Here’s how students in AP physics developed the idea of ‘turning effect’ (eventually named ‘torque’) using a bike tire, brooms (push-o-meters), meter sticks, and spring scales (pull-o-meters).
1. Observe the following scenarios, record any observations. (more details on these here)
2. In a small group, establish a ‘set of rules’ to describe your observations. Make your rules simple and applicable to as many of the scenarios as possible.
3. Since ‘turning effect’ depends on the location of the force (radius) and the amount/direction of the force (must be perpendicular to the radius), investigate the relationship between ‘radius’ and ‘perpendicular force’ for a simple object. Hey, how about a meter stick?… it’s already got the radii markings on it! Hang a mass on one side, then use a ‘pull-o-meter’ to measure the force at different radii.
4. Graph F vs. r. (gives inverse relationship) Linearize by graphing F vs. 1/r. Write an equation. Example equation: F= (0.5 Nm) 1/r. Groups will end up with different slopes.
Compare graphs with other groups. Realize that slope was due to the ‘turning effect’ caused by the location and size of the hanging mass chosen. Rearrange equation to yield: F*r = 0.5 Nm . Define the quantity F*r = Torque!
Formalize by including the sine of the angle between F and r.