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Can you speed up Earth's rotation by spinning?

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Hey,
Got into a discussion with my friends over this:
If you spin in your chair clockwise, since the earth spins counterclockwise, as you start spinning by conservation of momentum the Earth would also start speeding up. Then, frictional dissipative forces from the air would slow you down to a stop, but since the air is fairly uncoupled to the Earth, this angular momentum probably wouldn't find it's way back to Earth (or at least not completely) Thus you could (technically) speed up the Earth by spinning. Similarly, if you started spinning counterclockwise, you could slow the Earth.

I know that in an ideal situation (i.e. no frictional forces, no air, just you and Earth), it's impossible for a situation to exist where you are not spinning anymore but the Earth is spinning faster/slower, but with friction, is the above example true?

Thanks,
Ari

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