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#yellowvan Drawing and the Brain

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#yellowvan Drawing and the Brain

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General
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Tuesday, 09 August 2016
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Adam Rangihana

 

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Category
General
Created
Tuesday, 09 August 2016
Group Admin
Adam Rangihana
  • Adam Rangihana
    How to Calculate the Force of Gravity on the Earth’s Surface
    Started by Adam Rangihana Wednesday, 17 August 2016 2 Replies
    Adam Rangihana

    Part of the problem is the word time and how it is misused. Time can mean, among other things, the reading on a clock at a particular moment or the difference in two such readings. The former should be more correctly called a clock reading while the latter should be more correctly called a duration. Another part of the problem is that authors use the same symbol, usually just tt, to represent both of these quantities! While tt is fine for a clock reading, a better symbol for duration is ΔtΔt. I fault the authors of physics textbooks, especially introductory textbooks, for perpetuating this obfuscation and its resulting confusion to students. Anyway, there is hardly ever (I can't think of one as I write this) a case in physics when we need to substitute a clock reading into a kinematic or dynamic equation. In every case I can think of, what we really deal with is duration ΔtΔt, and there are two reasons for this. The first is that the numbers on a clock, although astronomical in origin, are otherwise completely arbitrary and thus have no inherent physical significance. The second is that the difference between two clock readings does indeed have great physical significance. It is the latter, duration, that appears in the definitions of velocity, acceleration, and any other physical quantity that involves "time" (note the quotes). Now, to specifically address your question about the meaning of acceleration, consider that the correct articulation of the definition of average acceleration is the change in an object's velocity compared to the duration through which that change in velocity happens. That is far more physically accurate than the sloppy and overly simple distance over time. I always make sure my students learn the more correct definition; it prevents so many errors. Next, look at the unit for acceleration. It must be the unit of velocity (m/sm/s) compared to the unit of duration (ss). This can correctly be written as the obtuse (and nearly devoid of physical meaning) combination m/s2m/s2 but this hides the meaning so clearly articulated by the better definition given above. So, write the unit of acceleration as m/ssm/ss and read it from the bottom up. An acceleration of, say, 3m/ss3m/ss would be read and interpreted as "For every second of duration, the object's velocity changes by 3m/s3m/s." Remember that acceleration is a vector quantity so there could, in general, be both a change in magnitude and a change in direction. Any such arbitrary change can be decomposed into a change that is parallel (or antiparallel) to the original acceleration and a change that is perpendicular to the original acceleration. My point is we should also quote a direction, but I didn't do that here. Your point about the meaning of time squared is a great question and one that should be brought up by more students. Time squared means nothing. Duration squared, on the other hand, is physically meaningful and is the basis of our physical understanding of motion. You bring up another issue, and that is the term distance. It too has been somewhat abused, but I'll save that for another time if anyone asks. I really wish the community would hold textbook authors accountable for this serious abuse of terminology and notation.

    Last replied by Adam Rangihana on Friday, 19 August 2016
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