1. Chapter 1 Measurement Lecture Notes
Phy 201: General Physics I
Chapter 1 Measurement
Lecture Notes

2. Observations
The sciences are ultimately based on observations of the natural (& unnatural) world
There are 2 types of observations:
Qualitative
Subjective, touchy-feely
Example: the outside temperature is hot today
Quantitative
Objective, based on a number and a reference scale
Quantitative observations are referred to as measurements
Example: the outside temperature is 80oF today
Notes:
Quantitative observations are only as reliable as the measurement device and the individual(s) performing the measurement
The accuracy associated with a measurement (or set of measurements) is the often specified as the % Error:
The precision associated with a set of measurements is the often specified as the % Range:

3. Systems of Measurement
There are several units systems for measurement of physical quantities
The most common unit systems are the metric and the USCS systems
For consistency, the l’Systeme Internationale (or SI) was adopted
The SI system is a special set of metric units
International System (SI) base units:
Mass Kilogram kg
Length meter m
Time second s
Temperature Kelvin K
Current Ampere A
Luminous Intensity candela cd
Amount of substance mole mol
All of the other SI units are derived from these base units
Examples of derived units:
1 Newton = 1 N = 1 kg.m/s2
1 Joule = 1 J = 1 kg.m2/s2
1 Coulomb = 1 C = 1 A.s

4. Common Metric Prefixes
Symbol
Meaning
Power of 10
Giga G
1,000,000,000
109
Mega M
1,000,000
106
kilo k
1,000
103
centi c
0.01
10-2
milli m
0.001
10-3
micro
0.000,001
10-6
nano n
0.000,000,001
10-9
Using Metric prefixes:
1 mm = 1x10-3 m  35 mm = 35 x 10-3 m or 3.5 x 10-2 m
1 kg = 1x103 g  12 kg = 12 x 103 g or 1.2 x 104 g

5. Unit Conversion
In physics, converting units from one unit system to another (especially within the Metric system) can appear daunting at first glance. However, with a little guidance, and a lot of practice, you can develop the necessary skill set to master this process
Example: How is 25.2 miles/hour expressed in m/s?
Eliminate: {assign mi units to the denominator and hr units to the numerator of the conversion factor}
Replace: {assign m units to the numerator and s units to the denominator of the conversion factor}
3. Relate: {assign the corresponding value to its unit, 1 mi = 1609 m & 1 hr = 3600 s}

6. Length, Time & Mass Length is the 1-D measure of distance
Quantities such as area and volume, and their associated units, are ultimately derived from measures of length
Definition of SI Unit: The meter is the length of the path traveled by light (in vacuum) during a time interval of 1/299,792,458 s (or roughly ns)
Examples of units derived from length (in this case radius, r):
Area of a circle: {units are m2}
Volume of a sphere: {units are m3}
Time is the physical quantity that measures either:
__ when an event took place
__ the duration of the event
Definition of the SI Unit: The second is the time taken by 9,192,631,770 oscillations of the light emitted by a cesium-133 atom
Mass is the measure of inertia for a body (or loosely speaking the amount of matter present)
Definition of the SI Unit: The kilogram is the amount of mass in a platinum-iridium cylinder of 3.9 cm height and diameter.

7. Trigonometry (remember: SOHCAHTOA)
The relationships between sides and angles of right triangles
Consider the following right triangle:
The 3 primary relations between the sides and angles are:
The Sine:
The Cosine:
The Tangent: B A C q

8. Vectors & Scalars
Most physical quantities can categorized as one of 2 types (tensors notwithstanding):
Scalars:
described by a single number & a unit (s).
Example: the length of the driveway is 3.5 m
Vectors:
described by a value (magnitude) & direction.
Example: the wind is blowing 20 m/s due north
Vectors are represented by an arrow:
the length of the arrow is proportional to the magnitude of the vector.
The direction of the arrow represents the direction of the vector

9. + = Properties of Vectors A B R + = A B R + = Ax Ay A
Only vectors of the same kind can be added together
2 or more vectors can be added together to obtain a “resultant” vector
The “resultant” vector represents the combined effects of multiple vectors acting on the same object/system
Direction as well as magnitude must be taken into account when adding vectors
When vectors are co-linear they can be added like scalars A B R + = A B R + =
Any single vector can be treated as a “resultant” vector and represented as 2 or more “component vectors
To add vectors of this type requires sophisticated mathematics or use of graphical techniques Ax Ay A + =

10. Vector Addition A. Graphic Method R2 = A2 + B2+ 2AB cos q R B A
To add 2 vectors, place them tail-to-head, without changing their direction; the sum (resultant) is the vector obtained by connecting the tail of the first vector with the head of the second vector
R=A+B means “the vector R is the sum of vectors A and B”
R¹ A+B : the magnitude of the vector R is NOT equal to the sum of the magnitudes of vectors A and B
R2 = A2 + B2+ 2AB cos q
Note:
For co-linear vectors pointing in the same direction, R = A + B
For co-linear vectors pointing in opposite directions, R = A - B R A B q

11. Vector Addition (cont.)
B. Component Method
Express each vector as the sum of 2 perpendicular vectors. The direction of each component vector should be the same for both vectors. It is common to use the horizontal and vertical directions (These vectors are the horizontal and vertical components of the vector)
Example:
vector A  Ax (horizontal) and Ay (vertical) or
vector B  Bx (horizontal) and By (vertical) or
Note: The unit vectors x and y indicate the directions of the vector components
The common component vectors for A & B can now be added together like scalars to obtain the component vectors for the resultant vector:
Rx = Ax + Bx and Ry = Ay + By thus:

12. Vector Addition (cont.)
To calculate the magnitude of the resultant from the component vectors by using the Pythagorean Theorem:
The angle of the resultant vector (from the x axis) obtained from the ratio of component vectors:
To calculate the components from the magnitude R and the angle it makes with the horizontal direction: Rx q R Ry x y

13. J. Willard Gibbs (1839-1903) American mathematician & physicist
Considered one of the greatest scientists of the 19th century
Major contributions in the fields of:
Thermodynamics & Statistical mechanics
Formulated a concept of thermodynamic equilibrium of a system in terms of energy and entropy
Chemistry
Chemical equilibrium, and equilibria between phases
Mathematics
Developed the foundation of vector mathematics
"A mathematician may say anything he pleases, but a physicist must be at least partially sane."