Q:

Will a, lets say super-fast, spinning top in a perfect vacuum on Earth spin basically forever? I read it's true. If so, wouldn't this would mean it would spin like this even up off the floor without losing speed and falling as long as faster than gravity? Then you could push it 1 time and deliver large loads to space like this?? If not just push it really hard from underneath so it's faster than gravity and stays this speed!?

- ADVANCESSSS (age 19)

- ADVANCESSSS (age 19)

A:

The motion of a spinning top is a bit more complicated than you imagine. Beside the spin, its axis will be tracing a cone (precession) due to gravitational torque. To make the things worse depending on the initial conditions -i.e. how much your hands shake- there will be a slow change of the level of this precession trace (nutation). So, you need to keep this oscillation range small enough so that the top does not hit the table plane. I do not think this could happen in a perpetual top on Earth, because spin-precession-nutation will occur around axes fixed in an inertial frame and Earth is not an inertial frame due to its spin. The trajectory and the top's fate is quite hard to describe quantitatively. Qualitatively, conserving angular momentum vector would mean flipping your top after 12 hours, assuming 0° latitude.

When you give an upward kick to the top, you impart a certain linear momentum to it. The center of mass of the system should follow the trajectory of a point particle thrown of same momentum independent of the complex rotational motion. Your top will therefore come down in (initial upward speed)*2/g seconds, so no levitation.

Tunc

*(published on 07/13/2015)*