Physics and Mathematical Tools
Unit 1
What is Physics?
• Physics (from Ancient Greek:
φύσις physis "nature") is a natural science that
involves the study of matter and its motion
through space-time, along with related
concepts such as energy and force.
• Physics is the general analysis of nature,
conducted in order to understand how the
universe behaves.
The Basic Science - Physics
• Physics is regarded as the fundamental
science, because all other natural sciences
use and obey the principles and laws set
down by the field.
• The ideas of physics are fundamental to
chemistry and biology.
• Physics supports chemistry, which in turn
supports biology.
Areas of Physics
Name
Subjects
Examples
Mechanics (Kinematics and
Dynamics)
Motion and its causes,
Falling objects, friction, weight,
interaction between objects spinning object
Thermodynamics
Heat and temperature
Melting and freezing processes,
engines, refrigerators
Electromagnetism
Electricity, magnetism, and
light
Electrical charge, circuitry,
permanent magnets,
electromagnets
Optics
light
Mirrors, lenses, color, astronomy
Waves and vibrations
Specific types of repetitive
motions
Springs, pendulums, sound
Relativity
Particles moving at any
speed, including very high
speed
Particle collisions, particle
accelerators, nuclear energy
Quantum Mechanics
Behavior of subatomic
particles
The atom and its parts
Applications of Physics Principles
The Nature of Science
• Observation: important first step toward
scientific theory; requires imagination to tell
what is important.
• Theories: created to explain observations; will
make predictions.
• Observations will tell if the prediction is
accurate, and the cycle goes on.
Scientific Method
• Make observation
• Define a problem (ask a
question)
• Develop a hypothesis
• Test the hypothesis with
experiments
• Conclusion – an
interpretation of
experimental results
Scientific Facts and Theories
Scientific fact is a close agreement by competent
observers who make a series of observations
on the same phenomenon.
Scientific theory is a synthesis of a large body of
information that encompasses well-tested and
verified hypotheses about a certain aspect of
natural world.
Scientific theories are always being debated,
tested, modified, and changed over time by
different scientists from many countries.
How did the universe come into being?
• The Big Bang Theory
• Theoretical support for the Big Bang comes from mathematical models.
•
Observational evidence for the Big Bang includes the analysis of the
spectrum of light from galaxies
Scientific Law
• When hypotheses are tested over and over again and
not contradicted they may become known as laws or
principles.
• Newton’s Laws of Motion
• Newton’s Law of Gravity
• The Law of Conservation of Energy.
• Scientific theories, laws, and principles must be
testable.
• If the statement can not be proved wrong, it is not a
scientific statement.
Scientific Hypotheses Must be
Testable
• Albert Einstein:
“No number of experiments can prove me right; a
single experiment can prove me wrong.”
Scientific or not?
1. The intelligent life exists on other planets.
Not scientific.
2. No material object can travel faster than light.
Scientific.
Physics Uses Models to Describe
Phenomena
• The physical world is very complex, physicists
often use models to describe the most
fundamental features of various phenomena.
• Models simplify phenomena.
• Models include diagrams, equations, computer
simulations.
• To analyze the basketball’s motion – disregard
characteristics that do not affect motion.
• .
Models Can Help Build Hypothesis
• A scientific hypothesis is a reasonable explanation for
observations and that can be tested with additional
experiments.
• A hypothesis must be tested in a controlled
experiment.
• Controlled experiment - experiment that tests only
one factor at a time.
• For example, you want to test if the velocity of an
object rolling on an inclined plane depends on its
mass.
Mass – a controlled or independent variable.
Velocity - a dependent variable.
Science Vs. Technology
• Science (from Latin: scientia meaning "knowledge")
is a systematic enterprise that builds and organizes
knowledge in the form of testable explanations and
predictions about the world.
• Science is the study of a particular subject, while
technology is an applied science.
• Science is focused more on analysis, while
technology is all about the synthesis of design.
• Science is all about theories, while technology is all
about processes.
The Goals of Physic
• Physicists develop a conceptual understanding
of the universe and describe them in Theories,
Laws, and Models.
• Physicists test their understanding by making
measurements to compare with these
models.
• Anything that can not be tested through a
measurement is not physics.
Measurements
• Measurement is the process or the result of
determining the magnitude of a physical
quantity, such as length or mass, relative to a
unit of measurement, such as a meter or a
kilogram.
• Standard of measurement - A physical object
that defines the meaning of a physical
measurement.
Standards
• Why is it important for there to be global
standards?
• Sometimes the master standard is stored in
one place in the world.
If so, then there needs to be a mechanism to
replicate and share this.
• In other cases, standards are defined in a way
that makes it easy for scientists to create their
own replicas.
1-5 Units, Standards, and the SI System
Quantity Unit
Length
Time
Mass
Meter
Standard
Length of the path traveled
by light in 1/299,792,458
second.
Second
Time required for
9,192,631,770 periods of
radiation emitted by cesium
atoms
Kilogram Platinum cylinder in
International Bureau of
Weights and Measures, Paris
Meter
• 1791 - one ten-millionth of the distance from
the Earth's equator to the North Pole (at sea
level).
• 1889 to 1960 - Historical International
Prototype
Meter bar, made of an alloy of platinum and
iridium
• Since 1983, it is defined as the length of the
path travelled by light in vacuum in 1⁄299,792,458
of a second.
Kilogram
• The kilogram is defined as being equal to the
mass of the International Prototype Kilogram
(IPK), which is almost exactly equal to the
mass of one liter of water.
• The IPK is made of a platinum–iridium alloy
and is stored in a vault at the International
Bureau of Weights and Measures in Sèvres,
France.
Second
• Early definitions of the second were based on
the apparent motion of the sun around the
earth. The solar day was divided into 24 hours,
each of which contained 60 minutes of 60
seconds each, so the second was 1⁄86 400 of the
mean solar day.
• Since 1967, the second has been defined to be
the duration of 9,192,631,770 periods of
radiation emitted by cesium atoms
Derived Units
• We do not need many standards.
• Most units can be defined in terms of the
basic units.
• Speed m/sec
• Density kg/m3
Speed, density, volume,
force are derived units.
• Volume m3
• Force N = kg m/s2
SI System
• Système international d'unités
(France – 1960) - SI System
• The system has been adopted nearly globally.
Three principal exceptions are the U.S., Liberia
and Burma
• The SI is founded on seven SI base units for
seven base quantities assumed to be mutually
independent
1-5 Units, Standards, and the SI System
We will be working in the SI system, where the basic
units are meters, kilograms, and seconds. It is also
called MKS System.
Other systems: cgs; units are grams,
centimeters, and seconds.
British engineering system has force
instead of mass as one of its basic
quantities, which are feet, pounds,
and seconds.
M.K.S. System
•
•
•
•
In MKS System the fundamental quantities are
Meter - Length
Kilogram - Mass
Second - Time
• M.K.S.
1-5 Units, Standards, and the SI
System
For simplicity in communication,
the SI unit system uses
abbreviations for certain powers
of 10.
These are the standard SI prefixes
for indicating powers of 10.
The ones that are most
frequently used are highlighted.
Orders of Magnitude
• An order of magnitude is a factor of 10
• Physics is studied over many orders of
magnitude
1-6 Converting Units
Converting between metric units, for example from
kg to g, is easy, as all it involves is powers of 10.
Converting to and from British units is considerably
more work.
For example, given that 1
m = 3.28084 ft, this 8611m mountain is 28251 feet
high.
Converting Metrics Units
1 km = 1000 m
1m=0.001km
Kilo = 1000
1 cm = 0.01m
1m=100cm
Centi = 0.01
1 mg = _____ g
1g=__________mg
1 ns = ______ s
1s=_________ns
1 μm= ______m
1m=________ μm
1 MW = ______W
1W=________MW
Using Conversion Factors
Method we are going to use to convert
measurements from one sets of units to another
is based on multiplying by a conversion factor.
Example: Your textbook is 11 in long. Express
this length in centimeters.
Step 1: Write your initial measurement with
units as a fraction over 1.
11in
1
Step 2: Write down you goal. in  cm
Step 3: Write down the math fact that relates
inches and centimeters 1 in = 2.54 cm
Step 4: Write this fact as a fraction with units of
measurement that you want to get in you
answer in the numerator. The value of this
factor = 1
2.54cm
1in
Step 5: Multiply your measurement by the
conversion factor. Cancel units of
measurements.Multiply.
11in 2.54cm

 27.9cm
1
1in
• Convert 2 hr to minutes
2hr 60 min

 120 min
1
1hr
1hr = 60min
How many kg are there in 250 g?
1kg=1000g
250 g
1kg

 0.25kg
1
1000 g
Converting km/h to m/s
• If you have two units at a time, you use two
conversion factors. For example, to convert
50 km/h to m/s you convert km to m and 1h
to s:
50km 1000m

 50000m
1km=1000m
1
1km
1h = 3600s
50km 50000m
m

 13.9
1h
3600 s
s
Converting mph to m/s
1. Converting three units at a time, requires you
use three conversion factors. For example, to
convert 50 mi/h to m/s you convert mi to km,
km to m and to s:
1mi = 1.61km
1km=1000m 1 hr=3600s
50mi 1.61km 1000m 1hr
m



 22.4
1hr
1mi
1km
3600 s
s
Converting mph to m/s
• How many 60.6 mi/h to m/s
Converting Units
• RULE: Always multiply by 1
• Trick: Express 1 as a ratio of two units
1 pizza 8slices
• 1 pizza = 8 slices
1

8slices
• 1 hour = 60 seconds
1
1 pizza
1hr
60 min

60 min
1hr
Solve the Following Problems:
a)How many minutes are there in 1 year?
b) A building is 555 ft high. Express this height in
meters.
1ft = 30.48cm 1 in = 2.54cm 1cm=0.01m
c) Convert 2.5 km to meters
1km=1000m