Air resistance, changing position in free fall?

[Henrybar]

Let's say that I have a stick with weight evenly distributed throughout. I attach a fan to one end of the stick, then balance it from its new centre of mass. I measure the distance from the ground to the stick then drop it. The stick tilts up towards the side generating more air resistance (fan attached) and lands on the side with no fan first. This is a hypothetical situation, so the numeric values for mass, surface area, distance from ground, air pressure, and weight are those which make this motion possible.

Compare this to an identical stick with no fan attached. I drop the stick from the same distance, under the same conditions, and from its centre of mass. While the stick is falling, it maintains its horizontal position unlike the other stick; it lands horizontally as well.

Shouldn't stick 1 touch the ground first?
- Assume that air resistance isn't great enough that it cancel out this effect and instead slows it down

 

[BobG]

What makes you think the non-fan side of stick 1 would hit the ground first?

If the fan is rotating, blowing air, then the stick is going to be constantly rotating. In fact, if the fan is blowing perfectly perpendicular to the stick, then the force from the fan will create torque and won't affect the linear velocity of the stick at all (granted, just having the fan on the stick probably increases air drag to some extent, so the stick with the fan will probably fall at least a little slower, but not because of the fan blowing).

I guess the laws of probability dictate that the rotating stick will have one end lower than the center of mass, and therefore one end of the rotating stick should hit the ground before the horizontal stick.

 

[Henrybar]

What makes you think the non-fan side of stick 1 would hit the ground first?

If the fan is rotating, blowing air, then the stick is going to be constantly rotating. In fact, if the fan is blowing perfectly perpendicular to the stick, then the force from the fan will create torque and won't affect the linear velocity of the stick at all (granted, just having the fan on the stick probably increases air drag to some extent, so the stick with the fan will probably fall at least a little slower, but not because of the fan blowing).

I guess the laws of probability dictate that the rotating stick will have one end lower than the center of mass, and therefore one end of the rotating stick should hit the ground before the horizontal stick.

 

[Henrybar]

"Fan" as in a manual fan, not a fan that rotates and blows air.

 

[mrspeedybob]

Let's say that I have a stick with weight evenly distributed throughout. I attach a fan to one end of the stick, then balance it from its new centre of mass. I measure the distance from the ground to the stick then drop it. The stick tilts up towards the side generating more air resistance (fan attached) and lands on the side with no fan first.

Here you posit a force which retards the acceleration of the stick, granted, an asymmetric force, but a force non-the-less.

- Assume that air resistance isn't great enough that it cancel out this effect and instead slows it down

Here you state the the force which retards the acceleration of the stick should be neglected.

So you're asking what would happen in a situation given a force which we are supposed to neglect.

 

[BobG]

"Fan" as in a manual fan, not a fan that rotates and blows air.

Then stick 1 hits the ground first.

The center of mass of each should hit the ground at the same time. By rotating to a vertical position, one end of stick 1 will be lower than its center of mass and will hit first.

 

[mfb]

The same effect that induces rotation also slows the fall of the center of mass, as both come from an upwards force on the fan.

There is a region in parameter space where object 1 hits the ground first (in general, a low-mass, high air drag fan and a very small dropping distance), but it is also possible (and more realistic) to make stick 2 hit the ground first.