Introduction to Physics
Significant Figures:
Is a digit significant?
All non-zeroes are significant.
Zeroes might or might not be.
Use the box-and-dot method to determine the sig figs
in a given quantity.
?
1. Identify the leftmost AND rightmost non-zeroes.
2. Draw a box around these AND everything in-between.
3. Everything in the box is significant.
4. NOTHING on the box’s LEFT is significant.
5. If there is a decimal point ANYWHERE, the digits
on the box’s RIGHT ARE significant. Otherwise, no.
3
80.0
3
0.0944
2
0.0032
1
2000
6
1300.40
5
124.00
3
0.00304
3
0.0250
In scientific notation, the
exponent has no effect on
the number of sig. figs.
3
1 . 4 0 x 109
3
5 . 0 6 x 10–3
4
7 . 1 2 0 x 105
2
7 2 0 x 103
7.2 x 105
Rules:
Significant Figures and Mathematical Operations
1. When multiplying or dividing, the answer must
have the same number of sig. figs. as does the
quantity with the fewest sig. figs.
.
1.52 C . 3.431 s = 0.443 C/s
.
0.0251 N x 4.62 m . 3.7 s = 0.031 N.m/s
2. When adding or subtracting, the answer must be
rounded to the place value of the least precise
quantity.
2.53 s + 117.4 s =
119.9 s
2.11 m + 104.056 m + 0.1205 m = 106.29 m
3. Because conversion factors are exact numbers,
they do NOT affect the # of sig. figs. Your answer
should have the same # of sig. figs. as does the
quantity you start with.
Round to the correct number of significant figures.
Calculator
says…
2 sig. figs.
3 sig. figs.
5 sig. figs.
75.6
76
75.6
75.600
0.528396
0.53
0.528
0.52840
387600
390,000
388,000
* 3.8760 x 105
4200
4,200
* 4.20 x 103
4.2000 x 103
8.4845E-4
8.5 x 10–4
8.48 x 10–4
8.4845 x 10–4
* = requires scientific notation
SI Prefixes to Memorize
exp
Prefix
gigamegakilodecicentimillimicronanopico-
Symbol
G
M
k
d
c
m
m
n
p
Meaning
109
106
103
10–1
10–2
10–3
10–6
10–9
10–12
109
106
103
10–1
10–2
10–3
10–6
10–9
10–12
10–15
Giga
“Got
Mega
my
kilo
kilt,
deci
Dad!
centi
Can’t
milli
miss
micro midsummer’s
nano
nopico
pants
femto Friday!”
Math Review
Conversions
Convert 4.83 cm to nm.
1 cm = 1 x 10–2 m
equivalence statements:
(
1 nm = 1 x 10–9 m
)(
–2 m
1
x
10
4.83 cm
1 cm
=
48,300,000 nm
=
4.83 x 107 nm
)
1 nm
1 x 10–9 m
Convert 418 km/h to m/s.
equivalence statements:
418 km
h
(
1 x 103 m
1 km
1 km = 1 x 103 m
1 h = 3600 s
)(
1h
3600 s
)
=
116 m/s
=
1.16 x 102 m/s
Solving Equations for a Variable
L
Solve for g. T  2
g
-- Divide both sides by 2.
-- Square both sides.
-- Cross-multiply.
-- Divide both sides by T2.
T
L

2
g
T2 L

2
4
g
2
2
gT  4 L
4 2L
g
T2
Solve for Qc.
ni sin Qc  nr
-- Divide both sides by ni.
-- Take the
sin–1
of both sides.
nr
sin Q c 
ni
 nr
Qc  sin 
 ni
-1



Trigonometric Functions
SOHCAHTOA
Find h and s.
29.8 cm
h
62.1o
s
29.8
Since… sin 62.1 
h
29.8
then… h 
= 33.7 cm
sin 62.1
29.8
Since… tan 62.1 
s
29.8
then… s 
= 15.8 cm
tan 62.1
Error – All measurements contain error
• Relative Error –
• Absolute Error –
absolute error divided
actual difference
by the accepted
between the
value. Usually
measured (observed)
expressed as a
value (O) and the
percentage
accepted value (A)
𝐸𝑎
• 𝐸𝑎 = 𝑂 − 𝐴
• 𝐸𝑟 =
𝑥 100
𝐴
Deviation
• Absolute Deviation
- difference between
a single measured
value and the
average of several
measurements
• 𝑫𝒂 = 𝑶 − 𝑴
• Relative Deviation
• 𝑫𝒓 =
𝑫𝒂
𝑴
𝒙 𝟏𝟎𝟎
Physics: the study of the
natural world
few concepts
few equations
F
a
m
V
I
R
p  mv
describe many
phenomena
F  kx
E
hc

Areas of Physics
Mechanics: forces and motion
Vibrations and Waves
Optics:
light, mirrors, color, lenses
electricity
Electromagnetism: and
magnetism
Relativity:
counterintuitive
properties of
space and time
Quantum
Mechanics:
the probabilities
and behavior of the
infinitesimally small
?
heat,
work,
Thermodynamics:
order vs. disorder
Physics is the most basic of the sciences.
biology
chemistry
physics
mathematics
The Nature of Science
Science
or
Religion?
science
religion/philosophy
investigates
observable
universe
relationship
defines
purpose
-- cause-effect
-- why we are here?
-- demands evidence
-- what should we do?
-- belief system
-- belief system
Pure vs. Applied Science
pure science: the search for knowledge
-- facts
-- relationships between things
-- theories
applied science using knowledge
(technology): in a practical way
-- tools
-- techniques
-- using science creatively
The Scientific Method
Credited to…
Galileo Galilei (1564 – 1642)
and
Sir Francis Bacon (1561 – 1626)
Activities of the Scientific Method
Observe events. -- Quantitative data
are most useful.
Propose a hypothesis: a reasonable and testable
answer or explanation
Carry out controlled experiments:
the experimental and control
groups differ by one variable
Draw a valid conclusion.
Other Important Terms
We cannot study everything at once.
system: what we choose to study
surroundings: everything else
Models simplify phenomena.
To understand,
we must simplify.
Law or Theory?
law: states what happens
-- states a relationship between two or
more quantities (often via an equation)
e.g., conservation laws, gravity
theory: tries to explain why or how
something happens
-- based on current evidence
-- can be revised (or thrown out)
e.g., phlogiston theory, atomic theory, KMT
Measurements in Experiments
Measurements have
dimensions and require units.
give the quantity
LENGTH………………….
MASS……………………..
TIME………………………
ELECTRIC CURRENT….
SI base units
give the scale
meter (m)
kilogram (kg)
second (s)
ampere (A)
derived units: these result when base units are
.
combined by X or .
e.g.,
area  m2
density  kg/m3
volume  m3
momentum  kg.m/s
Accuracy and Precision
All numerical data are the result
of uncertain measurements.
precision: a measure of the degree of
fineness of a measurement; it
depends on the extent to which the
instrument is calibrated
e.g.,
10 m
vs. 10.00 m
vs. 10.00000 m
When repeated, precise measurements yield
similar answers each time.
e.g., precise…
0.653 m
0.652 m
0.654 m
imprecise…
0.7 m
0.8 m
0.6 m
A good rule of thumb is…
It is the % difference that is important.
accuracy: how close a measured
value is to the true value
Three types of error can affect accuracy.
human error: mistake in reading instrument
or recording results
-- minimize with repeated measurements
method error: using measuring instrument improperly
e.g., parallax in measuring with a meter stick
instrument error: measuring device is
improperly calibrated
e.g., bathroom scale that reads 5 lbs. too heavy
Extrapolating or Interpolating
Between Data Points on a Graph
For the line between
(4.5 s, 12.4 m) and
(8.3 s, 17.6 m), find
the slope, with units.
Position (m)
Position v. Time
(8.3 s,
17.6 m)
(4.5 s,
12.4 m)
Time (s)
Δy 17.6 m - 12.4 m
m
m
 1.4

Δx
s
8.3 s - 4.5 s
Position v. Time
Position (m)
Find the time at
which y = 65.3 m.
y
Since m 
x
then
and
y
x 
m
(4.5 s,
12.4 m)
Time (s)
x  t - 8.3 s
Solve for
(8.3 s,
17.6 m)

65.3 m - 17.6 m

1.4 m
s

65.3 m - 17.6 m
t
 8.3 s
1.4 m
s
 42 s
How Does the Universe Work?
Formulating a Data-Driven Model
Scientists must base their models of the
universe on measurable, observed data.
1. Given the examples below, what are the two basic
“objects” in that universe?
Adapted from Helen Quinn, “Of Quarks, Antiquarks, and Glue,” Stanford Magazine, Fall 1983, p. 29.
2. What are the rules that govern the forces
(i.e., attachments) between objects?
Observed Objects
Not Observed
1. Basic particles: square and triangle.
2. Rules for attachments:
-- squares must be attached on two,
and only two, sides
-- triangles must be attached on one,
and only one, side
3. Come up with two more examples of objects
that could be observed.
Step 3 is similar to what particle
physicists do when studying the
products of subatomic collisions.
Significant Figures
Rules: Is a digit significant?
1. All non-zeroes are significant.
2. Place-holder zeroes are
NOT significant.
3. Any final zero used after a
decimal point is significant.
2
0.0032
3
0.0944
1
2,000
3
0.0250
5
124.00
3
52.0
Rules: Is a digit significant? (continued)
4. Zeroes sandwiched between
“significants” are significant.
5. In proper scientific notation,
all figures to the left of the
“x 10exp” are significant. The
exponent has no effect on the
number of sig. figs.
3
0.00304
3
80.0
6
1300.40
3
1 . 4 0 x 109
3
5 . 0 6 x 10–3
4
7 . 1 2 0 x 105
2
7 2 0 x 103
7.2 x 105