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There is no rule behind naming axes, but it is tradition to call the principle horizontal direction + x. Attach these directions (called axes) to a point in space (called the origin) and you've just created a coordinate system. Identifying the appropriate perpendicular directions in a kinematics problem is one of the first steps in solving it. It is correct to say that "pressure is orthogonal to volume", however. The situation here is a bit more complicated than just saying "pressure is independent of volume", but it should be apparent that saying "pressure is perpendicular to volume" doesn't make any sense. In thermodynamics (the study of heat and work) pressure and volume behave like up-down and left-right do in kinematics. Any two measurable things that are independent of one another can be considered dimensions. The thing with dimension is that it refers to more things than just the number of independent directions. Since "perpendicular" is a completely adequate word, "orthogonal" may seem unnecessarily pretentious. Orthogonal directions are always perpendicular to one another. I really can't decide to "turn up" while walking in the same way that I can decide to "turn left". That one option results in upward motion while the other results in downward motion seems more a function of the surface of the Earth than in any choice on my part. The freedom to go "up" or "down" a hill is really just the freedom to choose between going "forward" or "backward". That's why walking is not normally considered a three-dimensional activity. Walk east or west all you like, you'll never see any north-south change in your position. Two directions are orthogonal if there is no way that motion along one of these directions could result in motion in any of the other directions. These choices are mutually exclusive of one another - a property that is known as orthogonality. There are always three choices available to the people and animals that fly… forward or If I walk far enough my altitude is also sure to change, so you might consider walking a three-dimensional activity, but this is merely a response to the Earth's surface.įlying on the other hand is a truly three-dimensional activity especially for helicopter pilots and hummingbirds. This second degree of freedom makes walking a two-dimensional activity. I also have the option to move forward or backward that is, across the street or back into my apartment. When I step out of my apartment on to the sidewalk there is essentially one decision I have to make… left orīut I'm not some sort of computer-driven robot forced by the definition of "sidewalk" to choose only between these two options. During one-dimensional motion, the objects moving have only one degree of freedom. In previous sections, we discussed how the kinematic variables of distance, displacement, speed, velocity, and acceleration can be used to analyze motion in a straight line.
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