Chapter 1
Introduction and Mathematical Physics
1.1 The Nature of Physics
• Physics helps to explain our physical world.
• Application of physics have been applied to
technology, rocketry, transportation, electronics,
and the medical profession.
• Physics requires a new way of thinking. You will be
forced to reason, analyze, and apply.
• In the end, you will have a better understanding of
the world around you.
1.2 Units
• Accuracy and precision are important.
• SI units will be used most often in this text.
o Meter, kilogram, and second will be used most often.
• Refer to table 1.1 on pg. 2 for common units of
measurement. Also, look at the inside cover of your
text!
Dorky Facts!
• A meter is defined as the distance that light travels
in a vacuum in a time of 1/299792458 second.
o Since the speed of light is constant at 299792458 m/s, this would make
sense to any reasonable person taking AP physics.
• A kilogram is the mass of a standard cylinder of
platinum-iridium alloy.
• One second is defined as the time needed for
9192631770 electromagnetic wave cycles to occur
as emitted by cesium-133 atoms in an atomic clock.
Units
•
•
•
•
Base Units
Length
Mass
Time
“base” refers to the fat
that these units are
used along the various
laws to define
additional units for
other physical
quantities
Derived Units
Velocity
Acceleration
Force
Energy
Units are combinations
of base units
• Sometimes units are
derived and then
abbreviated
•
•
•
•
•
Prefixes
• Prefixes are used very often in physics (as well as
any type of science or technology)
• Refer to Table 1.2 on pg. 3 for common prefixes with
their units. Tag this page in your text with a post it.
• Use the “EE” button on your calculator, NOT the
stupid “^”.
• You are now expected to be able to use prefixes
correctly.
1.3 The Role of Units in
Problem Solving
• WRITE DOWN all units in all problems.
• If units don’t agree with one another, convert
before you solve the problem.
• If your units don’t give the desired algebraic result,
you did something wrong. Try again!
• Units are often the key to success when you forget
an equation!
• After working with stoichiometry in chemistry, you
should all be very familiar with the concept of
Dimensional Analysis. This is NOT for babies or idiots.
You should use this method if you are in doubt of
your conversion.
1.4 Trigonometry
• Sine, cosine, tangent, and theta are used all the
time in physics. Review these functions and be
prepared to use them as defined in SOHCAHTOA.
• Be prepared to solve for both angles and sides of
triangles.
• The unit for the angle theta is degrees.
• Remember, SOHCAHTOA can only be used for right
triangles.
• Don’t forget the Pythagorean Theorem!
1.5 Scalars and Vectors
Scalars
Vectors
• A single number with a
unit giving size or
magnitude.
• Temperature
• Distance
• Speed
• Time
• Mass
• energy
• A quantity that deals with
both MAGNITUDE and
DIRECTION.
• Often more descriptive
than scalar.
• Scalar quantities are
often part of vector
quantities.
• Displacement
• Velocity
• Acceleration
• Force
Vector Quantities
Arrows are used to represent all vectors, regardless of the type of quantity being
represented. The size of the arrow represents the magnitude of the quantity. The
direction of the arrow represents the direction of the quantity with respect to the origin.
1.6 Vector Addition and
Subtraction
• Graph paper works best in the beginning.
• Define an origin and draw a quadrant system.
• Draw the first vector with the tail at the origin and the tip
facing in the defined direction.
• Draw a NEW origin and quadrant system at the head of
the first vector.
• Connect the tail of the second vector to the head of the
first vector.
• Repeat until all vectors have been added.
• The RESULTANT vector is drawn from the tail of the 1st
vector to the head of the last vector.
• Measure both magnitude and direction.
Mathematical Addition
• When adding only two vectors, follow method of
adding vectors head-to-tail.
• Draw resultant vector.
• Instead of measuring magnitude and direction of
resultant or missing sides, use SOHCAHTOA,
Pythagorean Theorem, Law of Sines, or Law of
Cosines to solve for missing sides and/or angles.
• This method is more accurate than using a ruler and
protractor. (Quicker too!)
Subtraction
• When a vector is multiplied by -1, the magnitude of
the vector remains the same, but the direction of
the vector is reversed.
• Vector subtraction is done the same as vector
addition, EXCEPT you need to reverse the indicated
direction of the subtracted vector.
1.7 The Components of a
Vector
• When drawn on a coordinate system, every vector
can have x- and y- components.
• For instance vector A, is resultant of adding vectors
Ax and Ay.
• x- and y- components would be perpendicular to
one another.
• Understanding components is helpful because
components are often easier to add than the
individual vectors. This is especially true when
multiple vectors are being added.
Scalar Components
• Once x- and y- components have been defined, it
is easier to refer to vector directions as (+) and (-)
along the x- or y- axis.
Resolving a Vector into its
Components
• When magnitude and direction of a vector are
known, a vector can be “resolved into it’s
components.”
• Set vector up on coordinate system and use
SOHCAHTOA to determine x- and y- components.
1.8 Addition of Vectors by
Means of Components
1. Determine x- and y- components of EACH vector.
2. Place magnitudes with (-) or (+) direction in an xy- chart.
3. Add all vector components so that you have total
x- and y- magnitude.
4. Set up a coordinate system and add total x- and
total y- using Pythagorean Theorem.
5. Determine angle of resultant using SOHCAHTOA.
Helpful Websites
• www.wiley.com/college/cutnell
• http://www.physicsclassroom.com/Class/vectors/
o Complete Lesson 1 for an excellent tutorial
• http://dev.physicslab.org/Lessons.aspx
o Click on “Introductory Mathematics.” Choose topics you are having
difficulty with. Try some of the worksheets. Answers are given when you
type in your own answers for most worksheets.