The Rotating Cup

Place a cup with a handle on a shelf at eye height. Now walk in a straight line at a nearly constant speed past the cup, all the while rotating your head to observe the orientation of the cup. Notice what you see. The cup appears to rotate in the direction opposite your walking direction, at first very slowly, then quickly, then slowly again. Now consider yourself to be stationary and imagine the cup itself moving past in a straight line with constant speed. You could try to demonstrate this with the cup in your hand. What do you see now?

Answer

Done properly, you would see the same sequence in both cases. The cup appears to rotate with changing rotation rates as time passes. We have here an example of Galilean relativity for uniform motion. At these familiar slow speeds compared to the speed of light, the behavior of the rotating cup produces no surprises. We can walk past the cup, or the cup can move past our stationary location.

In a later chapter, where we introduce the special theory of relativity (STR), we examine an object such as a cube moving past a stationary observer at enormous speed, and we could consider the opposite case, of the observer moving past the stationary object. Of course, one sees the same behavior in both cases, just like the symmetry we observe in Galilean relativity. However, in STR an effect, now called the Terrell effect, explains why a cup approaching and passing by at near-light speeds appears additionally rotated, the observer being able to see the back side of the cup as it approaches!