GENERAL PHYSICS • Chemical Physics: The study of physics in

WHAT IS PHYSICS? chemical systems. Chemical physics focuses on

It is the science that deals with the using physics to understand complex phenomena
structure of matter and the interactions between at a variety of scales from the molecule to a
the fundamental components of the observable biological system. Topics include the study of
universe. In the broadest sense, physics (from the nano-structures or chemical reaction dynamics
Greek physikos) is concerned with all aspects of
nature on both the macroscopic and Computational Physics: The application of
submicroscopic levels. Its scope of study numerical methods to solve physical problems for
encompasses not only the behaviour of objects which a quantitative theory already exists.
under the action of given forces but also the
nature and origin of gravitational, • Electromagnetism: The study of electrical and
electromagnetic, and nuclear force fields. Its magnetic fields, which are two aspects of the
ultimate objective is the formulation of a few same phenomenon.
comprehensive principles that bring together and
explain all such disparate phenomena. • Electronics: The study of the flow of electrons,
generally in a circuit.
-Physics is sometimes broken INTO TWO
BROAD CATEGORIES, based on the history of • Fluid Dynamics / Fluid Mechanics: The study
the science: of the physical properties of "fluids," specifically
Classical Physics, which includes studies that defined in this case to be liquids and gases.
arose from the Renaissance to the beginning of
the 20th century • Geophysics: The study of the physical
Modern Physics, which includes those studies properties of the Earth.
which have been begun since that period. Part of
the division might be considered scale: modern • Mathematical Physics: Applying
physics focuses on tinier particles, more precise mathematically rigorous methods to solving
measurements, and broader laws that affect how problems within physics.
we continue to study and understand the way the
world works • Mechanics: The study of the motion of bodies in
a frame of reference.
Another way to divide physics is applied or
experimental physics (basically, the practical • Meteorology / Weather Physics: The physics
uses of materials) versus theoretical physics of the weather.
(the building of overarching laws as to how the
universe works) • Optics / Light Physics: The study of the
CLASSICAL PHYSICS physical properties of light.
Before the turn of the 19th century,
physics concentrated on the study of mechanics, • Statistical Mechanics: The study of large
light, sound and wave motion, heat and systems by statistically expanding the knowledge
thermodynamics, and electromagnetism. of smaller systems.
Classical physics fields that were studied before
1900 (and continue to develop and be taught • Thermodynamics: The physics of heat.
today) include:
MODERN PHYSICS
Acoustics: The study of sound and sound Modern physics embraces the atom and
waves. In this field, you study mechanical waves its component parts, relativity and the interaction
in gases, liquids, and solids. Acoustics includes of high speeds, cosmology and space
applications for seismic waves, shock and exploration, and mesoscopic physics, those
vibration, noise, music, communication, hearing, pieces of the universe that fall in size between
underwater sound, and atmospheric sound. In nanometers and micrometers. Some of the fields
this way, it encompasses earth sciences, life in modern physics are:
sciences, engineering, and the arts.
Astrophysics: The study of the physical
• Astronomy: The study of space, including the properties of objects in space. Today,
planets, stars, galaxies, deep space, and the astrophysics is often used interchangeably with
universe. Astronomy is one of the oldest astronomy and many astronomers have physics
sciences, using mathematics, physics, and degrees.
chemistry to understand everything outside of the
Earth's atmosphere.
Atomic Physics: The study of atoms, specifically
the electron properties of the atom, as distinct Plasma Physics: The study of matter in the
from nuclear physics which considers the nucleus plasma phase.
alone. In practice, research groups usually study
atomic, molecular, and optical physics Quantum Electrodynamics: The study of how
electrons and photons interact at the quantum
Biophysics: The study of physics in living mechanical level.
systems at all levels, from individual cells and
microbes to animals, plants, and entire Quantum Mechanics / Quantum Physics: The
ecosystems. Biophysics overlaps with study of science where the smallest discrete
biochemistry, nanotechnology, and bio- values, or quanta, of matter and energy become
engineering, such as the derivation of the relevant.
structure of DNA from X-ray crystallography.
Topics can include bio-electronics, nanomedicine, Quantum Optics: The application of quantum
quantum biology, structural biology, enzyme physics to light.
kinetics, electrical conduction in neurons,
radiology, and microscopy. Quantum Field Theory: The application of
quantum physics to fields, including the
Chaos: The study of systems with a strong fundamental forces of the universe.
sensitivity to initial conditions, so a slight change
at the beginning quickly become major changes Quantum Gravity: The application of quantum
in the system. Chaos theory is an element of physics to gravity and unification of gravity with
quantum physics and useful in celestial the other fundamental particle interactions.
mechanics.
Relativity: The study of systems displaying the
Cosmology: The study of the universe as a properties of Einstein's theory of relativity, which
whole, including its origins and evolution, generally involves moving at speeds very close to
including the Big Bang and how the universe will the speed of light.
continue to change.
String Theory / Superstring Theory: The study
Cryophysics / Cryogenics /Low-Temperature of the theory that all fundamental particles are
Physics: The study of physical properties in low- vibrations of one-dimensional strings of energy, in
temperature situations, far below the freezing a higher-dimensional universe
point of water.
MEASUREMENTS
Crystallography: The study of crystals and It is the process of associating numbers
crystalline structures. with physical quantities and phenomena.
Measurement is fundamental to the sciences; to
High Energy Physics: The study of physics in engineering, construction, and other technical
extremely high energy systems, generally within fields; and to almost all everyday activities. For
particle physics. that reason, the elements, conditions, limitations,
and theoretical foundations of measurement have
High-Pressure Physics: The study of physics in been much studied. See also measurement
extremely high-pressure systems, generally system for a comparison of different systems and
related to fluid dynamics. the history of their development.

Laser Physics: The study of the physical Measurements may be made by unaided
properties of lasers. human senses, in which case they are often
called estimates, or, more commonly, by the use
Molecular Physics: The study of the physical of instruments, which may range in complexity
properties of molecules. from simple rules for measuring lengths to highly
sophisticated systems designed to detect and
Nanotechnology: the science of building circuits measure quantities entirely beyond the
and machines from single molecules and atoms. capabilities of the senses, such as radio waves
from a distant star or the magnetic moment of a
Nuclear Physics: The study of the physical subatomic particle.
properties of the atomic nucleus.

Particle Physics: The study of fundamental

particles and the forces of their interaction.
 There are two types of physical quantities, that is,
base quantities and derived quantities.

Base quantities are physical quantities that

cannot be defined in terms of other quantities.

Table shows five base quantities and their

respective SI units.

PHYSICAL QUANTITIES
• Physical quantities are quantities that can be
measured.

• Usually, a specific scientific instrument is used

to measure a particular physical quantity.

• To describe a physical quantity, we first define

the unit in which the measurement is made.
There are many systems of units but the most Other quantities, called derived quantities,
common system of units used by scientists is are defined in terms of the seven base quantities
based on the metric system. via a system of quantity equations. The SI derived
units for these derived quantities are obtained
• The modernized version of the metric system is from these equations and the seven SI base
called International System of Units, officially units.
abbreviated as SI.

SI UNITS
For many years, scientists recorded
measurements in metric units, which are related
decimally, that is, by powers of 10. In 1960,
however, the General Conference of Weights and
Measures, the international authority on units,
proposed a revised metric system called the
International System of Units (abbreviated SI,
from the French Système Internationale d’Unites).
Prefixes are used to simplify the description of
We can represent a physical quantity by physical quantities that are either very big or very
the symbol of the quantity, the numerical value of small in SI units. Table lists some commonly used
the magnitude of the quantity and the unit of SI prefixes and their multiplication factors
measurement of the quantity. For example,
Figure shows a footballer scoring a goal. The ball
was kicked a distance of 8 m.
 UNIT CONVERSION AND CONVERSION the calculation steps can be especially helpful
FACTORS when problem-solving errors.
A unit conversion expresses the same •Do not round any quantities used within
property as a different unit of measurement. For the calculation.
instance, time can be expressed in minutes •Only round the final calculated quantity.
instead of hours, while distance can be converted Many unit conversion problems will require only a
from miles to kilometers, or feet, or any other single unit conversion factor. However, multiple
measure of length. Often measurements are factors may be required to solve a problem.
given in one set of units, such as feet, but are These figures illustrate both examples.
needed in different units, such as chains. Remember that Step 3, identifying the conversion
factor, is often the most challenging step. If an
A conversion factor is a numeric incorrect (or approximate) conversion factor is
expression that enables feet to be changed to used, a correct solution will not be achieved.
chains as an equal exchange. A conversion factor
is a number used to change one set of units to
another, by multiplying or dividing. When a
conversion is necessary, the appropriate
conversion factor to an equal value must be used.
For example, to convert inches to feet, the
appropriate conversion value is 12 inches equal 1
foot. To convert minutes to hours, the appropriate
conversion value is 60 minutes equal 1 hour.

This process uses the fact that any

number or expression can be multiplied by "one"
without changing its value. This allows the
conversion of units by multiplying the initial
measurement by one (or more) forms of the
number 1. While the multiplication by 1 does not PRECISION AND ACCURACY
change the value of the measurement, it does The terms precision and accuracy are often used
change the measurement units. It’s very easy to in discussing the uncertainties of measured
systematically apply unit conversion process to values.
solve conversions within or between
measurement systems. It may be necessary to Precision is a measure of how closely individual
multiply by more than one conversion ratio in measurements agree with one another.
more complex conversions. Use these steps to
construct a unit conversion problem so one (or Accuracy refers to how closely individual
more) of the units cancel until only the desired measurements agree with the correct, or “true,”
unit remains: value.

Step 1. Identify the unit you have. These are the

Starting Units.
Step 2. Identify the unit you want. These are the
Desired Units.
Step 3. Identify appropriate unit conversion
factor(s). These are the Linking (or Ratio) Unit(s).
Use EXACT conversion factors whenever
available.
Step 4. Cancel units and perform the math
calculations (e.g., multiply, divide). Repeat the
calculation (double check). Errors in Measurements
Step 5. Evaluate the result. Does the answer Systematic Error: occurs as a result of a flaw in
make sense the experimental design or apparatus
Random Error: caused by unpredictable
Best Practices changes in the experiment
•Multiply the numerators (across) and
denominators (across) to calculate an SIGNIFICANT FIGURES
intermediate answer, then divide. Documenting Except when all the numbers involved are
integers (for example, in counting the number of
students in a class), it is often impossible to
obtain the exact value of the quantity under
investigation. For this reason, it is important to LESSON 2: VECTORS
indicate the margin of error in a measurement by
clearly indicating the number of significant figures, REPRESENTING VECTORS
which are the meaningful digits in a measured or
calculated quantity. When significant figures are Vector quantities are often represented by
used, the last digit is understood to be uncertain scaled vector diagrams. Vector diagrams depict a
vector by use of an arrow drawn to scale in a
RULES FOR DETERMINING IF A NUMBER IS specific direction. Vector diagrams were
SIGNIFICANT OR NOT introduced and used in earlier units to depict the
• All non-zero digits are considered forces acting upon an object. Such diagrams are
significant. For example, 91 has two significant commonly called as free-body diagrams. An
figures (9 and 1), while 123.45 has five significant example of a scaled vector diagram is shown in
figures (1, 2, 3, 4, and 5). the diagram at the right. The vector diagram
• Zeros appearing between two non-zero digits depicts a displacement vector.
(trapped zeros) are significant. Example: 101.12
has five significant figures: 1, 0, 1, 1, and 2. Observe that there are several characteristics of
• Leading zeros (zeros before non-zero this diagram that make it an appropriately drawn
numbers) are not significant. For example, vector diagram.
0.00052 has two significant figures: 5 and 2. a scale is clearly listed
• Trailing zeros (zeros after non-zero numbers) • a vector arrow (with arrowhead) is drawn in a
in a number without a decimal are generally not specified direction. The vector arrow has a head
significant (see below for more details). For and a tail.
example, 400 has only one significant figure (4). • the magnitude and direction of the vector is
The trailing zeros do not count as significant. clearly labelled.
• Trailing zeros in a number containing a decimal
point are significant. For example, 12.2300 has
six significant figures: 1, 2, 2, 3, 0, and 0. The
number 0.000122300 still has only six significant
figures (the zeros before the 1 are not significant).
In addition, 120.00 has five significant figures
since it has three trailing zeros. This convention
clarifies the precision of such numbers. For
example, if a measurement that is precise to four
decimal places is given as 12.23, then the
measurement might be understood as having REPRESENTING A MAGNITUDE OF A
only two decimal places of precision available. VECTOR
Stating the result as 12.2300 makes it clear that The magnitude of a vector in a scaled
the measurement is precise to four decimal vector diagram is depicted by the length of the
places (in this case, six significant figures). arrow. The arrow is drawn a precise length in
accordance with a chosen scale. For example,
• The number 0 has one significant figure. the diagram at the right shows a vector with a
magnitude of 20 miles. Since the scale used for
• Any numbers in scientific notation are constructing the diagram is 1 cm = 5 miles, the
considered significant. For example, 4.300 x 10- 4 vector arrow is drawn with a length of 4 cm. That
has 4 significant figures is, 4 cm x (5 miles/1 cm) = 20 miles.

SCIENTIFIC NOTATION OR STANDARD INDEX

NOTATION
is a way of writing any number between 1
and 10 multiplied by an appropriate power of 10
notations. It is a shorthand method of writing
numbers that are very large or very small.
Scientific notation involves writing the number in
the form M x 10n, where M is a number between
1 and 10 but not 10, and n is an integer.

NOTE: Integer is a positive and negative whole

number.
 Using the same scale (1 cm = 5 miles), a
displacement vector that is 15 miles will be
represented by a vector arrow that is 3 cm in
length. Similarly, a 25-mile displacement vector is
represented by a 5-cm long vector arrow. And WHAT IS VECTOR QUANTITY
finally, an 18-mile displacement vector is A vector quantity is defined as the
represented by a 3.6-cm long arrow. See the physical quantity that has both direction as well
examples shown below. as magnitude. A vector with the value of
magnitude equal to one and direction is called
unit vector represented by a lowercase alphabet
with a “hat” circumflex. That is “ û “.

EXAMPLE OF VECTOR QUANTITY

Vector quantity examples are many, some of
them aregiven below:
• Linear momentum
• Acceleration
• Displacement
VECTOR VS. SCALAR • Momentum
• Angular velocity
VECTOR AND SCALAR QUANTITY • Force
Mathematics and Science were invented • Electric field
by humans to understand and describe the world
around us. A lot of mathematical quantities are
used in Physics to explain the concepts clearly. A
few examples of these include force, speed,
velocity and work. These quantities are often
described as being a scalar or a vector quantity.
Scalars and vectors are differentiated depending
on their definition.

WHAT IS A SCALAR QUANTITY?

Scalar quantity is defined as the physical quantity
with magnitude and no direction. Some physical
quantities can be described just by their ADDITION OF VECTORS
numerical value (with their respective units) 1. Stand up.
without directions (they don’t have any direction). 2. Move 5 steps to your right.
The addition of these physical quantities follows 3. Move 3 steps to your left.
the simple rules of the algebra. Here, only their 4. How many steps did you do?
magnitudes are added. 5. In the context of distance, how many
movements did you do?
6. In the context of displacement, how many
steps are you from your initial position to your
final position.

EXAMPLES OF SCALAR QUANTITY • Total steps 8.

There are plenty of scalar quantity examples, • Distance 8 (steps); regardless of the direction.
some of the common examples are: • Displacement 2 (steps) to the right;
• Mass displacement is the distance between initial and
• Speed final positions.
• Distance •Displacement has direction unlike distance.
• Time Displacement is vector; distance is scalar.
• Area
• Volume
• Density
• Temperature
 Distance and displacement are two
quantities that may seem to mean the same thing
yet have distinctly different definitions and
meanings.

• Distance is a scalar quantity that refers to "how Displacement of 1500 km 40° W of S

much ground an object has covered" during its Scale: 1cm = 500km
motion. 1500km = 3cm

• Displacement is a vector quantity that refers to

"how far out of place an object is"; it is the object's
overall change in position.

• Scalar quantity is defined as physical quantity

described by a magnitude only. They can be
described just by the numerical value and their
corresponding units of measure without specific
direction.
• Vector quantity on the other hand, is a physical Addition of vectors follow rules of vector algebra
quantity that is completely described by both different from rules of ordinary algebra.
magnitude and direction.
Two or more vectors can be added resulting to a
• Scalar quantity can be added just like an single vector known as resultant. Resultant vector
ordinary number. Five kilograms plus two is the algebraic sum of two or more vectors.
kilograms will give you seven kilograms. As
simple as that, but not for vectors. Addition and subtraction of vectors follow rules of
vector algebra which differ from the rules of the
• Vector quantities are important in the study of ordinary algebra. Vectors may be added either
physics. If scalar quantities follow ordinary rules, graphically or analytically.
vector quantities do not.
The graphical method is also known as the
For simplicity in representing vectors, they are geometrical method and requires no computation.
drawn in Addition of vectors is equivalent to composition of
the cartesian coordinate staring from the origin. vectors, and the sum of vectors is the resultant of
The cartesian coordinate is our reference frame, the vectors.
to show the direction of the vector.
TRIANGLE LAW OF VECTOR ADDITION states
that when two vectors are represented as two
sides of the triangle with the order of magnitude
and direction, then the third side of the triangle
represents the magnitude and direction of the
resultant vector.

A car accelerating at 2 m/s 2 30 ° N of E

Scale: 1cm = 1m / s2
2m / s2 = 2cm
 Eric leaves the base camp and hikes 11 km, north
and then hikes 11 km east. Determine Eric's
Statement of Parallelogram Law of Vector resulting displacement.
Addition: If two vectors can be represented by
the two adjacent sides (both in magnitude and This problem asks to determine the result of
direction) of a parallelogram drawn from a point, adding two displacement vectors that are at right
then their resultant sum vector is represented angles to each other. The result (or resultant) of
completely by the diagonal of the parallelogram walking 11 km north and 11 km east is a vector
drawn from the same point. directed northeast as shown in the diagram to the
right. Since the northward displacement and the
eastward displacement are at right angles to each
other, the Pythagorean theorem can be used to
determine the resultant (i.e., the hypotenuse of
the right triangle).

ANALYTICAL METHOD OF VECTOR

ADDITION

RESOLUTION OF VECTORS
Resolution of a vector is the splitting of a
single vector into two or more vectors in different
directions which together produce a similar effect
as is produced by a single vector itself. The
vectors formed after splitting are called
component vectors.

PYTHAGOREAN THEOREM
The Pythagorean theorem is a useful method for
determining the result of adding two (and only
two) vectors that make a right angle to each
other. The method is not applicable for adding
more than two vectors or for adding vectors
that are not at 90-degrees to each other. The HORIZONTAL COMPONENT DEFINITION
Pythagorean theorem is a mathematical equation In science, we define the horizontal
that relates the length of the sides of a right component of a force as the part of the force that
triangle to the length of the hypotenuse of a right moves directly in a line parallel to the horizontal
triangle. axis.
Let’s suppose that you kick a football, so now, the
force of the kick can be divided into a horizontal
component, which is moving the football parallel
to the ground, and a vertical component that
moves the football at a right angle to the
surface/ground.

COMPONENT METHOD
The component method of addition can be
VERTICAL COMPONENT DEFINITION summarized this way: Using trigonometry, find the
We define the vertical component as that part or a x-component and the y-component for each
component of a vector that lies perpendicular to a vector. Refer to a diagram of each vector to
horizontal or level plane. correctly reason the sign, (+ or -), for each
component. Add up both x-components, (one
from each vector), to get the x-component of the
total.
 Mechanics is the branch of Physics
dealing with the study of motion when subjected
to forces or displacements, and the subsequent
effects of the bodies on their environment.
KINEMATICS
The branch of classical mechanics that deals
with the study of the motion of points, objects
and a group of objects without considering the
causes of motion are called Kinematics. The word
kinematics originated from the Greek word
“kinesis”, meaning motion.

The motion of an object may be described by one

or more of the following properties:
• Displacement refers to the change of position
of an object. It is described by its magnitude and
direction; hence, it is a vector quantity. The SI unit
for displacement is meter (m).
• Average velocity is the displacement divided
by the time of travel. (Take note that speed is
interchangeably used with velocity. Velocity is a
speed with direction.)
• Instantaneous velocity is the velocity at a
specific instant of time or specific point along the
path.
•Acceleration is the rate at which velocity
changes.
SINE LAW •Instantaneous Acceleration is the acceleration
The ratio of any length of a side of a triangle to at a specific instant of time.
the sine of the angle opposite that side is the
same for all sides and angles in a given triangle.
COSINE LAW
The square on any one side of a triangle is equal
to the difference between the sum of the squares
of the other two sides and twice the product if the
other two sides and cosine of the angle opposite
to the first side

HORIZONTAL MOTION
If an object is under constant acceleration
and moves on the x-axis plane, it is known as a
uniformly accelerated motion on the horizontal
plane or dimension.

We are all familiar with the fact that a car

speeds up when we put our foot down on the
accelerator. The rate of change of the velocity of
a particle with respect to time is called
its acceleration. If the velocity of the particle
changes at a constant rate, then this rate is
called the constant acceleration.

• If the acceleration is constant, then so is the

change in velocity over equal time intervals
UNIFORMLY ACCELERATED MOTION and the velocity will increase at a constant rate.
MECHANICS
• Uniform acceleration means the acceleration is
constant in a fixed direction; the change
in velocity is the same for every equal interval of
time. The moving body speeds up or
slows down at a constant rate

FREELY-FALLING MOTION
It is a uniformly accelerated motion. In the
absent of air resistance, there is only one force
acting freely falling body, gravity. Free fall is any
motion of a body where gravity is the only force
acting upon it. In the context of general relativity,
where gravitation is reduced to a space-time
curvature, a body in free fall has no force acting
on it. Acceleration due to gravity is the
acceleration of a freely falling object.

VERTICAL MOTION
An object moves upward must be given an
initial velocity. This velocity in its ascent
decreases because of the force of gravity until it
reaches a point (maximum height) where it stops
momentarily and then start to descend. Consider
the time travel of the object from the ground up to
the maximum height or peak point is equal to the
time travel of the object downward.

FREE FALL
Do heavier objects fall faster Galileo?

For thousands of years, people erroneously

thought that heavier objects fell faster than lighter
ones. It was not until Galileo studied the motion of
falling objects that it became clear that, in the
absence of air resistance, gravity causes all
objects to fall at the same rate.

Galileo made a continuous

experimentation and observation from the theory
of motion by Aristotle. He observed that the ratio
of distance to the square of the time remains
constant for the same angle. Galileo concluded
that all freely falling body objects have the same
acceleration at the same place near the earth’s
surface. This acceleration due to gravity, (g), was
found to have a constant value of 9.80 m/s2 which
varies slightly with location on earth.

A hammer and a feather fall with the same

constant acceleration if air resistance is
negligible. This is a general characteristic of
gravity not unique to Earth, as astronaut David R.
Scott demonstrated in 1971 on the Moon, where
the acceleration from gravity is only 1.6 m/s/s and
there is no atmosphere