Arm Wrestling and Torque

Do you remember the last time you were in an arm wrestling match? Maybe it was a rainy lunchtime at school and you and your friends decided to try to prove your strength by arm wrestling? With everyone crowded around the table, you would challenge each other to see who was the strongest. Maybe you were a better cheerleader than arm wrestler, and you weren’t very good at winning matches. Maybe you just weren’t as strong as some of the other kids. What you probably didn’t know, though, is that there is more to arm wrestling than just strength.

Arm wrestling is all about torque (symbol τ), which is the force needed to cause an object to rotate around its axis. The SI unit for torque is N·m (or Newton meters). In an arm wrestling match, whoever creates the most torque is likely going to win. 

Did you know?

Arm wrestling is actually an organized sport that was founded by a California newspaper columnist named Bill Soberanes in 1952. There are competitions at the local, national, and international levels.

How do you create torque? 

There are three factors that determine the amount of torque on an object:

1) the force applied to the object (force vector)

2) the distance between the axis of rotation and the force being applied (distance vector)

3) the angle between the force vector and the distance vector (?)

The relationship between force, distance, and torque can be seen in the mathematical expression: 

Torque = Force x Distance 

To increase torque, either increase the force being applied or the distance between the point where force is being applied and the axis of rotation (the moment arm).

To understand this, let’s first imagine a door. The door has hinges on one side. To successfully open the door, you need to apply a force. This force will cause the door to rotate about its hinges, or its axis of rotation. 

But do you know of any buildings that have doors with handles across the front instead of doorknobs? You might have seen these in your school, or in an apartment building. Have you ever tried to open one of these doors by pushing close to the hinges? It won’t work, even if you use all of your strength. But if you push the handle on the side furthest away from the hinges, the door easily swings open. That’s because you have increased the distance between the force (you) and the axis of rotation (the door’s hinges).

In the case of an arm wrestling match, the object is your opponent’s hand and their elbow is the axis of rotation. Your ultimate goal is to apply enough force on your opponent’s hand so that your opponent’s forearm rotates at the elbow and ends up touching the table. 

Of course, your opponent is trying to do the exact same thing to you. So an arm wrestling match is basically a contest of who can create the most torque.

Because Torque = Force x Distance, you can see how being strong might help. More strength will produce more force. But there is a little more to this equation. When you arm wrestle, you’re trying to get our opponent’s hand on the table -- in other words, down. But in arm wrestling, the general strategy is to pull forward. Why is that?

The third component of torque is the angle at which the force is applied. Torque is at its maximum when the force is applied perpendicular to the moment arm. In other words, when the force is applied 90° to the direction of rotation. Angles of less than 90° result in less torque. If the force is applied parallel to the moment arm, there is no torque. What this means for arm wrestling is that you can get the most torque when you apply the force 90° from the direction that you want your object to end up going.

Think back to the door example. Your elbow is like the hinge. Your opponent’s hand is like the point on which you push the door handle. The force is applied to your opponent’s hand as you attempt to push to push it towards the table. The distance from where you are applying the force (their hand) to their elbow will determine how much torque you are able to apply. 

Did you know?

People may have actually been arm wrestling since 2 000 BCE. Paintings depicting a form of arm wrestling have been found in Egyptian tombs.

How do you increase the torque on an object?

In an arm wrestling match, there are two ways to increase torque (without cheating, of course). First, you can increase the amount of force you produce. This would mean you’d have to go to the gym regularly and get much stronger. Alternatively, you can increase the distance from where you are applying the force to the axis of rotation. In other words, you can increase the horizontal distance from your opponent’s hand to their elbow. There are a few ways you can do this. 

You may already know that professional arm wrestlers are very strong. However, the techniques they use are almost as important as how strong they are. The two most common arm wrestling techniques are the “hook” and the “top-roll.” 

In the hook technique, you roll your wrist forward around your opponent's in a "hooking" motion, which deprives them of leverage. It also allows you to use your shoulder and back muscles to help your arm muscles.

In the top-roll technique, you rotate your wrist over the top of your opponent’s wrist so that your grip is higher on their hand. From there, you pull your hand towards your body to cause your opponent to lose their balance and leverage. 

You can even use the top-roll and hook techniques in conjunction with one another!
Both techniques involve rotating your opponent’s hand towards you, which increases the distance from their hand and their elbow. This way, the force you apply is creating more torque. At the same time, it’s causing your opponent to apply less torque. This gives you an advantage and improves your odds of winning!

Summing up...

When you arm wrestle, being strong will give you an advantage. But knowing how to increase the distance from your opponent’s elbow to where you are applying force will also help you win. Remember: arm wrestling isn’t just a test of strength. It’s also a test of your understanding of physics. So the next time you find yourself dueling it out against your friends, don’t forget to flex your muscles and your knowledge of torque!