Gymnasts make the wolf look easy. Physics shows that it is not


Yes, this is just a picture – but it is really balanced. If you run the code, you can see that it really rests and does not roll over. It seems pretty clear that this should work – I mean, we humans do it all the time to stay upright.

Rotate about the axis of rotation

If it was about turning the wolf just about balancing on one leg, it probably wouldn’t be in the beam routine at the Olympic level. Turning really makes this thing so difficult.

The great thing about building my human model with three masses is that I can also rotate it. If you take a hard object (like a phone or a key) and throw it in the air, it will crash. We call this the rotation of a rigid body, and as I mentioned, physics becomes super complicated. But if you just want a little taste of great stuff, here’s a blog post with all the details –have fun with it.

However, with a mass spring model, the same balancing calculations will work just fine. So here is a diagram of a rotating object with two equal masses evenly spaced. I added a vertical line that represents the axis of rotation and shows that it passes straight through the equilibrium point – the foot.

Illustration: Rhett Allain

Again, I really don’t think there are any surprises here. Everything is symmetrical, balanced in the middle and rotates around an axis that goes down the middle.

But wait! What if we rotate an asymmetrical housing? Let’s see what happens. (I should note that I added lateral force to the lower swivel mass so it wouldn’t “fall” off the support: Check.)

Illustration: Rhett Allain

In case it is not clear, this object is balanced at the point of rotation, but it will not rotate around a fixed axis. To want it to rotate about that vertical axis, you would have to either press the external torque on the object or change the position of the masses. (Like I said, rigid body rotations can be really complicated.)

In fact, there is another real situation that is just that-balancing the wheels on your car. Even if the center of mass of the car’s wheels is exactly on the axis of rotation (in this case its actual axle), the wheel can still try to swing as it turns. The solution is to add some extra small mass to the rim of the wheel until its axes of rotation are in the same direction as the axle.

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