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This will probably sound like a silly question, but here goes....

Let's say I have an actuator, with a torque rating of 1 Nm. I then connect it to a wheel, which starts rotating at a constant speed. From Newton's second law, I know that Net Force = Mass * Acceleration, or in this case, Net Torque = Mass * Angular Acceleration. Given the input torque of 1 Nm, this would mean that the wheel would have a net torque of 1 Nm applied to it. Therefore, the wheel should experience an acceleration of 1 Nm/mass. However, the wheel doesn't keep on accelerating -- it just rotates at a constant speed. So why doesn't the wheel accelerate, when the actuator is applying a fixed torque?

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  • $\begingroup$ Are you trying to understand the theory behind an actual device? $\endgroup$
    – Wasabi
    Jun 9 '16 at 17:51
  • $\begingroup$ Well I'm trying to relate Newton's second law to the real-world behaviour of an actuator. It doesn't make sense to me to say that an actuator applies a torque of 1 Nm, but then the device it is connected to just rotates at a constant speed... $\endgroup$ Jun 9 '16 at 17:54
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    $\begingroup$ The constant acceleration assumes no friction, while in the real world you do have friction, which often a function of velocity. $\endgroup$
    – fibonatic
    Jun 9 '16 at 18:53
  • $\begingroup$ Also worth noting acceleration of rotation is dependent on moment of inertia not mass per see even a small mass gan have a huge inertia if far away from the center. $\endgroup$
    – joojaa
    Jun 10 '16 at 9:50
  • $\begingroup$ Net Torque = Mass * Angular Acceleration can't be true. It's not homogeneous. Torque = moment of inertia * Angular Acceleration. $\endgroup$
    – Jacen
    Jun 10 '16 at 12:23
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There are two things going on.

First, even if this "actuator" can produce constant torque, the torque required to keep the load spinning will be at least in part a function of the spinning speed. There will be some friction and other forces that increase with increased speed. Viscous friction increases linearly with speed, and other effects, like air resistance, increase even more strongly with speed. Therefore, even with constant torque, eventually the friction forces rise to exactly oppose the torque and the object no longer speeds up.

Second, your "actuator" probably can't supply constant torque, even over its rated speed range. For a electric motor, for example, torque decreases with speed at a fixed applied voltage. The motor has a finite unloaded speed that is mostly proportional to applied voltage. That is the speed at which it's externally available mechanical torque drops to 0.

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The torque rating for the actuator depends on the speed it's running at - as it approaches its "top speed" it can't deliver the full rated torque.

The reasons depend a lot on the actuator type. For example with a DC electric motor the coil induces a back-EMF at higher speeds causing a tail off on the torque curve. For other actuator types there will be other losses which affect their performance. (All in addition to friction in bearings, etc.)

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The torque rating of the motor is basically the maximum torque that the motor can generate, generally at standstill(ie. 0rpm).the performance characteristics of a dc motor would look like this enter image description here.

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