full speed. The motor must also be able to generate enough torque to get moving from a standstill. If it isn't allowed to move, and full voltae is applied, it can get too hot.

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