Magical spool

What can you do here
Place the spool in the middle of the track. Unwind the ribbon to around 1 metre length. The place where the ribbon touches the spool should be at the bottom.

1. Gently pull the ribbon, holding it so that it forms a small angle with the horizontal plane. What can you see? Which way is the spool rolling?

2. Try gently pulling the ribbon, holding it so that it forms a bigger angle with the plane. Which way is the spool rolling now?

3. Try make the spool slide but not roll at the same time.

How does it work
The movement of the spool consists of two components: progressive movement and circular movement. By pulling the ribbon we apply some force to the spool. The distance between the point of force application and rotation axis is the same as the spool’s radius. In circular movement we have so called torque – its vector direction agrees with the spool’s rotation axis. We can determine where the vector points by using the right-hand rule. If the angle between the spool’s track and the stretched ribbon is big, then the torque causes the spool to unwind and move away. Similarly, if the angle is small enough the torque causes the spool to wind and come closer. There is also a third possibility: the torque does not apply and the spool slides without rotation.

Interesting facts
In case of car engine, the torque of value 100 Nm (newton metres) means that the crankshaft is able to perform a full rotation when an arm of length 1 m is fixed to it and a weight of 10 kg is attached to its end.