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I know that when a motor runs it generates torque and that torque can be used to do useful work. On the other hand, the motor needs strong support that absorbs the reaction torque. In our case let us assume that that support is provided by a workshop floor on which the motor is firmly attached (the workshop floor is essentially the Earth). The Earth receives the reaction torque and being the massive object it is, it doesn't move.

Now let us imagine that we took our motor into space where there is no gravitational field. What would happen if we tried to run the motor? Assuming the motor is powered by a battery pack. The battery pack and its control electronics are neatly packed around the stator.

Would the motor rotate at all? Would the rotor and the stator rotate in opposite directions? Would there be a transfer of energy from the batteries to rotational mechanical energy?

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Initially

  • Assume an ideal motor with no mechanical losses and

  • Operation in a perfect vacuum.

  • Call the two portions rotor and stator - with all attached parts such as controller and power pack forming part of one or the other.

  • Start at rest relative to a "fixed" frame of reference.

Rotor and stator will rotate in opposite directions with the 'momentum of each portion being equal and opposite. If you manage to produce identical moment of inertia in rotor and stator they will rotate with equal and opposite rotational velocities. In the moments of inertia are in the ratio N:1 they will accelerate and, and will rotate with velocities of 1:N relative to the fixed frame of reference. The energy content in rotor and stator relative to the zero energy level initially will be equal.

If there are non idealities such as bearing drag and eddy current or other losses they may affect rate of acceleration or final velocity depending on how the motor is controlled. A "brushless dc motor" whose speed is controlled by sensors or field sensing so that a fixed RPM rate is achieved will rotate so that differential rotor-stator speed is what the controller sets, and relative rotation rates relative to the fixed reference frame will relate to the relative moments of inertia as above. A motor such as a series wound "universal" motor whose speed is set only by losses (such as is typically used in vacuum cleaners) will increase in speed until losses from bearings, eddy current, copper losses etc equal power in. In such an environment an unloaded motor would usually easily accelerate to an immensely high speed and "self-dismantle". (Even everyday vacuum cleaner motors which depend on the aerodynamic loading of their fans will usually rev to destruction if operated without the fan.

For a rotational drive it is possible to introduce rotational realignment around the axis of rotation but not translation.

A motor with offset mass relative to the axis of rotation will do interesting things but still imparts equal and opposite inertial variations to the two parts.

If you now "add air" all bets are off - you can achieve arbitrary translation and velocity in desired (or undesired :-) ) directions because you have introduced an independent medium which reactive force can be developed against. You can also arrange energy losses differentially between the two portions so that eg a rotor could be spun up and the stator braked to rest while "floating".

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  • $\begingroup$ Your answer is clear and enlightening. In the case of the unbalanced stator and/or rotor mass relative to the axis of the motor, would the motor system rotate about the common center of mass or the rotor axis. Could it be possible to make motor orbit about a point external to the motor system? $\endgroup$
    – Edgar
    Jul 24 '15 at 16:50
  • $\begingroup$ Where did you get that sqrt from? $\endgroup$
    – CodesInChaos
    Jul 24 '15 at 18:10
  • $\begingroup$ Some of the things you say are incorrect. The velocities of each part will be inversely proportional to their moment of inertia. There is no square or square root in there. Friction and other losses have no affect on the momentums, but do affect the total kinetic energy. However, the energy of each part will not be equal and opposite, the momentums will be. $\endgroup$
    – Olin Lathrop
    Jul 24 '15 at 21:26
  • $\begingroup$ @OlinLathrop Edited. There is something flickering around the edges of the brain that relates but so far refuses to come home to roost. I may come back and comment on energy. $\endgroup$
    – Russell McMahon
    Jul 25 '15 at 8:48
  • $\begingroup$ @CodesInChaos Edited. Sqrt came from thinking in terms of given radial accelerations providing different velocity for differing moments of inertia. There is something worth saying there but it will probably suggest itself in the next while while I'm doing other things :-). $\endgroup$
    – Russell McMahon
    Jul 25 '15 at 8:50
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The stator and the rotor would rotate relative to each other in the same way as if one end were attached to the Earth. If your frame of reference was attached to either the stator or the rotor, you would see the things attached to the other part rotating in the same way as if you were standing on Earth. The only difference is that, in space, you would need to consider the conservation of angular momentum to determine how much the two portions rotate with respect to some external reference frame such as the stars.

Using a motor to spin a flywheel is one of the ways that spacecraft rotate while in space. Interestingly, the people who designed the Voyager spacecrafts neglected to account for this effect in the spinning tape recorders that were used to record data. They ended up having to engage external thrusters every time the recorders were in use in order to maintain the correct pointing of the spacecraft.

To answer your questions more directly:

  1. Would the motor rotate at all? Would the rotor and the stator rotate in opposite directions? Yes and yes. The motor produces the same amount of torque between the rotor and stator (for a given load and speed) no matter what each is attached to.

  2. Would there be a transfer of energy from the batteries to rotational mechanical energy? Yes, rotational energy would be put into the object attached to the stator as well as the object attached to the rotor.

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Newton's third law states that for every action, there is an equal and opposite re-action.

In the case you presented on earth, the stator and the rotor exert equal electromagnetic force on each other, but while the rotor is free to rotate, the stator is held in equilibrium by the bolts exerting an equal force in the opposite direction.

In space, all the same laws apply, but now there is no force holding the stator in place. When the equal force is applied to each, they will move in opposite directions with accelerations proportional to their relative masses, per Newton's second law: F=ma.

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  • $\begingroup$ this principle is used to de-spin satellites which are launched into space on rockets that are spin-stabilized during boost. The satellite is separated into two halves, a payload attached to the stator of a motor and a flywheel which is attached to the rotor (or vice versa). Once in orbit, the motor is turned on to run in the direction opposite the spin of the payload and its speed precisely adjusted until the payload is "de-spun". $\endgroup$
    – niels nielsen
    Nov 2 '17 at 5:45

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