Big Tire Energy

Grab a bike tire by the hub with both hands, then have someone start it spinning.

Something funny happens when you try to move the spinning tire around, doesn’t it? It feels almost like something is pushing back into you, or there’s a wall there or something. What’s going on?

What is this big tire energy?

First, rotational inertia is similar to the type of inertia Newton described in his first law, except instead of continuing to travel in a straight line, it describes what happens when something is going around in a circle.

There’s a useful trick that shows why rotational inertia around a circle works the same way as inertia of an object traveling in a straight line. Here’s how I described infinitesimals:

Imagine trying to draw a circle, but with only straight lines. You can make an octagon with just eight lines, and you know that if you add a few more lines, the shape will start to look more like a circle.

If you had a hundred of these lines, you might not be able to tell the shape isn’t a circle any more. It’s still a shape with straight lines, but it seems more circle-like to you now. You might say that the shape is approaching a circle as you add more lines.

So, when you’re pushing against that tire in space and you try to stop its spin, you feel that same linear inertia pushing back into your hands. That seems intuitive enough.

But what about when you push at the tire from the side? Instead of just moving easily, it seems to twist around, almost like it has a mind of its own. This is called gyroscopic precession, and you can see it any time you spin a top around and observe how it resists falling.

You have to change its angular momentum. To do this, you need torque—the push from the side where you feel the tire pushing back at you. When you apply force from the side, it combines with the already-existing force to create a new vector that’s always perpendicular to the force you apply.

This little thought experiment makes my mind spin, too. I know that mass and energy are the same thing at a fundamental level, but it’s not like you can experience the feel of atomic energy, exactly. It all seems really abstract, even when we know it’s true.

However, here’s something we can really feel for ourselves. The act of spinning adds energy to the tire itself, in a manner of speaking. The mass stays the same here, but the energy of the “system” increases.

Random jump: here’s a detective story about bicycles I once wrote that all started with a flat tire: