Gravity is Optional
Tippy Tops

We have all played with tops. Normally, the heavy part is down and a short light stem is up.

Now, imagine a top the appears to defy gravity. When the top is spun, the heavy part is down .. just like with a normal top. Then, after a few seconds, it flips over. The heavy part moves away from the Earth.

These have been a mystery for a long time.

According to Marko Horbatsch, the name is spelled either tippy-top or tippe top. Wikipedia prefers Tippe top.

Well, these are no longer easy to find .. so Dave decided to make his own.

Of course, the first question was how long to make the stems.

Actually, that was easy to answer - just make a lot of tops with different lengths and see which ones work best .. so he did.

After a few days of experimenting, he found a master's thesis explaining the physics.

TIPPE TOP INVERSION AS A DISSIPATION INDUCED INSTABILITY considers tippe top inversion to be a dissipation-induced instability. Yeah, I think they have it wrong.

In my opinion, the thesis is way too complicated to get the point across .. so this is my attempt to make the physics understandable.

A spinning top is a gyroscope. For a gyroscope, it is easy to demonstrate that the reaction to a force is a rotation at right angles to that force. This explains why a gyroscope precesses - a weight that tries to make a gyroscope fall over actually causes it to move in a circle.

In the same way, a top is a gyroscope .. but with the rotating axis touching the ground. Get it? A gyroscope is a flywheel mounted in a non-rotation frame, but a top is a flywheel with the axis touching the ground (table top, whatever). As the axis spins, there is friction where it contacts the ground. When the top tries to fall over, this friction causes a small force at right angles to the direction of fall and this force causes the top to precess.

The stem of the tippy top does not come to a point. Instead, it is either rounded (spherical) or a cylinder. This causes an increased distance between the point of contact (point where the surface friction is applied) and the axis of rotation, which, in turn, causes the top to stabilize in the upright position. It turns out that friction is very important to making this work.

The flipping is a bit more difficult to explain. Conceptually, a tippy top is a sphere with a stem sticking out one side. However, that configuration would put the center of mass on the same side of the sphere as the stem. In order to work, the center of mass must be located "some distance" from the geometric center of the (imaginary) sphere that that forms the base .. and opposite the stem. As a result, part of the sphere is cut away. Again, friction makes the top precess and, in this case, causes the stem to touch the ground. If the center of mass is colocated with the center of the sphere, then there is no precession and the stem will never touch the surface. If the center of mass is on the same side as the stem, then the precession is in the wrong direction and the stem never touches the ground (until the top stops spinning).

So, in summary, friction on the sphere causes the top to precess so that the stem touches the ground. Additional friction on the edge of the stem causes additional precession which causes the top to "stand up".

As a result, if the tippy top is spun on a waxed, low friction, floor, it does not work very well. Remember - no friction means no flipping.

Eugen Schlaak provides very clear construction details. Notice that when the tops are not spinning, the stems are all pointing up .. not touching the ground.


You can make your own tippy top using 4 marbles.

The physics is slightly different than the ones described above .. the top does not actually turn over .. but the stable state has 3 marbles spinning over one.

My video will go here

Author: Robert Clemenzi
URL: http:// / TippyTops.html