| Here's the intuition that clicked for me, similar to the above but with a different twist at the end. Imagine a large flat parking lot, and drive around the parking lot in a circle. Say you have a small pendulum swinging freely, suspended in your car. If you drive the full 360 degrees, the pendulum will appear from the reference frame of the inside of the car to have rotated a full 360 degrees. (Let's say that you are driving fast enough to render the rotation of the earth, the latitude of the parking lot, etc. negligible.) Whatever fraction of the circle you drive, the pendulum will appear to rotate that same fraction as viewed from inside the car. Now, here is the fun part. Imagine that you are driving at some fixed latitude on a large sphere. Create a big cone that is just tangent to the sphere on your path. What happens if you drive the entire distance and return to your starting point? Cut the cone in a vertical straight line starting at its apex, and then flatten out the cone. It will form a flat circle, but with a pie slice removed. If you had driven the perimeter of this partial circle in the parking lot, you would see that the pendulum only rotated part-way around. The same thing will happen if you drive the full distance around the sphere at the corresponding latitude. |
Not to digress, but IF the earth was stationary and everything rotated around it, can you think of a mechanism to explain the pendulums behavior? (Could be ether, or some medieval conception of ptolemic shells, you name it... but it has to be consistent and sort of reasonable sounding.)