“Torque” isn’t just a terrible movie from 2004…

…it’s also an important concept that many of my physics students have studied recently.

Conceptually, torque is the quantity required to make an object rotate around a given point. I’m being very careful to avoid phrases like “how hard you have to turn something”, because there are ways to increase your torque without increasing the force you’re applying.

Distance from the point the object is rotating around is also a factor, as evidenced by the device I found in my parents’ kitchen.

Screen Shot 2016-02-07 at 11.13.07 PM
This photo is from Amazon, but I think my parents got theirs from the kitchen supplies equivalent of an Avon rep.

It helps you open those stubborn soda bottles. Simply place the round part over the cap, grab the other end, and voilà! You won’t have to push nearly as hard to unscrew the cap. This is because a certain torque is required to unscrew it, not simply a certain force.

Torque is the product of the distance from the point of rotation (this distance is usually denoted by r), the applied force (usually denoted by F), and one other factor (which we will discuss in just a moment). The closer you are to the point of rotation, the more force you need to apply to achieve a given torque. Similarly, if you increase r by moving further away from the point of rotation, you can decrease F and still obtain the same torque. That’s why the weird plastic gadget is useful; the required torque may be unattainable when your hand is directly on the cap, since r is low and the necessary F is high, but it is easily achieved when you move farther out and a much smaller force is necessary.

One more factor determines torque: the angle between r and F.

Take our soda-bottle-opener example. In this case, we have a nice physical representation for r: the device itself. You’ll produce the maximum amount of torque if your force is perpendicular to r, like this.

Screen Shot 2016-02-08 at 1.51.27 AM

If you push just as hard, but at a different angle…

Screen Shot 2016-02-08 at 2.09.41 AM

…the cap will not rotate as much as it did in the previous case. This means that the change in angle causes you to produce less torque, even though you’re applying the same force at the same distance.

If you pull the device straight out…

Screen Shot 2016-02-08 at 1.51.45 AM

…the cap won’t rotate at all. No torque is produced.

Let’s use the Greek letter θ (read: “theta”) to refer to the angle between r and F. The exact relationship between θ and how much of the maximum possible torque you’re producing is perfectly modeled by that high school trig standby sin(θ).

Put all of these pieces together and you get a formula:

torquer * F * sin(θ)

That’s all for now. “Torque” to you later!

Sorry. I’ll go put myself in pun time-out.

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