Physics Lesson 18.1.1 - Inertial Frames of Reference. Galilean Relativity

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Welcome to our Physics lesson on Inertial Frames of Reference. Galilean Relativity, this is the first lesson of our suite of physics lessons covering the topic of Relativity. Galilean Transformations. Einstein's Postulates and Newton's Laws, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Inertial Frames of Reference. Galilean Relativity

In physics, a frame of reference is an arbitrary set of axes used to determine the position of an object or the physical laws that govern its motion. When explaining the motion of objects in Section 3, the first thing we did, was appointing an (fixed) origin and a positive direction to any possible motion and then, calculating the corresponding quantities (especially any change in them) accordingly.

Thus, for example, if we say: "An object is at x₀ = 2m and then it moves at x = 7m" we mean: "The object was initially 2 m away from the fixed origin in the positive direction and then, it moved for other 5 m still in the positive direction and finally reached the position x = 7m. Therefore, the displacement of the object is Δx = x - x₀ = 7m - 2m = 5m."

However, as pointed out above, these values are obtained when we assume the origin as fixed (non-moveable). If the moving object was a car and one was inside the car, he would not agree with our opinion about the above numbers (the change in coordinate). He would probably choose any point inside the car (for example his seat) as origin and measured any change in coordinates accordingly. In this case, this person would get the values x₀ = 0 and x = 0 and for the corresponding displacement: Δx = x - x₀ = 0m - 0m = 0m.

In the above example, there are two frames of reference. The first frame is connected to the observer at rest (the person who is standing up outside the car), while the other is connected to the observer in motion (the person sitting inside the car). If they are looking to each other, they obtain the same value for the displacement. Thus, for the observer at rest, the car (and the person inside it), moves by 5 m due right. The same thing occurs to the person who is sitting inside the car; it seems that the observer at rest is moving by 5 m due his right as well, when he looks from the car window.

Thus, in the above example, we have two distinct frames of reference (i.e. places that are moving at constant speed relative to each other): one is at rest (as it looks to the observer at rest) and the other is in synchronized motion to the moving observer. It is obvious that Newton's Laws of Motion can be applied in both the above reference frames with the proper corrections. Thus, if the car is moving at constant speed v, there is no acceleration detected by any of observers, as for the first observer (the one at rest), we have:

and for the one who is sitting inside the car (v = 0), we have:

The above example involves a one-dimensional motion but we can generalize it in three dimensions as well. In this way, we obtain the definition (and explanation) of "inertial frames of reference":

Inertial frames of reference are three-dimensional coordinate systems, which travel at constant velocity. In such frames, an object is observed to have no acceleration when no forces are acting on it. If a reference frame moves with constant velocity relative to another inertial reference frame, it represents an inertial reference frame as well. There is no absolute inertial reference frame; this means there is no state of velocity that is special in the universe. All inertial reference frames are equivalent. One can only detect the relative motion of one inertial reference frame to another.

The term "inertial" derives from the concept of "inertia" discussed in the Newton's First Law of Motion, which implies that an object moves at constant velocity unless an unbalanced force acts on it.

The idea of relativity of motion was not invented by Einstein (who is the first person that comes in our mind when speaking about relativity) but had instead existed in scientific circles long before him. It deals with Newtonian mechanics as well. The key point of relativity concept is that the results of experiments done in any inertial frame will be the same; i.e., one will not be able to determine by some experimental means what frame is at "absolute rest" and which are moving, as all motion is relative. As explained above, an inertial frame is one in which Newton's laws of motion are satisfied. These laws prescribe accelerations, not velocities, so a frame that is moving at constant relative velocity with respect to an inertial frame is an inertial frame as well.

The non-priority of an inertial frame of reference to another inertial one constitutes the Galilean Principle of Relativity, formulated in 1635, long before Einstein generalized the concept of relativity by including non-inertial reference frames as well.

Mathematically, the Galilean Principle of Relativity expresses the invariance of mechanical equations with respect to transformations occurring in the coordinates of moving points (and time) when there is a transition from one inertial system into another. This means we have four variables included in such situations: the three spatial coordinates x, y, z and the time t.

You have reached the end of Physics lesson 18.1.1 Inertial Frames of Reference. Galilean Relativity. There are 5 lessons in this physics tutorial covering Relativity. Galilean Transformations. Einstein's Postulates and Newton's Laws, you can access all the lessons from this tutorial below.

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