Chapter 1
ALL THE BACKGROUND INFO
YOU NEED TO KNOW
Standards of Length, Mass and Time
 We will use a standard system of units, called SI
(Systeme International) adapted from the metric system.
 The fundamental units of length, mass and time in the SI
system are:



Meter (m)
Kilogram (kg)
Second (s)
 There are a few other fundamental units, but we’ll get to
them later.
 THE MKS SYSTEM – Don’t forget it!
 TEXT: Look up definitions of the meter, kilogram and
second.
Other Measurement Systems
 If you are using smaller measurements, you might use
the Gaussian or cgs system where the units of length,
mass and time are:



Centimeter (cm)
Gram (g)
Second (s)
 The U.S. Customary system uses:



Foot (ft.)
Slug
Second (s)
 But, we’re going to stick with the MKS system.
 TEXT: Complete the following tables.
Prefixes Used with SI Units
Power
Prefix
Abbreviation
10-15
femto
f
10-12
pico
p
10-9
nano
n
10-6
micro
µ
10-3
milli
m
10-2
centi
c
10-1
deci
d
101
deka
da
103
kilo
k
106
mega
M
109
giga
G
1012
tera
T
Dimensions
 The dimensions of length, mass and time are used in
many different combinations throughout physics.
 Length, mass and time are considered base units. (They
cannot be broken down into any more “basic” units.)
 Think about some quantities that you know of that
combine these units.
 Some examples:





Speed : mile/hour (mph), meter/second (m/s)
Volume : cubic meter (m3)
Area : meters squared (m2)
Density : kg/m3
Acceleration : (m/s2)
 These are called derived units.
Dimensional Analysis
 Dimensional analysis uses the fact that dimensions
can be treated as algebraic quantities.
 Examples:


Show that the expression v = vo + at is dimensionally correct
where v is velocity (m/s), a is acceleration (m/s2), t is time (s)
Find a relationship between acceleration (a), velocity (v), and
distance (r) for a particle traveling around a circle.
Significant Figures
 When taking measurements, we can measure to the
smallest increment of the instrument and then
estimate one more digit.


For example, for a ruler that can measure to 1.0 cm, a
reading might be 16.4 ±0.5 cm.
The ±value indicates the accuracy of the measurement,
which depends on the:
 Instrument
 Skill
of the user
 Number of times the measurement is repeated
When are numbers significant?
 Nonzero digits are always significant
 All final zeros after the decimal point are significant,
e.g. 354.0000 ( 7 sig figs)
 Zeros between two other significant digits are always
significant, e.g. 300004 (6 sig figs)
 Zeros used solely as placeholders are not significant,
e.g. 0.000009 (1 sig fig) or, any zeros preceding a
non-zero digit are not significant.
Rules for Sig Figs
 Multiplying and Dividing:
 The answer has the same number of sig figs that as the least
accurate measurement in the equation.
 Adding and Subtracting:
 The answer has the same number of decimals places as the
measurement with the least number of decimal places.
 Scientific Notation and Sig Figs:
 The format for scientific notation is:
M x 10n where 1  M  10 and n is an integer
 The M value contains the sig figs in the number.

Conversions
 ALWAYS USE THE FACTOR LABEL METHOD TO
CONVERT.
 Steps:




List the conversion factors that are needed. (You can skip this
step after you are good at converting.)
Make fractions with the conversions that will cancel the units
we don’t want.
Multiply the quantity you are converting by the conversion
fraction(s) .
Cancel units as you would algebraic quantities.
Conversion Examples
 Examples:
 If a car is traveling at a speed of 28.0 m/s, is the driver
exceeding the speed limit of 55.0 mi/hr?
 The traffic light turns green, and the driver of a high
performance car slams the accelerator to the floor. The
accelerometer registers 22.0 m/s2. Convert this reading to
km/min2.
Coordinate Systems
 Cartesian Coordinate System (Rectangular
Coordinate System):

Points are labeled with the coordinates (x, y)
9
8
7
6
5
4
3
2
1
0
0
2
4
6
Coordinate Systems (cont.)
 Plane Polar Coordinates:
 (u, θ)
 The standard references are usually the (0,0) point of a graph
and the positive x-axis.
 We’ll talk more about this later.
Trigonometry
 Basic trig is a very important tool in solving physics
problems.
 Pythagorean theorem:

r2 = x2 + y2
 Trig functions:
 sin α = y/r (opposite/hypotenuse)
 cos α = x/r (adjacent/hypotenuse)
 tan α = y/x (opposite/adjacent)
r
y
α
x
Trigonometry Example
 A person measures the height of a building by walking out a
distance of 46.0 m from its base and shining a flashlight
beam toward the top. When the beam is elevated at an
angle of 39.0 with respect to the horizontal, as shown in the
picture, the beam strikes the top of the building. Find the
height of the building and the distance the flashlight beam
has to travel before it strikes the top of the building.
39.0
ْ
46.0 m
Graphing Data
 Independent variable: x-axis
 Dependent variable: y-axis
 Title written: y vs. x
 Set minimums and maximums on axes based on your data.
 Title your axes with value name and value units, e.g. Time
(seconds).
 Always draw BEST FIT straight line or smooth curve. DO NOT
use a series of straight line segments that “connect the dots”.
 If using a computer program:



Find equation of the line or curve.
Substitute appropriate variables for x and y.
Add appropriate units after equation coefficients.
Distance (m) vs. Time (s)
70
60
Distance (m)
50
40
30
20
10
0
0
2
4
6
Time (s)
8
10