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Assume to identical motors are placed vertically on-top of a table and they are not fixed able to move/fall etc...and they have gears attached to them and are attached to one another like this image:

enter image description here

Now, I powered both motors, and the torques of the two are the same and opposing one another as illustrated here:

enter image description here

OR:

enter image description here

What I think would intuitively happen due to the two torques($t_1$ & $t_2$) being the same and opposing one another is that the rotors/gears would be at rest. However, is there a form of linear force acting on the motors? Due to them opposing one another would that cause the first or second motor to fall from the table due to a unknown linear force?

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The center of mass of each motor will move in accordance with the sum of all forces acting on the entire subsystem (motor plus rotor). This means that the motors will indeed move - they are "pushing away" from each other in the same way that one of them would move if it tried to spin its rotor against, say, a wall or a floor. Put your picture on its side, replace one rotor with a solid surface, and it looks like you are looking at half a car... what happens if the engine in the car starts driving the wheel?

The same thing happens here.

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  • $\begingroup$ But how are they pushing away from each other? The rotors are at rest because they oppose one another, how would that create a form of linear force that moves the motor itself? $\endgroup$ – Pupil Mar 9 '15 at 16:10
  • $\begingroup$ Maybe that it's due to the reaction force(Newtons 3rd law)? $\endgroup$ – Pupil Mar 9 '15 at 16:10
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    $\begingroup$ How does a car start moving when it is at rest and it tries to move its wheels? Yes, it is the reaction force. Note that the motors will spin in a direction opposite to the motion of the rotors if they are not connected to anything. $\endgroup$ – Floris Mar 9 '15 at 16:12
  • $\begingroup$ AH! I forgot, if the motors are stuck (rotors net torque) the bottom part will rotate. I remembered once i held motor's rotor and they motor can move freely, the motor itself rotated! Thanks for the reminder. $\endgroup$ – Pupil Mar 9 '15 at 16:17
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    $\begingroup$ Nope. If you had a single motor + rotor, one would spin clockwise and the other counterclockwise, with a net angular momentum of zero. As it is, there is a net force on each rotor/motor pair, so they will move away from each other. In the process they (the pair of motors) will end up with a net angular momentum, and this is compensated for by the fact that the individual motor/rotor combinations will have angular momentum that opposes that. See this interesting video around 2:40 - 3:00 is particularly interesting in this context. $\endgroup$ – Floris Mar 9 '15 at 16:49

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