Pulling a Spool

You pull on film in a spool as shown. What direction does the spool move?

A) To the right while spinning clockwise

B) To the right while spinning counterclockwise

C) To the left while spinning clockwise

D) To the left while spinning counterclockwise

E) Depends

Solution: E. It depends on the angle you pull and the friction from the surface.

1) If there is little or no friction, then you will exert a counterclockwise torque and a force  to the right. The spool will unwind (spinning counterclockwise) as it moves toward you and slips across the surface.
2) If there is significant friction and you pull directly to the right or at a small angle above horiztonal, then the surface will exert a clockwise torque greater than your counterclockwise torque and a force to the left that is less than your for force to the right. So there will be a net clockwise torque and a net force to the right. The spool will spin clockwise and wind up as it moves to the right.
3) If there is significant friction and you pull at just the right angle (called a critical angle), then the spool won't move at all!
4) If there is significant friction and you pull at a large angle from horizontal, then the surface will exert a clockwise torque less than your counterclockwise torque and a force to the left that is greater than the horizontal component of your force to the right. So the spool will unwind (spin counterclockwsie) as it rolls away from you to the left.