Brain Meets Brawn - the Physics of Arm Wrestling

CurioCity
23 January 2012

Remember the last time you were in an arm wrestling match? Perhaps it was at the party where everyone was trying to impress that cute girl from French class. Or perhaps, you were just trying to liven things up in the cafeteria on that drab rainy day.

What you probably don't know is that this popular pastime is actually an organized sport, founded in 1952 by Bill Soberanes. Like many other sports, there are competitions at the local, national, and international levels.

Did you know? Arm wrestlers from all over the world meet in Petaluma, California every year for a chance to win the coveted World Wrist wrestling Championship title.

Now, if I were to ask you to list three qualities that a champion arm wrestler might have, “brute strength” might come up on your list. Having huge biceps probably gives you an advantage over lesser-built opponent, but if you were to arm wrestle someone your own size (it’s only fair!), then it’s time to put some science to work!

Torque is a force applied to an object to make it turn around an axis of rotation. In the case of an arm wrestling, the ultimate goal is to apply enough force on your opponent’s hand (the object), so that your opponent’s forearm rotates at the elbow (the axis of rotation) and ends up touching the table.

Since your opponent is trying to do the exact same thing to you, what an arm wrestling match really boils down to is a contest to see who can create the most torque.

The two factors that determine the magnitude of torque are 1) the force applied to the object and 2) the distance between the axis of rotation. The relationship between force, distance, and torque can be seen in the mathematical expression: Torque = Force x DistanceTorque can be increased by either increasing force on the object or by increasing the distance between the site where force is applied and the axis of rotation.

Based on this equation, it is easy to see why having larger muscles help, since larger muscles produce more force when they are used. Now interestingly, there is a little more to this equation. Even though we might be trying to get our opponent’s hand on the table (down), the general strategy is to pull sideways. Why is that?

Only the perpendicular component of the force (the force applied 90° to the direction of rotation) contributes to an object’s torque. Since only the perpendicular component “counts”, it’s much more efficient to pull sideways (at 90° to the direction that you want your “object” to end up going).

Let’s not forget about working the distance component into our arm wrestling strategy. The most basic arm wrestling move, the hook, is performed with a bent wrist (that’s why arm wrestlers need really strong wrists!). This strategy shortens the distance between your hand (object) and elbow (axis of rotation), making it harder for your opponent to generate a large torque.

So by now you may be wondering, will I have an advantage arm wrestle with a friend who is as strong as me but has longer arms? Why don’t you challenge him or her to a match and find out!

Learn more!

Giancoli D.C. Physics for Scientists and Engineers with Modern Physics 3rd edition

Canadian Arm Wrestling Association Website

The United States Arm Wrestling Federation Website

Ultimate Arm Wrestling Website

Irene is a graduate student at the University of British Columbia who works in a diabetes research lab and likes hiking, photography, and travel.

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