Accelerating Reference Frames

and Fictitious Forces

BHS -> Staff -> Mr. Stanbrough -> Physics -> Mechanics -> Newton's Laws -> Newton's First Law -> this page

When you start pulling the wagon, you notice that the ball ends up in the back of the wagon. Why? There are (at least) two possible lines of reasoning:

1. Viewed from beside the wagon: The ball was at rest in the wagon. The ball has inertia, so when the wagon began to accelerate (because you were pulling it), the ball "wants" to stay at rest. The ball ends up in the back of the wagon because the wagon accelerated, and the ball stayed were it was.
2. Viewed from inside the wagon (or moving with the wagon): The ball suddenly started rolling toward the back of the wagon. What pushed it? I don't know - "g forces", maybe. What exerted this mysterious "g force" on the ball? I don't know, maybe the acceleration of the wagon exerted the "g force".

Notice that in the first case, Newton's First Law gives a very simple, straightforward explanation. The ball was at rest, it stayed at rest. End of story.

In the second case, life is not so simple. Here, the ball no longer obeys Newton's First Law - it suddenly jumps up and takes off toward the back of the wagon all by itself! No, wait a minute - that can't happen. There has to be some force that pushed the ball - but where did this force come from? You didn't see anything pushing the ball - but something has to be pushing, Oh my! What a mess!

One of the points of this "thought experiment" is that all reference frames are not created equal. In dynamics, some reference frames are clearly easier to use than others, and you need to know the difference. In the first case, your frame of reference is the Earth, which is not accelerating (Ok, see below...). In this frame of reference Newton's First Law works simply and wonderfully. A reference frame that is not accelerating is called an inertial reference frame - because the Law of Inertia works there.

On the other hand, when you were moving with the wagon, you were viewing the motion from an accelerating reference frame (often called a non-inertial reference frame). In this reference frame, Newton's First Law does not seem to work, since the ball seems to "take off" toward the back of the wagon all by itself. Since people seem to have a deeply-ingrained belief that balls don't "just take off by themselves", they tend to believe that there must be a force acting on the ball to cause this behavior - the "g force". This, however, leads to even more problems and muddled thinking - what exerts this mysterious "g force"?

The easy answer is - There is no force! Certainly, no force was necessary to explain the (same) motion in situation 1 - and a force is either there, or it isn't. You can't have a force when you look at a situation in one way, and no force when you look at the same situation in another way! This "g force" is an example of a fictitious force - there is actually no force! Fictitious forces tend to appear when you are viewing a motion from an accelerating reference frame.

G forces, centrifugal forces, etc. are all fictitious forces that arise merely because you are viewing the motion from an accelerating reference frame - they do not actually exist. See "Riding in a Car" for more details.

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Some Minor Backpedaling:

"You said above that the Earth was an inertial, that is non-accelerating, reference frame. But isn't it true that the Earth both rotates on its axis and revolves about the Sun? Since the direction of a point on the Earth's surface is constantly changing, doesn't that mean that the Earth is, in fact, accelerating?"

Yes, it is true that every point on the Earth's surface is accelerating as the Earth goes about its daily rotation on its axis and yearly revolution around the Sun. However, these accelerations have only very small (though measurable) effects. For all practical purposes, the Earth is an inertial frame of reference.

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