A magical spool

What you can do here
Place the spool in the middle of the track. Unwind around 1 metre of the ribbon. The spot where the ribbon touches the spool should be at the bottom.
  1. Gently pull the ribbon, holding it so that it is at a small angle with the horizontal plane. What can you see? Which way does the spool roll?
  2. Gently pull the ribbon, holding it so that it is at a bigger angle with the plane. Which way does the spool roll now?
  3. Try to make the spool slide but not roll at the same time.

How it works
The movement of the spool is made up of two components: progressive and rotational movement. By pulling the ribbon you apply some force to the spool. The distance between the point of force application and the rotation axis is the so-called lever arm. In the present case, a transitory rotational axis is where the spool comes in contact with the ground. In the rotational motion, the so-called moment of force (torque) occurs. Its vector direction coincides with the spool rotation axis, while its sense depends on the mutual location of the force applied and the lever arm. If the rotational axis of the spool (place of its contact with the ground) is exactly on the linear extension of the pulled ribbon, the torque does not apply and the spool slides without rotation (picture b.). If the angle between the spool track and the stretched the ribbon is larger than in the previously mentioned case, the torque makes the spool unwind and move away (picture a.), while if this angle is smaller, the torque makes the spool wind and come closer (picture c.).


Interesting facts
A bucket of water may be pulled out from a well using a reel. In order to make this possible, the moment of the force you apply to the reel must be at least equal to the moment of gravitational force of the bucket with rope. If the acting force is perpendicular to the lever arm, the value of the moment of force is equal to the product of the force value and distance from the point of its application to the axis of rotation. Since the crank on which force acts is located further from the axis of rotation than the rope with the bucket, you can use less force than when pulling the rope with the bucket directly.