The gymnasts make the wolf turn easy. Physics shows this is not the case

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

Rotate around an axis of rotation

If the wolf’s trick was just to balance on one foot, it probably wouldn’t be in an Olympic-level beam routine. It’s the spin that really makes this thing so difficult.

The nice thing about building my human tri-mass model is that I can spin it as well. If you take a hard object (like your phone or a key) and throw it in the air, it will fall. We call it a rigid body rotation, and like I mentioned, the physics get super complicated. But if you just want a little taste of the cool stuff, here’s a blog post with all the details – have fun with it.

However, with the mass-spring model, the same calculations for balancing will work just fine. Here is a diagram of a rotating object with two equal masses regularly spaced. I added a vertical line to represent the axis of rotation and to show that it passes through the point of balance, the foot.

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

But wait! What if we turned the non-symmetrical case? Let’s see what’s going on. (I should mention that I added a lateral force on the lower pivot mass so that it does not “fall” from the fulcrum: check it.)

Just in case it isn’t clear, this object is balanced at the pivot point but will not rotate around a fixed axis. If you wanted to force it to rotate around this vertical axis, you would either have to exert an external torque on the object or change the position of the masses. (Like I said, rigid body rotations can be very complicated.)

There is actually another real situation that looks like this: balancing the wheels of your car. Even if the center of mass of a car wheel is right on the axis of rotation (its actual axis, in this case), the wheel may still try to wobble as it turns. The solution is to add a few small additional masses to the rim of the wheel until its axis of rotation is in the same direction as the axis.