It is all too easy to tip over a drinking glass. In a controlled experiment you can see that there is a "critical" angle of tilt. If the glass is tilted less than this angle, it will right itself. But if the tilt is greater than this angle, then the glass falls. The determining factor is how much mass (mostly the liquid inside the glass), is on each "side" of the point where the glass touches the table.

1. Tilt a glass on its edge. Approximate the volume on each side of the balance point. (Start with a cylindrical glass.) You can use the angle of the side with the ground or the ratio of the height of the glass to the distance the top of the glass is tilted. What is the "critical tilt"? Hint: It will be difficult to come up with an exact answer, so strive for a "good enough" approximation. Doing experiments is OK, but use plastic glasses and do this someplace where you don't mind spilling.
2. Determine the critical angle for different shape glasses.
3. How does the shape of the glass determine the critical angle?
4. What shape glasses are more "stable"?
5. What about "extreme" glasses (with long stems)?

Many glasses are narrower on the bottom and wider on the top. Explain why this would make them more likely to tip. Also, explain why they are designed this way. Can you come up with an optimal glass shape?

Communicated by G. Hall.