Tricks With Torque

Purpose:
To demonstrate torque in a simple system.

Equipment:
Spool with two strings attached to a handle

Equipment Location:
Other

Procedure:
To start make sure that the string is wound around the inner spool with about two feet left out for you to be able to pull on. For the first part of the demonstration pull on the rope while it is parallel or at a small angle to the ground, the spool should roll towards you (right on the diagram). Next you will pull the rope directly up, perpendicular to the ground, and the spool should roll away from you (left on the diagram). The last part of the demonstration requires that you line up the rope so that the line made by the rope points directly at the point of contact between the spool and ground. When you pull on the rope, the spool should slide (not roll) towards you.

Hints:
To make sure that all the three examples will work for you, try them before class. The sliding spool is the hardest to perform and therefore will require extra practice to make them work. You also want to be careful if you are performing this demonstration on a table because the spool will continue to roll of the table and may be damaged. Each example can be counter intuitive so you may wish to poll the class on which way the spool will roll. The class will likely require a detailed explanation using the torque about the point of contact.

Relevant derivations/explanations:
Consider the torque about the point of contact between the spool and ground. In the first example rxF where r is drawn from the point of contact (point A) to where the string leaves the inner spool (point B), is into the page. In the second example rxF is out of the page In the third example rxF is equal to 0 so the torque is 0 and the spool slides. Consider the net Force in each case. In the first example any vertical component of the tension is balanced with gravity and the normal force of the table. Since the spool rolls to the right, the force of friction is also to the right. So the net force is to the right. In the second example, again gravity, the normal force and the vertical string tension add to zero. Since the spool rolls to the left, the frictional force is to the left. Since you give no horizontal string tension, it is the force of friction that causes the spool to move to the left. In the third example, the friction is to the left, but it is overcome by the horizontal component of the string tension which is to the right