Why Does the Wheel Appear to Rotate Counterclockwise When Projected?

[mellah]

Homework Statement

A wheel with 16 spokes rotating in the clockwise direction is photographed on film. The film is passed through a projector at the rate of 24 frames/s, which is the proper rate for the projector. On the screen , however, the wheel appears to rotate counterclockwise at 4.0 rev/min. Find the smallest possible angular speed at which the wheel is rotating.

Homework Equations

1 revolution= 2pi radians
angular speed = angular acceleration x time

The Attempt at a Solution

Since the wheel is actually turning clockwise, its acceleration will be negative, but when its shown on the projector, the acceleration is positive. I assume that the "proper rate" means that the acceleration as shown on the projector is of the same magnitude as that in real life. I set up angular speed1= acceleration1 x time and angular speed2= acceleration2 x time (where 1 is on the projector and 2 is actual). Since time is the same, I set the two equations equal to each other and got speed1/acceleration1=speed2/acceleration2 or speed2 = (acceleration2 x speed1)/acceleration1. Because the projectors working at the "proper rate" acceleration1= negative acceleration2 and so speed2=-speed1.

I don't think I'm following this right because I'm only using one of the numbers in the problem, unless the other two are just extraneous information.

Thanks in advance.

 

[LowlyPion]

Homework Statement

A wheel with 16 spokes rotating in the clockwise direction is photographed on film. The film is passed through a projector at the rate of 24 frames/s, which is the proper rate for the projector. On the screen , however, the wheel appears to rotate counterclockwise at 4.0 rev/min. Find the smallest possible angular speed at which the wheel is rotating.

Homework Equations

1 revolution= 2pi radians
angular speed = angular acceleration x time

The Attempt at a Solution

Since the wheel is actually turning clockwise, its acceleration will be negative, but when its shown on the projector, the acceleration is positive. I assume that the "proper rate" means that the acceleration as shown on the projector is of the same magnitude as that in real life. I set up angular speed1= acceleration1 x time and angular speed2= acceleration2 x time (where 1 is on the projector and 2 is actual). Since time is the same, I set the two equations equal to each other and got speed1/acceleration1=speed2/acceleration2 or speed2 = (acceleration2 x speed1)/acceleration1. Because the projectors working at the "proper rate" acceleration1= negative acceleration2 and so speed2=-speed1.

I don't think I'm following this right because I'm only using one of the numbers in the problem, unless the other two are just extraneous information.

Thanks in advance.

4 revs in a minute is 15 seconds to make the "virtual" revolution.

Doesn't that mean the precession will appear slower by 1 revolution over that many frames?
If it was turning at exactly that speed wouldn't it appear to be not moving at all?

 

[mellah]

I'm sorry but I don't think I'm following what you said in the second part of your reply. Could you explain?