Physics and Measurement
What is physics?
Why do we study it?
•
•
•
•
•
Model
Theory
Observation
Law
Empirical Law
Significant Digits
• 23.21 m
• 0.062 m
• 8200 m
6.2x102 m
Scientific notation helps!!!
Area  0.062 m  23.21 m  1.43902 m
2
• The final result of multiplication or division
can have only as many significant digits as
the component factor with the least number of
significant figures
• The final result for addition or subtraction
can have no more decimal places than the
term with the least number of decimal places
Area  1.4 m
2
Perimeter = 46.54 m
Base Units
Redefining the meter:
In 1792 the unit of length, the meter, was defined as one-millionth the
distance from the north pole to the equator.
Later, the meter was defined as the distance between two finely engraved
lines near the ends of a standard platinum-iridium bar, the standard meter
bar. This bar is placed in the International Bureau of Weights and Measures
near Paris, France.
In 1960, the meter was defined to be 1 650 763.73 wavelengths of a
particular orange-red light emitted by krypton-86 in a discharge tube that
can be set anywhere in the world.
In 1983, the meter was defined as the length of the path traveled by light in
a vacuum during the time interval of 1/299 792 458 of a second. The speed
of light is then exactly 299 792 458 m/s.
Typical Lengths
Typical Masses
What is Density?
m

V
Typical Times
Three unit systems
Physical Dimensional
Quantity
Symbol
Unit
System
SI MKS SI CGS
Length
[L]
m
cm
Mass
[M]
kg
g
Time
[T]
s
s
US
Customary
ft
s
Three unit systems
Physical Dimensional
Quantity
Symbol
Unit
System
SI MKS SI CGS
Length
[L]
m
cm
US
Customary
ft
Mass
[M]
kg
g
slug
Time
[T]
s
s
s
Unit conversion
AB
1 kg  2.2 lb
A
1
B
1 kg
1
2.2 lb
C 1  C
1 kg
200 lb 
 90.9 kg
2.2 lb
Metric Prefixes
Dimensional (unit) Analysis
1 2
x  at
2
1 L
[L]  [ 2 ][T 2 ]  [L]
2 T
If your units do not work out, your answer cannot be correct!
Sometimes you can figure out the correct equation merely
by making the units work!
Estimating
• Often we are looking for order of magnitude
numbers.
• Is the number 1, 10, 100, 1000, 10000?
• Make assumptions. We will have some
standard assumptions:
– Surfaces are frictionless (at first)
– Strings have no mass
– Objects are all treated as if their mass is at a point in
space
– Pulley wheels have no mass
– Forces from springs are linear with displacement
Example
• Enrico Fermi
• Nothing to do with Physics
• Shows the power of order of magnitude estimates
• How many piano tuners are in San Francisco?
(800,000 people in San Francisco)
Lab Data Recording
And Calculating
Uncertainty
• Precision = Repeatability
• Accuracy = Correctness
measurement = best measured value  uncertainty
uncertainty
fractional uncertainty =
best measured value
uncertainty
percent uncertainty =
100%
best measured value
Propagating Uncertainty
• Addition/Subtraction: Add the uncertainty in the
individual terms
If C=A+B, Then C=A+B
• Multiplication/Division:
– Add the fractional uncertainties of the factors
C A B
If C=AB, Then
=
+
C A B
– Use extreme values of factors and subtract
If C=AB, Then C=  A+A  B+B -AB
What does it mean to agree?
0.5
5.0
0.5
0.25
4.8
0.25
Measurement A
Measurement B
Do Measurements A and B agree?
What does it mean to agree?
0.5
5.0
0.5
0.25
4.2
Measurement A
0.25
Measurement B
Do Measurements A and B agree?
What does it mean to agree?
0.5
5.0
0.5
0.25
4.6
0.25
Measurement A
Measurement B
Do Measurements A and B agree?
What does it mean to agree?
0.5
5.0
0.5
0.25
4.4
0.25
Measurement A
Measurement B
Do Measurements A and B agree?