PHYSICS UNIT 0:
FOUNDATIONS
MEASUREMENT

Units of Measure - Metric System (SI)

Fundamental Units: defined by scientists
Dimension
length
mass
time
current
temperature

Unit
meter
kilogram
second
ampere
Kelvin
Symbol
m
kg
s
A
K
Derived Units: combinations of fundamental units
2
 ex: area measured in m , density measured in
g/cm3
Measurement





Important Ranges of Magnitudes to
remember
Distances – size of a nucleus(10^-15 m) to
size of the universe (10^25 m)
Masses – mass of an electron(10^-30 kg) to
mass of the universe (10^53 kg)
Times – time for light to pass a nucleus
(10^-23 s) to age of the universe (10^18 s)
So what are the order of magnitude
differences?
MEASUREMENT

prefixes: for larger or smaller quantities
Prefix
Giga
mega
kilo
deci
centi
milli
micro
nano
Symbol
G
M
k
d
c
m
m
n
Value
Example
109 30 Gb = 30,000,000,000 b
106 2.1 Mm = 2,100,000 m
103 3.5 kg = 3500 g
10–1 8.7 dL = 0.87 L
10–2 5.9 cs = 0.059 s
10–3 7.2 mmol = 0.0072 mol
10–6 4.4 mm = 0.0000044 m
10–9 9.0 ng = 0.000000009 g
MEASUREMENT

conversions from one prefix to another:
mega kilo
none deci centi milli
1000 1000 10
larger units
divide
10
10
micro
1000 1000
smaller units
multiply
nano
MEASUREMENT

conversion factors - multipliers that change units
without changing equation’s overall value
(factors have a value of 1)
 ex: 1 in = 2.54 cm
factors:  2.54 cm   1 in 




1 in
 

  2.54 cm 
set up so units cancel
ex: find the kilometers in 1 mile
1 mi
 5280 ft 


1
mi


 12 in   2.54 cm 

 

1
in


1
ft


 1m 


100
cm


 1 km 


 1000 m 
 1.60 km
MATHEMATICS

Scientific Notation: shorthand for large
& small numbers
form: 0.00 × 10 0 (number ≥ 1 & < 10 ×
power of 10)
 ex: 450,000,000 = 4.5 × 100,000,000 = 4.5
× 108
–6
 0.0000036 = 3.6 × 0.000001 = 3.6 × 10

MATHEMATICS

Scientific Calculators



4.5 × 108 is entered 4
and may appear as 4.5
3.6 × 10–6 is entered 3
and may appear as 3.6
5
.
08 or
.
6
-06 or
EE
8
4.5 08
EE
+/-
3.6 -06
some calculators use EXP instead of EE
6
UNCERTAINTY

Significant Figures
shorthand way of showing precision &
uncertainty
 number of sig. fig's = # of digits BUT don't
count beginning zeroes AND don't count
ending zeroes unless there is a decimal.
234.15
14.080
560,000
0.00282
5.6 × 105

UNCERTAINTY

Significant Figures
 calculations cannot be more exact than
measurements:
 a. round off to least number of sig. fig's
ex:(1.05)(39.04)(251,000)(0.0044)=45271.5
65
round off to 2 sig. fig's = 45,000
 b. round off once, at the end of all calculations
 c. when in doubt, round to 3 sig. fig's
PHYSICS
UNIT 0: FOUNDATIONS
The 2 Major Types of Error in
Experimental Physics




Systematic Error- Errors inherent in the
system of data taking. (Can not be cancelled
with lots of data)
Example – using an uncalibrated scale.
Random Error- are inherently unpredictable.
(Can be cancelled out with lots of data)
Example – stopping a stop watch too early
sometimes and too late other times.
Systematic Error

There are 3 major types of systematic error



human error: mistakes in reading & recording
 make repeat measurements (Do not include in lab
write up, instead fix human problem).
method error: mistakes in measurement methods
 choose the best method & use it consistently.
instrument error: mistakes due to damaged instruments
 check instrument calibration, use carefully.
UNCERTAINTY


Accuracy- the degree of closeness of experimental
result with theoretical result. (Low systematic
error)
Assessing accuracy: percent error (if you know
what the measurement should have been by other
methods)
|O – A|
|observed – accepted|
% Error = A
×100=
×100
accepted
UNCERTAINTY

Precision: limitations of a measuring instrument
(Sensitivity)
 the more digits you can read, the more precision
(less uncertainty)
 A precise measuring device will take repeated
measurements that are close to each other.
11
11
0.60.6
± 0.1
± 0.1
0.63
0.63 ±± 0.01
0.01
(less
(less
certain
certain
- 1- 1digit)
digit) (more
(more certain
certain --22digits)
digits)
GRAPHING



choose & show scale on
each axis - fit all data
label each axis: measured
quantity & units
 title graph
 dependent variable: y,
independent variable:x
 Uncertainty in data
should be included on
graph
 Include the equation that
best fits the data
Distance Fallen vs. Time
2
y = 5x
Distance Fallen (m)
purpose: finding patterns
& relationships
drawing graphs:

500
400
300
200
100
0
0
2
4
6
Time (s)
8
10
GRAPHING

graph interpretation:
 linear relationship: as x
increases, y increases
(y  x)
 y = mx+b
 m: slope, b:y-intercept
 Said “The distance
traveled by a car
moving at constant
speed is directly
proportional to the time
travelled.”.
GRAPHING

graph interpretation:




quadratic relationship:
as x increases, y
increases (y  x2)
y = kx2
k: appropriate constant
Said “The bacteria
population grew
exponentially with time.”
GRAPHING

graph interpretation:




inverse relationship: as x
increases, y decreases (y
 1/x)
y = k/x
k: appropriate constant
Said “For any given
constant force acting on
an object there is an
inverse relationship
between and object’s
mass and it’s acceleration”
UNIT 0 QUIZ PREVIEW


Concepts Covered:
 metric system: units, prefixes & conversions
 accuracy, precision & significant figures
 math skills – algebra, scientific notation,
estimation, types of graphs.
What’s On The Quiz:
 __ multiple choice/matching
 __ problems
Equations for Propagating Error
Sum
( A  A)  ( B  B)  ( A  B)  (A  B)
Difference ( A  A)  ( B  B)  ( A  B)  (A  B)
Product
 A100%   B100% 
( A  A)  ( B  B)  ( A  B)  


A  
B 

Quotient
 A100%   B100% 
( A  A)  ( B  B)  ( A  B)  


A  
B 
