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Unformatted text preview: LENGTH — TIME ~ MOTION
Once we have a way to measure the dimensions of length along three mutually
perpendicular directions we can locate the position of any object in the universe. We begin by choosing a point which we call the origin (0) and draw three mutually
perpendicular lines which we label x-axis, y—axis and z-axis x9 left-r1 ght
y-> up—down z—> back and forth The location of any point is then uniquely determined by the triplet of numbers called
“coordinates”. For instance, if we write (3m, 4m, 5m) that ﬁxes the point where starting
for O we go 3m right, 4m up and 5m forward. Altemately (-3m, 4m, ~5m) is a point
reached by going 3m left, 4m up and 5m back. - So we have a well deﬁned method for ﬁxing the position of any object in our
universe. However, if all objects always remained ﬁxed the universe would be very dull.
It is far more fun to take the next step: our “point” object is moving. This requires us to
introduce the next “player” in our description of the universe. TIME All of us are aware of the passage of time, but establishing a succinct deﬁnition of
time is by no means easy. Indeed, we use concepts of “before” and “after” or
alternatively “cause” and “effect” to put a sequence of eventsin order to mark the flow of
TIME. It is therefore not surprising that a meaningful method of measuring time
developed long after people had learned to gauge the extent of space; the development of
the simple clock owes its existence to the brilliant observation made by Galileo that the
time elapsed for the chandeliers, in a cathedral, to swing back and forth was controlled
only by their length (incidentally, he made the measurement with reference to his pulse
beat). We will discuss the precise reasons for this much later, but once this ﬁnding
became available the simple pendulum clock followed 'soon after and measurement of time got a ﬁrm footing, As you will learn in the very ﬁrst experiment the period of a
pendulum of length l is T = 27r(—l—)% Where g = 9.8m/sz.
g So, in our master table the next row is TIME T 1 second scalar and the intervals of every day interest are: minute 6OSec
Year** 365 % days *Time taken by Earth to turn on its axis once.
* *Time taken by earth to complete one revolution around the Sun. MOTION Once we have a measure of both position and time we can introduce the simplest
parameter to describe motion: speed (S) S: distance traveled
time taken S LT ‘1 m/sec scalar
It is useful to look at an everyday speed to relate it to SI units. 60mph = 88ft/sec = 26.82m/sec ...
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- Spring '10