When we create a new physics concept or principle that is represented by an equa

Question

When we create a new physics concept or principle that is represented by an equation, in some cases the
equation corresponds closely to common-sense intuitions, while in other cases the equation seems rather
arbitrary and indirectly related to experience. Does the equation for torque correspond to common sense,
or is it one of those more arbitrary equations?
• Give a mathematical denition of torque.
• Explain why you think the equation is either intuitive or counterintuitive. As part of your explanation
discuss a relevant personal experience or experiment.

Explanation / Answer

Torque is defined mathematically as the rate of change of angular momentum of an object. Your experience may be different, but for me torque does not easily correspond to common sense. When we think about rate of change it is usually pretty easy to think about linear applications. We've all had the experience of walking, then walking quickly, sometimes running, then walking slowly. Now think about it in angular terms. We don't generally walk around in circles for hours at a time and if we do walk around in circles we end up dizzy. Hardly a good experience to draw from when trying to conceptualize a new physics concept. That's not to say it's impossible to grasp. With considerable effort one can begin to notice some of the less obvious angular movements during a day. For instance, when you are carrying a large pile of heavy books and you need to open a heavy door, do you push the door at the middle, or do you go toward the edge furthest from the hinges? Do you ever choose the edge nearest the hinges? Have you ever seen a very young child go toward a door on the hinge side? An experiment you can do for yourself but it works better to ask someone else to do it--the lesson is in the observation: on a piece of paper draw a large stick figure. Now give your stick figure a cap style hat. Put some sort of logo on the picture. If you are watching for it you will notice that as people draw smaller pictures their grip placement moves down the pencil or pen. Think about how this relates to torque. So we all know a little more that we think we know about torque and all those other angular physics things. The examples are harder to identify. My observation is that the angles are so small or so large they aren't obvious. The more obvious angles lead to dizziness and, unless you are a cat, that's no way to learn anything.

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