Introduction to Torques: A Question of Balance, Featuring the Sledge Hammer of the Sierra Madre

Students should gain conceptual understanding of what a torque is, and should be dissuaded of the common misconception that in order for an extended object to be balanced, there must be equal weight or mass on opposite sides of the pivot point.

Educational level: Introductory Physics, all levels.
Setting: High school or college, all class sizes. This in an Interactive Lecture Demonstration classroom activity.
Time required: 15 to 20 minutes.
Special equipment: Torque meter, overhead or lcd projector, audience response system, the Sledge Hammer of the Sierra Madre.
Pre-requisite knowledge: Forces, Newton's Laws, and introductory reading over torques and static balance.

Prior to instruction students are expected to read introductory material in their text on torques and static balance. After this reading and at least one hour prior to class, students should be encouraged to take an online quiz on basic concepts and the definition of torque based on the reading assignment. The lesson should start with a short introduction to torque and the balancing of forces and torques necessary for static equilibrium. The level and depth of this introduction should be determined by the results of the online reading quiz and the level of the class.

If students do not demonstrate understanding that a net torque will result in a change in angular velocity in the online quiz, the whirligig demonstration is useful to show that a constant torque will clearly produce a changing angular velocity (this links to a figure titled "Adjustable Angular Momentum", though it is the rotational inertia that is adjustible, and the angular momentum changes due to a constant torque).

As a demonstration, have one small student engage two or three larger students in a "push of war" where the small student tries to close a door by pushing on the edge near the doorknob while the other students try to keep it open while pushing only near the hinges. An additional demonstration using a torque beam or torque meter is also suggested.

For discussion, pose the torque balance concept test question as a peer instruction activity, preferably with an audience response system. Have each student answer individually, then divide the class into discussion groups to arrive at a consensus. Have each group present their answer and reasoning.

Even after discussion, many students may hold to the idea that there must be equal weight on either side of the pivot point. To demonstrate that this is not true, conduct the sledge hammer of the Sierra Madre demonstration. Balance the sledge on your finger to determine the place to cut the handle.

Sample questions for pre-lecture reading quiz or survey (Microsoft Word 27kB Jul30 07)
Torque balance concept test question (Acrobat (PDF) 35kB Jul16 07)

For the torque meter demonstration, if a smaller griping dowel is used, students with smaller hands will have the advantage.

The following tale may be of interest with the sledge hammer of the Sierra Madre demonstration: Two prospectors searching the Sierra Madre find a golden sledge hammer. After encounters with bandits, and other trials, they must divide the gold into two equal shares. They decide to do this by balancing the hammer at a point on the handle, and cutting the sledge in two right at the balancing point. Did they divide it fairly?

A follow-up lab using a torque beam may be useful.

A more numerical version of the torque balance concept test question works well as an exam question.

More torque demonstrations can be found by searching for "torque" in the PIRA Demonstration Bibliography.