Stacked motors thought experiment

Question

first of all, I'm not a mathematician, just curious about something that came up to my mind and maybe you can help me out. Scenario:

I have a motor that spins let's say at 20K revolutions per minutes. Now I attach another motor to that first motor, and another, and another and so on. Let's imagine everything is perfectly balanced and that they're wireless.

Is it possible to make the first motor shaft to theoretically spin to close to the speed of light? can it go even faster? if not, what limits its speed?

Related (possible duplicate): http://physics.stackexchange.com/q/2774/ — dmckee --- ex-moderator kitten, Apr 03 '16 at 17:13
What exactly is a grinder? I feel like there's a better word. — , Apr 03 '16 at 18:33
Not even theoretically, since the ideal motor shaft would become heavier and heavier as its circumferential velocity approaches c. — dominecf, Apr 03 '16 at 19:14

score 0 · Accepted Answer · answered Apr 03 '16 at 20:50

What you need is attach the shaft of one motor to the housing of the next motor. If you just connect all the shafts, then all the shafts are going to spin at the same 20k speed.

By daisy chaining the motors each contributes a relative speed of 20k and all-together the combined output shaft speed would be a multiple of the motor speed.

Almost!, As soon as you reach relativistic speeds the kinetic energy needed to increase the speed by one unit goes up exponentially. This manifests itself as an apparent increase of the mass moment of inertia proportional to a factor of $$\gamma = \frac{1}{\sqrt{1-\left( \frac{v}{c} \right)^2 }}$$ where $v$ is the tangential velocity of the moving parts, and $c$ the speed of light.

Stacked motors thought experiment

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