# Why do office chairs rotate when pushed/pulled out?

A common source of frustration when I'm at work is the fact that my rolling office chair's wheels rotate whenever I push it forward or backward from my desk, which can cause it to bump my computer tower or any other object on the floor nearby. This happens no matter how carefully I avoid turning my torso, or how straight back I push.

What physical phenomenon causes office chairs to rotate in this way? It has five wheels, if that's important.

My suspicion is that there is some interaction among the friction forces of the wheels on the ground that gives rise to this behavior, but I don't understand how to connect the dots from "opposite the force of the push" to "circularly about the support column".

This is different from other physics.se office chair questions like these three because I am asking about the rotation along the vertical axis of the wheelbase, not why the chair has five wheels or how it can move without my feet on the ground.

• Is this like a chair where the part you sit on can rotate independent of the rotation of the part that has all of the wheels? i.e. fun spinny chairs :) – Aaron Stevens Mar 14 at 20:11
• If your five wheels have uneven friction (or if they can independently turn, and thereby start out at random angles) you get a moment of force about the vertical axis. Any left/right symmetry breaking caused by friction would do this. – flaudemus Mar 14 at 20:15
• @flaudemus That should be an answer – Aaron Stevens Mar 14 at 20:17
• Like anything else in Dynamics which follow Murphy's laws, the answer is "because it can." More formally, any unconstrained degree of freedom is going to exhibit motion sooner or later. – ja72 Mar 14 at 20:25
• No. Asymmetry wouldn't explain a continual rotation; merely a rotation to an angle where there is a balance of friction. – Paul Childs Mar 14 at 20:31

The problem is, that the bearings are not perfect. Especially the ones that are used to turn the "feet" of the chair. Those bearings are under a quite heavy load, and they are not designed to turn without friction.

As such, your chair's feet always want to remain in the same position as they are, and that is usually not exactly the direction into which you want to move your chair. Frequently, you cannot move into any direction without turning some feet.

So, when you push your chair back, the feet of the chairs basically hold a contest on who's the first to turn. Now, like all the feet, the ones that remain in position relative to the chair's base, are generally not aligned with your movement either, and they provide the chair's base with some rotating force.

You can make the test of aligning all five feet straight to the back, and then slowly drawing the chair back. You'll see that you'll be able to move the chair for some distance without the base turning. However, once the imperfections of the setup amplify, one or more feet become significantly out of direction, and that's when the chair's base will start turning.

If your five wheels have uneven friction (or if they can independently turn, and thereby start out at random angles) you get a moment of force about the vertical axis. Any left/right symmetry breaking caused by friction or imperfect fabrication (e.g. unequal lengths of the legs on which the wheels are mounted, or slightly different distances of the wheels from the axis) would do this, where left and right are separated by a plane through the vertical axis of your chair and the midpoint between your feet. I assume that both of your feet push with the same force.

Of course, as it was mentioned by Paul Childs in the comments, this mechanism would only rotate the five legs of your chair until a balance of friction is reached. However, depending on the degrees of freedom of the wheels, this may not happen so quickly.

Anyway, other mechanisms of rotation are conceivable, but we would require more details about how your chair is constructed for providing more educated guesses.

I suggest that you test my suggestion by inspecting the wheels of your chair in terms of friction, and to check, if they can independently turn. If they do, you may find them in different orientations, when you start pushing. This may already break the symmetry according to my experience.

I believe it is related to the helicity of the screw thread and or spring in the chair. A lateral force on this will be turned into opposing torsional forces on the top and bottom parts.

In order to counteract this you would need to design a chair with two threads/springs with opposing helicities, like they do on some outboard motors to provide greater stability.