Sunday, January 07, 2007

Why Doesn't Angular Motion Count as Inertial?

Suppose you were in the dining car of a train traveling 50 mph and rudely tossed a bread roll across the table to your companion, who is sitting with her back to the locomotive. How fast does the roll travel? More than 50 mph? She would have to be very alert to catch a bread roll traveling at that speed!

But as Einstein told us, the motion of the roll is relative to the motion of the dining car, so even though the dining car is moving at 50 mph, the roll is moving within the car at perhaps 1 foot in a second at most.

Why? Because a frame of reference moving at a constant velocity is indistinguishable from one at rest. If there were no windows in the train, you wouldn’t even know you were moving.

You could throw a ball (or bread roll) back and forth with a friend on the moving train and have no trouble throwing or catching, even though the whole train is moving at high speed.

But if you are standing on a playground carousel and you try to throw a ball to your friend, it doesn’t work right. The ball seems to curve away from its target, opposite the direction of motion. Why?

The “correct” answer is that the carousel is not a uniformly moving frame of reference. But what is so special about angular motion that makes it non-uniform and makes the ball curve away?

Traditionally, we appeal to Newton’s laws of inertia, which say that a body in motion will continue indefinitely until acted upon. But the centrifugal and centripetal forces are exactly balanced in an ideal spinning top, and in a frictionless environment, it would spin forever. Why is that not a stable inertial frame of reference? It seems extremely stable to me. The principle of the gyroscope depends on it.

It seems like Newton’s laws of inertia are mere descriptions without explanatory power if they just arbitrarily declare that angular motion “doesn’t count” as inertial motion. That doesn’t explain why the ball on the carousel curves away.