Noninertial Frames

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Chapter 11 Noninertial Frames

So far we have studied motion with respect to inertial observers. For these observers, Newton’s second law of motion takes the familiar form, $\vec F = m\vec a$ for a constant mass particle or in general, $\vec F = d\vec p/dt\text{.}$

Observers that have a non-zero acceleration with respect to an inertial observer are called non-inertial. When the second law of motion is written in a non-inertial frame, the equation of motion is modified. The new equations of motion contain force-like terms that are not present in the inertial frame; these new force-like terms are called fictitious or inertial forces. We will study these modifications in this chapter.

A particularly important application of these modified equations is to the frames fixed to the Earth, also called Earth-based frames. Since Earth is rotating about its axis, all observers on the Earth are accelerating with respect to any fixed inertial frame, say a non-rotating frame fixed to the center of the Earth. This makes all Earth-based frames that rotate about the fixed frame non-inertial.

We will see below that two inertial forces arise, viz., centrifugal and Coriolis forces arise in Newton’s second law of motion in a rotating frame. We will study their implications in some detail in this chapter. But, first we will study a simple frame that is accelerating in a straight line with respect to an inertial frame and then we study rotating frames.

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