# Inertial Frames of Reference

## Accelerated Motion and Inertial Frames of Reference

### Inertial Frame of Reference and lack of sensation of motion

Imagine riding on a soundproof, maglev train on a very straight and level track. Do you feel like you are moving? If you look out the window, you can certainly see that the country side is moving by very fast; but can you feel the motion? You certainly can feel the motion if you are riding along on a horse drawn cart over a very bumpy road. But notice, when you glide along without bumps, sharp turns or sudden speed ups or slow downs, you do not feel the motion. Your frame of reference is an inertial frame of reference.

### We feel accelerations of our Frame of Reference

What is it about our sensation that makes us feel as if we are moving or standing still? Imagine an extreme case of the feeling of motion. You are a passenger in a car and have not buckled up. The tires skid on black ice and the car hits a tree. Suddenly, you are thrown through the windshield. That was certainly a sensation of motion: one moment you are stilling there quietly, and the next, you are airborne and flying through the window. It feels as if an invisible force picked you up and hurled you through the window. An example that is not so extreme helps us think about what it is that gives us the sensation of motion. You are riding on a roller coaster. As you go around a sharp turn, you sway toward the convex side of the turn. As you rise to the top of a downturn and begin to go down, you begin to rise out of your seat, and it also feels as if insides are moving up inside of you. From these experiences, we observe that the sensation of motion comes from feeling tensions within your own body in response to acceleration.

### Accelerations of physical objects in our frame of reference correlate with our sensations of motion

Another observation links the experiences of motion with physics. Suppose that you are riding along with a friend who has a trinket dangling from his rear view mirror. Notice that when the car is on a straight, level stretch and moving at a constant speed, the trinket behaves just as it does in your living room. If it is hanging down, at rest, then it continues that way as long as the road remains straight and level and the speed of the car stays the same. But notice that when the car hits a bump in the road, the trinket is suddenly jerked and begins to dance around. Now suppose that the trinket is again still, and the car goes around a turn, the trinket then swings outward toward the convex side of the turn. We notice that our sensations of motion are linked with the response of the trinket to sudden changes of the motion of car. As far as motion is concerned our sensation of motion is linked with the way other physical objects respond to accelerations in our environment.

### Motion through space in an inertial frame of reference in not absolute

Galileo Galilei, and others following his lead, noticed that there is no physical way of detecting absolute motion. In fact, there is an infinite set of possible, moving platforms, in which physics experiments come out the same way, even if they are all moving at a constant speed and fixed direction relative to each other. Despite its spinning and orbiting the sun, the surface of our earth moves with such gentle acceleration that we do not feel the effect of its motion. It approximates the kind of platform that we are talking about here1. The same is true of the planet Mars. Scientists expect physics experiments performed on Mars to give the same results as those performed on Earth.

A platform relative to which we refer experimental measurements is called a frame of reference, and a frame of reference, within which no absolute motion is detectable, is called an inertial frame of reference. All inertial frames of reference move relative to each other at a constant speed and direction. To the extent that the ground approximates an inertial frame of reference, a bullet train moving along a straight and level track at a constant speed, also approximates an inertial frame of reference. When the acceleration of our frame of reference produces noticeable sensations, our frame of reference is not inertial.

### Velocity--speed and direction

Because both a change in speed and direction are important in physics, the idea of speed has to be generalized to velocity incorporates information about both speed and direction, namely a vector, which is defined as a mathematical object that is defined by both its magnitude and a its direction. The vector that describes the motion of an object is called velocity, which you can think of as an arrow pointing in the direction of an object's motion and having a length equal to its speed. An acceleration of the objects manifests itself as any combination of a rotation or variation of the length of the arrow, and is itself a vector. To really understand physics, which means mathematically as well as intuitively, you have to learn the mathematics of vectors: how to add and subtract them as well as how to multiply them.

### Relativity and everyday experience

Since every experiment that we can do in one inertial frame of reference turns out the same way in every other inertial frame of reference, we can say that every observer on an inertial frame of reference will agree on the same laws of physics. Even if you are not a physicist, but have some stake in the way matter moves, you will be able to operate the same in every inertial frame of reference, but not in an accelerated frame of reference. Say you are an expert ping pong player, you will do as well in every inertial frame of reference. However, to the extent that the frame of reference departs from inertial, you will be seeing the effects of phantom forces that cause the ball to behave in an erratic way. For example, suppose that a ping pong game began on a boat gliding over a glassy smooth sea, the players are operating in a nearly inertial frame of reference. Suddenly a squall stirs up heavy swells. Even though the game may be in and enclosure so that no wind gusts blow the ping pong ball off course, the rocking and pitching of the ship will throw off the trajectories of the ball in unforeseen ways. The experiences of the players that they practiced in inertial frames of reference (the rules of ping pong) will no longer work. Their skills will suddenly become invalid, and the game becomes one of chance.

In more modern times , Albert Einstein realized, that the concept of relativity is more involved that what Galileo described.

Einstein's theory is call the Special Theory of Relativity which preserves the same value of the speed of light in all inertial frames of reference.

1Actually, the rotation of the earth is detectable through experiment using a Foucault Pendulum, which is discussed in a later section. Further, planets in orbit are in free fall around the Sun, in which case neither the force of gravity nor the acceleration of the frame of reference is detectable. This effect is part of Einstein's General Theory of Relativity.

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