[Physics] Would a spinning object like a fan stop faster in a non-gravity environment

draginertianewtonian-gravitynewtonian-mechanics

Let's say there is a fan spinning and stops in exactly 1 minute on earth. Would it stop faster or slower or exactly same time in a spacecraft without gravity but exact same density of air. Btw: let's assume friction on the axis is zero. Just trying to understand if gravity has any effect of stopping a symmetrically spinning object like a perfect wheel or fan.

EDIT:
Because air is complicating things let's just assume we test this experiment in vacuum, on earth and in space. No air involved. Friction on axis is neglected.

EDIT2:
Why would it stop without any air and axis friction? That's right. Let's put air back in. Without the air the question doesn't make any sense.

Best Answer

Let's make your fan really big - say, as big as the moon.

You probably know the rotation of the moon is tidally locked to the earth - that is why we always see the same "face" of the moon.

The tidal friction is a real effect - it depends on the size of the object and the distance to the source of gravitational attraction, but it will produce a small decelerating torque on an object in a diverging gravitational field.

So your fan, in a spacecraft away from all gravity, will decelerate more slowly. Of course the difference will be incredibly small - for an object that loses all angular momentum in one minute there is no chance you could measure the effect. But that doesn't mean there isn't any.

There will be many other effects that would dominate the repeatability of your experiment before this effect comes into play - the unrealistically zero friction bearings, air currents in your space craft, thermal expansion of the fan blades, the pressure gradient in the gravitational environment, differential pressure on the fan blades due to solar wind particles, ... But if you start with a fan that will spin down in one minute, none of these other effects will come into play.

Afterthought

It is worth noting that quadratic drag (the normal form of drag force in air for macroscopic objects with Reynolds numbers above 1000) will never lead to an object stopping: the equation of motion would show velocity changing as 1/t , never reaching zero. Even Stokes drag (linear with velocity) would imply the object will never stop (exponentially decreasing velocity), but at least you can calculate the total distance it will move (integral of velocity with time is finite). But to actually stop a rotating object (zero velocity after finite time t), you need a component of force that is not dependent on velocity (like the drag in bearings). I wrote an answer relative to that recently - you might find it useful.

Related Question