Interactive Lecture Demonstration 15 – Yo-yo

A yo-yo is shaped like a spool of thread. There is a small diameter central rod around which a string is wrapped. There are also two large diameter discs that form the case of the yo-yo. 

In this demonstration, we will study the torques created on the yo-yo by the string as it pulls on the central rod.

Recall the definition of the torque made by a force F: t = F d or t = F L sin(q). L is the distance from the axis of rotation to the point where the force is applied to the object. q is the angle between a) the line connecting the axis of rotation with the point of application of the force, and b) the line along which the force acts. The lever arm, d, is the perpendicular distance between the line of force and the axis of rotation. It is related to the distance L by d = L sin(q).

Also recall what a torque does: it causes an object to have a rotational acceleration, i.e. to speed up or slow down its rate of rotation.

1. Refer to the diagram of the yo-yo above. The yo-yo is resting on a flat table. We can pull the string of the yo-yo in several possible directions. Two possible directions are indicated on the diagram by strings A and B. Suppose we pull along direction A i.e. we pull the string vertically. If we pull with a force of 1 Newton, what will be the magnitude of the torque made on the yo-yo ? Note that it is important to first specify the axis of rotation that we are choosing (and that axis is arbitrary). We will choose an axis going through the bottom of the yo-yo (the point where it touches the table) and heading straight into the paper.
2. If we pull along direction A, in what direction (clockwise or counterclockwise) will the yo-yo start to turn ?