Which speed, the speed of the Earth revolving on it's access, or the speed at which it is orbiting the sun.
Chip Monk missed a bit. If the Earth stopped spinning then your motion would be at a tangent to that rotation (not as some people thing, up into the air). Given that you are so small compared to the curvature of the earth you would really just go along the ground. That would be predictable and constant, you would always go in the same direction, at a tangent to the the spin.
If however the earth stopped moving along it's orbit around the sun, then you would move in a tangent to that orbit. So It would depend where you were relative to the orbit. If you were effectively at the back of the Earth, relative to the orbit then you would hit the Earth when it stopped and you didn't. If you were at the front then you would spiral into space, you would leave the earth because it had stopped, but you would still have the spin. You wouldn't spiral relative to the Earth, as it was still spinning but you would relative to other things.
If both motions stopped it would get really crazy.
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