The gymnast looks like the Wolf’s turn is easy. Physics shows that it is not

Yes, this is just a picture, but it’s really balanced. Bada run the code, you will see that it is really stationary and has not flipped. It seems pretty clear that it should work, that is, we humans do this to stay upright all the time.

Rotating about an axis of rotation

If the wolf’s turn was just balancing on one foot, it probably wouldn’t be an Olympic-level beam routine. It’s the rotation that makes this so difficult.

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

However, with the mass spring model, the same balancing calculations will work well. Here is a diagram of a rotating object with two equal masses. I added a vertical line to represent the axis of rotation and show that it passes through the equilibrium point (foot).

Again, I 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 happens if we rotate the non-symmetric case? Let’s see what happens. (I must mention that I added a lateral force to the bottom of the rotating mass so that the support point does not “fall”: Take a look.)

If it is not clear, this object is balanced at the pivot point, but will not rotate about a fixed axis. If you want to force it to rotate about this vertical axis, you should cause an external moment to move the object or change the position of the masses. (As I said, rigid body rotations can be very complicated.)

In fact, this is another real life situation …balance the wheels in your car. When the center of mass of the car’s wheel is on the axis of rotation (its actual axis, in this case), it can try to rock while the wheel is rotating. The solution is to add a few extra small masses to the edge of the wheel until the axis of rotation is in the same direction as the axis.