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Chapter 1. Physics and Measurement
The universe we live in is one of change and motion.
Although we all have intuition about motion, based
on our experiences, some of the important aspects of
motion turn out to be rather subtle.
TO SAY THE LEAST!!
Chapter Goals:
• to introduce the fundamental concepts of motion as a
measurable phenomenon, using ideas of length and time
• to introduce the concept (not needed yet) of mass
• to remind ourselves of the metric system (Système
Internationale), metric prefixes, and scientific notation
• to get warmed up to the mathematical rules of the game
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Translational Motion
Projectile Motion
Circular Motion
Rotational Motion
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Dimensions: length L
• L is measured in m(eter) [ft, mile, in, ly]
• let x be a position of a point object that can
move only in one dimension [different meaning
of dimension]: 1d motion
• the units of x are denoted [|x|] = m
• note the different fonts
• 1 m := distance traveled by light in vacuum in
1/299,792,458.0 s(econd)
• begs the question: what is a s?
• long ago, was a French platinum bar’s length
• then it was1,650,763.73 wavelengths of Cs light
• cm, km, m, nm, . . .
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Metric Prefixes & Conversion
• a metric prefix is one letter that corresponds to
multiplication of the unit by a power of 10
• sometimes capitalized, sometimes greek
• usually but not always by a power of 1000
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k = kilo = 1000 = 103; M = mega = 106
m = milli = 1/1000 = 10–3; m = micro = 10–6
c = centi = 1/100 = 10–2; cc = cm3 ≠ c(m3)!!
don’t forget that each power of a unit needs to be
converted!!
• example: 1 m3 = 1 m3 (100 cm/m)3 = 1,000,000 cc
• we have injected the number 1 in the conversion,
since 100 cm = 1 m so 1 = 100 cm/m
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Prefixes, cont.
Section 1.1
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A grab-bag of mathematical considerations
• if two things in an expression are added or subtracted,
they are called terms and their dimensions must agree
• you must make their units agree too when it comes to
putting in actual numbers
• the result will have the same units
• if two things in an expression are multiplied or divided,
they are called factors and their dimensions may differ
• the result will have units that obey the same algebra of
multiplication/division
• in complicated unit algebra, whatever is on the top of the
top, and the bottom of the bottom, is actually on the top
• whatever is on the bottom of the top, or the bottom of the
top, is actually on the bottom
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Scientific Notation and ‘Accuracy’ I
• handy for writing very small (close to zero or <<1) and
very large (far from zero or >>1)
• write it as some number between 1 and 10, times a power
of 10, by moving the decimal point that many times to
the L or R
• example: c = 299,792,458.0 m/s = speed of light to 10
significant figures
• jobs: round it off to 5 sig figs and express in sci not
• move decimal point 8 places to L: c = 2.99… x108 m/s
• round off: 6th sig fig is 0 < 2 ≤ 5: c = 2.9979 x108 m/s
• note: if rounded off to 4 sig figs: c = 2.998 x108 m/s
• note: if rounded off to 3 sig figs: c = 3.00 x108 m/s
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Scientific Notation and ‘Accuracy’ II
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example: mass of the electron is m = 9.11 x10–31 kg
[begs the question: what is a g(ram)?]
m = .000 000 000 000 000 000 000 000 000 000 911 kg
0.00000029042 has 5 sig figs
45,700 is probably 3 sig figs but might be 4 or even 5
.5700
is definitely 4 sig figs, while .57 is 2 sig figs
3.0000087800 has 11 sig figs
in this course, 3 sig figs is plenty!
The percentage accuracy is a different thing…
.11 is accurate to 2 sig figs, and to about 10% accuracy
.98 is accurate to 2 sig figs, and to about 1% accuracy!!
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
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Dimensions: time T
T is measured in s(econd) [hr, day, yr, ns]
let t be the time at which some event occurs
the units of t are denoted [|t|] = s
1 s := 9,192,631,770 times the period of vibration
of Cs atom’s radiation [9 or 10 sig fig]
• 1.00 day = (1.00 day)(24 .0hr/day)(60
.0min/hr)(60.0s/min) = 86,400 s [3 sig figs]
Dimensions: mass M
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M is measured in k(ilo)g(ram) [g, slug]
let m be the amount of matter in some object
the units of m are denoted [|m|] = kg
1 kg := the amount of stuff in a French Pt-Ir cylinder
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Derived Quantities
2
• example: area of a circle is A = pr where p = 3.14159
and r is the radius of the circle
• so since [|r|] = m and [|p|] = 1 [|A|] = m2
• Example: mass density of some object of mass m and
volume V is r := m/V
• so since [|m|] = kg and [|V|] = m3 [| r |] = kg/m3
• sometimes particular combinations get named:
• 1 N(ewton) = 1 kg-m/s2 and is capitalized in homage
• 1 Pa(scal) = 1 N/m2 = 1 kg/m-s2
• In all there are 7 fundamental dimensions [A(mpère) for
electromagnetism; K(elvin) for thermal physics;
c(an)d(ela) for illumination physics; mole for counting
large numbers of things in chemistry]
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