The Spool

QUESTION:

drawing of a spool When the spool is pulled horizontally to the right, it will roll toward the

right.
left.

ANSWER: A

The spool rolls toward the right. to see this, consider the peg being pulled by the string in the sketches below:

1. When pulled to the right, the peg moves toward the right.

2. It still moves toward the right when two "wings" are attached.

3. When the top is capped, the peg still moves to the right.

We can go further: the spool rolls because the applied force producs a torque on the spool. If the string is pulled at a slight angle above the horizontal, the torque still rolls it to the right.

drawing

Beyond a steeper angel, however, the spool will roll to the left. What angle? At the angle where the line of action of the string intersects the point where the spool makes contact with the surface.

No torque acts on the spool when the cosine of the angle equals r/R. For smaller angles, a torque is produced that makes it roll to the right; for larger angles, an opposite torque is produced that rolls it to the left.

The smaller the radius of the spindle compared to the outer radius, the higher the string must be pulled to make the spool roll in the opposite direction.

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