Measurements
What is Physics?
· Physics is everywhere in everyday life. We study the
structure and behavior of matter through observation:
· Physics is a science of observation of physical phenomena
and the generalization of the observations into simplest
possible theories.
Model
theory
principle
· Mathematics is the language of Physics
law
Measurement and Uncertainty
Physics is based on observation, but measurements always
have uncertainty. We always have to ask: how precise is the
measurement? The uncertainty depends on factors such as
equipment, method, and observer.
Example: Using a ruler to measure the length of the
textbook, l = 25.2 cm, and the uncertainty is dl = 0.1 cm,
so the length of the book is expressed as 25.2 ± 0.1 cm.
The percent uncertainty is δl/l = 0.1/ 25.2 = 0.4%
Fundamental Units
●
All things in classical mechanics can be expressed
in terms of the fundamental units:
Length L
– Mass
M
– Time
T
–
●
For example:
–
Speed has units of L / T (like miles per hour)
Distance
Radius of visible universe
To Andromeda Galaxy
To nearest star
Earth to Sun
Radius of Earth
Sears Tower
Football field
Tall person
Thickness of paper
Wavelength of blue light
Diameter of hydrogen atom
Diameter of proton
Length (m)
1 x 1026
2 x 1022
4 x 1016
1.5 x 1011
6.4 x 106
4.5 x 102
1.0 x 102
2 x 100
1 x 10-4
4 x 10-7
1 x 10-10
1 x 10-15
Units...
●
SI (Système International) Units:
–
–
●
British Units:
–
●
mks: L = meters (m), M = kilograms (kg), T = seconds (s)
cgs: L = centimeters (cm), M = grams (gm), T = seconds (s)
Inches, feet, miles, pounds, slugs...
We will use mostly SI units, but you may run across
some problems using British units. You should know
how to convert back & forth.
Converting between different systems of units
●
Useful Conversion factors:
–
–
–
–
●
1 inch =
1m =
1 mile =
1 mile
2.54 cm
3.28 ft
5280 ft
= 1.61 km
Example: convert miles per hour to meters per
second: 1 mi  1 mi  5280 ft  1 m  1 hr  0.447 m
hr
hr
mi
3.28 ft
3600 s
s
Significant Figures
Number of reliably digits in a measurement. 4 m? 4.0 m? 4.00m?
Vectors
●
A vector is a quantity that involves both
magnitude and direction.
–
–
●
A scalar is a quantity that does not involve
direction.
–
–
●
55 mph north
A downward force of 3 Newton
55 mph
18 cm long
Vectors are often identified with arrows in
graphics and labelled as follows: