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High School Physics - Core Concept Master Cheat Sheet

O1: Basic Skills in Physics
• Physics: Study of the physical world. Science of energy
• Metric System: System of measurement based on

multiples of 10.
• SI System: Systeme International d’Unites (International

system of units).
• Uncertainty: The last digit in a measurement is

uncertain—each person may see it slightly differently when

• Significant Figures: Digits that were actually measured
and have physical significance. (Also called “significant
digits”)

The metric system uses prefixes to indicate multiples of 10

Metric Prefixes commonly used in physics
Prefix Symbol Multiple

Kilo k 1000
Deci d 0.1
Centi c 0.01
Milli m 0.001
Micro μ 0.000001
Nano n 0.000000001

The “base unit” is when there’s no prefix.

To determine the equivalent in “base units”:

1. Use prefix to determine multiple
2. Multiply number by the multiple
3. Write the result with the base unit

Examples:
1.25 mL “milli” means 0.001 0.00125 L
87.5 kg “kilo” means 1000 87500 g

02: A Mathematical Toolkit

If a # is … to a
variable,

then … the # to
solve for the

variable

Example

Added Subtract 5 = x + 2
-2 -2
5-2 = x

Subtracted Add 3 = x – 6
+6 +6
3-6 = x

Multiplied Divide 2 = 4x
1. 4
2/4 = x

Divided Multiply 2 · 6 = x · 2
2
2 · 6 = x

• Always use the ÷ key to designate a number is on the

bottom of an expression.
• Always use the EE (or EXP) key to enter scientific notation.
• Always use parenthesis around addition or subtraction

when combining it with other operations
• To make something negative (when taking the number to a

power), keep the negative outside of the parenthesis.

Important Formulas:

hypotenuse
opposite

sinθ =
opposite

tanθ =

hypotenuse

cosθ =
2a

4acbb
x

2 −±−
=

03: Solving Physics Problems
General Problem Solving Strategy:
Step 1: Identify what’s being given
Step 2: Clarify what’s being asked.
If necessary, rephrase the question
Step 3: Select a strategy
Trial & error, search, deductive reasoning,
knowledge-based, working backwards
Step 4: Solve using the strategy

Use the KUDOS method for solving word problems.

K = Known
U = Unknown
D = Definition
O = Output
S = Substantiation

Multiple-choice tips:
Scan all the choices
Avoid word confusion
Beware of absolutes
Essay tips:
Understand the question
Answer the whole question and only the question
Free-Response tips:
Show partial work
Don’t forget units
Don’t be fooled by blank space

04: Motion in One Dimension
• Vector: A quantity that represents magnitude (size) and

direction. It is usually represented with an arrow to indicate
the appropriate direction. They may or may not be drawn to
scale.

• Scalar: A quantity that can be completely described its
magnitude, or size. It has no direction associated with its
size.

• Velocity: Speed of an object which includes its direction of
motion. Velocity is a vector quantity.

• Acceleration: Rate at which an object’s velocity changes
with time; this change may in speed, direction, or both.

• v=d/t
• a = Δv/Δt=(vf-vi)/t
• d=vit+at2/2
• acceleration due to gravity = -9.8 m/s2

• For sign conventions, assign a direction as positive, keep

this convention throughout the problem, any quantities in
the opposite direction must be negative.

• Often, up and right are positive, while down and left are
negative.

The motion of an object moving with a constant acceleration is
pictured below. The distance moved in each unit of time
increases. In fact, it is proportional to the square of the time.

• An object moving with a constant velocity would cover

equal amounts of distance in equal time intervals.
• An object moving with a constant acceleration would cover

varying amounts of distance in equal time intervals.

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05: Vectors and Motion in Two Dimensions
• Resultant: the result of adding two or more vectors;

vector sum.
• Vector Component: the parts into which a vector can be

separated and that act in different directions from the
vector.

tip to tail.

• v=d/t
• a = Δv/Δt=(vf-vi)/t
• d=vit+at2/2
• Pythagorean Theorem: c2=a2+b2
• Sin θ = opp/hyp
• acceleration due to gravity = -9.8 m/s2
• Important formula note: All of these formulas could

apply to any direction. Common subscripts are shown that
indicate the direction of a particular quantity

• v or y = vertical direction
• h or x = horizontal direction

• Projectiles move with a constant acceleration due to

gravity only in the vertical direction.
• Projectiles move with a constant velocity only in the

horizontal direction.
06: Forces and the Laws of Motion

• Static Equilibrium: A motionless state where all the
forces acting on an object yield a net force of zero.

• Dynamic Equilibrium: A condition of constant
motion/zero acceleration where all the forces acting on an
object yield a net force of zero.

• Friction Force: A force that acts to resist motion of
objects that are in contact.

• Normal Force: Support force that acts perpendicular to a
surface. If the surface is horizontal, this force balances the
weight of the object.

• Force: A vector quantity that tends to accelerate an object;
a push or a pull.

• Net Force, Fnet: : A combination of all the forces that act
on an object

• Fnet=ma
• μ=Ff/FN
• Fnet=ΣF = the sum of all forces

• Newton’s 1st law: An object at rest wants to stay at rest,

an object in motion tends to stay in motion; inertia.
• Newton’s 2nd law: Fnet=ma.
• Newton’s 3rd law: For every force that is an equal and

opposite force; action and reaction.

07: Work and Energy
• Work: Product of force on an object and the distance

through which the object is moved.
• Power: Work done per unit of time.
• Energy: The ability to do work.
• Base level: An arbitrary reference point from which

distances are measured.
• Kinetic Energy: The energy an object has due to its motion.
• Gravitational Potential Energy: The energy an object has

due to its position above some base level.
• Work Energy Theorem: The work done is equal to the

change in energy.
• Conservation of Energy: energy is not created or

destroyed, just transformed from one type to another.

• W= F d = mad
• W = F d cos θ
• P = W/t
• a = Δv/Δt
• cos θ = adjacent / hypotenuse
• KE = ½ mv2
• PE = mgh

• Work is done only when a force acts in the direction of

motion of an object
• If the force is perpendicular to the direction of motion, then

no work is done.
• Power is the ratio of work done per time
• Energy may appear in different forms, but it is always

conserved.
• The total amount of energy before and after some

interaction is constant.
• Work and energy are interchangeable.

08: Momentum and Collisions
• Momentum: A vector quantity that is the product of mass

and velocity of an item. It may be considered as inertia in
motion.

• Impulse: A change in momentum. The product of force
and the time through which the force acts.

• Conservation of Momentum: The momentum of a system
will remain constant. Momentum isn’t created or destroyed
unless an outside force is acting on the system.

• Elastic Collision: A collision where there is no kinetic lost,
momentum is still conserved, the object have no
deformation.

• Inelastic Collision: A collision where kinetic energy is lost
due to heat, deformation, or other methods. However,
momentum is still conserved for the system.

• P=mv
• Ft=mΔv
• J=Ft

• Explosion: one object breaking into more objects.
0=mv+mv+…
• Hit and stick: one object striking and joining to the other.
m1v1+m2v2=(m1+m2)v3
• Hit and rebound: one object striking and bouncing off of
the other. m1v1+m2v2=m1v3+m2v4

Note how momentum is conserved. In the X direction, the
moments add up to the original momentum before the
collision. In the Y direction, the moments cancel out since
there was no momentum in that direction initially.

A B

A

B

m

θ

F║

FN

F┴

W

An inclined
plane showing
all the forces
acting on the
object:

Ff

Vertical
component

Velocity of a projectile

Horizontal component

Ball A strikes
motionless ball B.
After the collision
they move off as
shown.

Page 3

09: The Law of Gravity and Circular Motion
• Centripetal Force: a center seeking force for an object

moving in a circular path.
• Centrifugal Force: An apparent, but nonexistent, outward

pointing force for an object moving in a circular path. A
rotating object may seem to be pushed outward, but
actually must be pulled inward in order to maintain any
circular path.

• Inverse Square Law: A relationship relating the strength
of an effect to the inverse square of the distance away from
the source.

• Gravitational Field: The map of influence that a massive
body extends into space around itself.

• Linear Speed: Straight path distance moved per unit of
time, also referred to as tangential speed.

• Rotational Speed: Number of rotations or revolutions per
unit of time, often measured in rpm, revolutions per
minute.

• Universal Gravitational Constant: A proportionality
constant that relates the strength of gravitational attraction
in Newton’s law of universal gravitation.

• Fg=Gm1m2/d2
• G=6.67x10-11Nm2/kg2
• ac=v2/r
• Fc=mv2/r

• Weightlessness: Astronauts “floating” in space may

appear to be weightless. However, the pull from gravity
definitely still acts on them. If it didn’t, their inertia would
carry them off in a straight line never to return to the
earth. Instead, the pull from gravity acts as a centripetal
force to maintain their orbit about the earth.

10: Rotational Equilibrium
• Torque: The rotational quantity that causes rotation; the

product of force times lever arm.
• Lever Arm: The distance from the axis of rotation to the

location where the force is applied.
• Moment of Inertia: The rotational equivalent of linear

inertia; a measure of the ease of rotating some object.
• Angular Momentum: The rotational equivalent of linear

momentum that describes the tendency of an object to
continue rotating.

• Rotational Equilibrium: The situation when the net
torque on an object equals zero.

• Radian: A unit of rotational displacement; one revolution

• I=Σmr2
• L=Iω
• Ƭ=F l

Linear motion formula

Rotational motion
formula

• θ= angular displacement
• ω=angular speed
• α=angular acceleration
• Ƭ=torque
• I=rotational inertia
• Draw a diagram if needed. Identify all given information.

Be sure to make diagrams or calculations with direction in
mind. Draw all forces and components.

11: Solids and Fluid Dynamics
• Solids: Matte with definite shape and volume
• Fluids: Matter with indefinite shape and definite volume
• Thermal expansion: Volume of matter increase with

temperature
• Stress: Force causing deformation
• Strain: Degree of deformation
• Buoyancy: The force caused by pressure variation with

depth to lift immersed objects
• Surface tension: The force to attract surfaced molecular to

make the surface area of fluid as small as possible
• Capillary action: The phenomena of fluids automatically

raising in open-ended tubes
• Viscosity: The inter-friction mechanism in fluid to dissipate

energy
• Laminar flow: Every particle passing a particular point

moves exactly along the smooth path followed by particles
passing that point early

• Turbulent flow: The irregular flow when the velocity of the
flow is high

• Thermal expansion: ( ) ( )00 TTLL −=− α
• Pressure variation with depth: ghP ρ=
• Buoyancy (Archimedes’ principle): gVB ρ=
• Bernoulli’s equation (along any streamline):

const
2
1 2 =++ ghvP ρρ

• Stress
force Applied

=

12: Temperature and Heat
Kelvin: The Kelvin scale measures absolute temperature. At
0 Kelvin, particles in an object are still. Other temperature
scales related to the Kelvin scale.
Celsius: A temperature increase of 1°C is equal to an increase
in temperature of 1K. However, 0°C ≠ 0K. The Celsius scale
is based on the boiling and freezing points of water. Thus,
water freezes at 0°C and boils at 100°C

Fahrenheit: The Fahrenheit scale is set such that water
freezes at 0°F and boils at 212°F.

For changes in temperature:

TCmQ pheat Δ××= m = mass; ΔT = T2 – T1
For increases in temperature that cross several phases simply
sum the Qfus, Qvap, and Qheat as needed.
For changes in state: Temperature doesn’t change as the
added energy is used to break intermolecular forces.

Melting: fusfus LmQ ×=Δ Qfus = heat of fusion

Boiling: vapvap LmQ ×=Δ Qvap = heat of vaporization
Heat, Work, and Internal Energy: The internal energy U of
a system is defined as the sum of the heat energy Q in the
system and the work W done on or by the system.

Calorimetry: Calorimetry is used to measure the heat given
off from or taken up by a reaction. Calorimetry assumes that
heat released by the system to the surroundings is used to
heat or cool the surroundings.

gssurroundinsystem QQ Δ−=Δ

t
d

v =

∆t
∆v

a =

/2attvd 2i +=

2
f +=

∆t
∆θ

ω =

∆t
∆ω

α =

/2αttωθ 2i +=
θ2αωω 2i

2
f +=

KC =+ 273�D

32
5
9

+= CF �D�D

WQU +=

Page 4

13: Thermodynamics
• Zeroth Law of Thermodynamics: Objects in thermal

equilibrium are at the same temperature. Objects in
contact will eventually come to thermal equilibrium.

• 1st Law of Thermodynamics (Law of Conservation of
Energy): Energy cannot be created nor destroyed in a
chemical or physical process.

WQU +Δ=Δ
U = internal energy (in J)
Q = heat (in J);
W = work done on (W>0) or by (W<0) the system
• Entropy (S): Disorder or random-ness

Has less entropy Has more entropy
Solid Liquid
Liquid Gas
Solute Crystals in Solvent Dissolved Solution
Simple molecules Large, complex molecules
Less molecules More molecules

• 2nd Law of Thermodynamics: The total entropy of the

universe can never decrease.

0≥Δ totalS

Note that the entropy of the system may decrease so long as
the entropy of the surroundings increases by an equal or
greater amount.

0≥Δ+Δ gssurroundinsystem SS

Living things utilize this concept by couplings the building of
organized molecules such as DNA to the release energy as
heat and an increase in the total entropy of the surroundings.

14: Vibrations and Waves
• Wave motion: The process in which the disturbance in a

point in the medium is transmitted to other parts of the
medium without the bodily movement of the particles.

• Longitudional Waves: The particles in the medium move
parallel to the direction of the wave. Eg. Sound waves

• Transverse waves: In a transverse wave the particles in
the medium move perpendicular to the direction of the
wave. Eg. Light waves, waves on strings.

• Time period (T): The time taken by a body to complete
one vibration.

• Frequency: Frequency is the number of oscillations
completed in a unit time

• Amplitude (r): The maximum displacement of the body in
vibration.

• Mechanical waves: A mechanical wave is just a
disturbance that propagates through a medium

• Electromagnetic wave: An electromagnetic wave is
simply light of a visible or invisible wavelength. Oscillating
intertwined electric and magnetic fields comprise light.
Light can travel without medium.

• Crest: The maximum displacement position in a wave is
called a crest.

• Trough: The minimum displacement position in a wave is
called a trough

• Period of a swinging pendulum: T = 2π√(l/g)
• Period of a mass on a spring: T = 2π√(M/K)
• Wave speed equation: v=fλ
• f = 1/T

• Reflection of a wave at a boundary: When a wave is

progressing towards an open end or from a medium of
greater to lesser density it reflects back with the same
direction of displacement. When a wave is progressing
towards a fixed end it gets inverted.

15: Sound
• Sound: A form of energy .When Matter vibrates very

quickly it transports energy in the form of waves. It
stimulates our sense of hearing. Sound waves are pressure
waves (energy per unit area). Sound cannot travel through
vacuum. A wave is a carrier of sound energy.

• Beats: The periodic and repeating fluctuations heard in the
intensity of a sound. Two sound waves of nearly same
frequencies interfere with one another to produce beats

• Pitch: The highest or lowest sound an object makes.
• Audible sounds: The audio spectrum extends from

approximately 20Hz to 20,000 Hz. These sounds can be
heard by human ear

• Below 20 Hz – Infrasonics
• Above 20KHz – Ultrasonics
• Doppler Effect: The apparent change in the frequency of

sound due to relative motion between the sound source and
observer is called Doppler Effect.

• Intensity: The loudness οφ sound is directly proportional to
the square of the amplitude or intensity (I). It is convenient
to use a logarithmic scale to determine the intensity level
β = 10 log (I/I0)

• Reference intensity or threshold of hearing , I0 = 1.00
x 10-12 W/ m2 ; β = 0 dB

• Stationary or Standing waves are formed due to
superposition of two identical waves moving in opposite
directions.

• There is no net flow of energy in the medium.
• Node: The points of no displacement when standing waves

are formed.
• Antinodes: The points along the medium which vibrate

back and forth with maximum displacement.
• Echo: The sound obtained by reflection at a wall, cliff or a

mountain is called an echo.

16: Interference,Diffraction and Polarization
• Electromagnetic Spectrum: A diagram that illustrates all

the varieties of electromagnetic waves based on their
relative frequency/wavelengths. Our eyes observe only a
small amount of this spectrum.

• Principle of Superposition: When two or more waves
occupy the same region of space simultaneously, the
resulting wave disturbance is the sum of separate waves.

• Constructive Interference: Two or more waves
superimposing to create a resulting wave that has larger
amplitude.

• Destructive Interference: Two or more waves
superimposing to create a resulting wave that has smaller
amplitude.

• Diffraction: The bending of waves around corners or small
openings.

• Young’s Double Slit Experiment: Experiment that
measured the wavelength of light by interference from two
small slits

• Polarization: Light where the electric field fluctuates in only
one direction.

• 3x108m/s speed of light in a vacuum
• sinθ=mλ/d bright fringe formula
• sinθ=(m+1/2) λ/d dark fringe formula
• sinθ=mλ/d diffraction grating formula
• S=Socos2θ Malus’ law

Unpolarized
light
Unpolarized
light

Polarizing
filter
Polarizing
filter

Polarized
light
Polarized
light

Here a
polarizing filter
changes
random
unpolarized
light into a
wave that
vibrates in only
one direction.

Page 5

17: Reflection, Refraction and Lenses
• Law of Reflection: The angle of incidence equals the

angle of reflection.
• Virtual Image: An image that cannot be projected onto a

screen. The rays of light don’t actually converge there;
they just seem to originate from that location.

• Real Image: An image where the rays of light actually
meet at a location. It can be projected onto a screen.

• Refraction: The bending of light due to its change in
velocity in various media.

• Index of Refraction: The ratio between the speed of light
in a vacuum and a particular medium.

• Total Internal Reflection: The complete reflection of
light when it strikes the boundary between two media at
greater than a critical angle.

• 1/f=1/do+1/di
• m=hi/ho=-di/do
• n=c/v
• n1sinθ1=n2sinθ2

18: Electric Forces and Fields
• Charge: A fundamental intrinsic property of matter that

gives rise to the attractions and repulsions between
electrons and protons.

• Charging by Contact: The transfer of electric charge from
one object to another by simple contact or conduction.

• Charging by Induction: Redistribution or charging or an
object by bringing a charged item in close proximity to, but
not touching, an uncharged object.

• Coulomb’s Law: Mathematical relationship between
electric force, charge, and distance. The electric force
varies directly with the product of the charges, and
inversely to the square of the distance between the
charges.

• Polarized: Separation or alignment of the charges in a
neutral body so that like charges are grouped together,
resulting in a positive and a negative region.

• Electric Field: A force field that fills the space near any
charge.

• Electric Potential: The ratio of electric potential energy to
electric charge at a particular spot in an electric field. It is
often referred to as voltage since it is measured in volts.

• Equipotential Line: A line where all points have an equal
electric potential, or voltage.

• FE=kq1q2/r2
• k=9x109Nm2/C2
• k=1/4
• 1 Coulomb = 6.25x1018 electrons
• E=F/q
• V=PE/q
• V=kq/r

Diagram shows the electric field
surrounding an area of negative
charge. The E field lines always point in the direction that a
small positive test charge would move in the field.

19: Conductors, Capacitors and Dielectrics
• Conductor: Material where electrons are loosely bound and

are able to flow throughout due to the free electrons.
• Insulator: Materials where electrons are bound and don’t

flow easily.
• Semiconductor: Materials in between insulator and

conductor.
• Superconductor: A material where electrons flow without

any resistance. Generally, superconductivity only occurs at
very low temperatures.

• Resistor: A device used to control or regular the amount of
electric charge flowing.

• Resistivity: An intrinsic property of a material that partially
determines the resistance of a wire.

• Capacitor: A device used to store or accumulate electric
energy. This is done by oppositely charging two nearby
conductive surfaces that are not in contact with each other.

• Dielectric: an insulating material is inserted between the
plates of a capacitor.

• Dielectric Constant: the factor that describes the
between the plates of a capacitor.

• R= L/A
• q=CV
• C=

• V=PE/q

Factors that determine the resistance of a wire:
• Resistivity of wire material
• Length of wire
• Cross sectional area of wire
• Temperature of wire

20: Circuits
• Series Circuit: A circuit where the components form one

continuous loop. The current is constant throughout.
• Parallel Circuit: A circuit where each component is

connects to form its own separate independent branch. The
voltage is constant throughout.

• Internal Resistance: Resistance from the processes inside
a voltage source; resistance due to the battery itself.

• Kirchhoff’s Laws: Two laws, the junction and loop rule,
that help describe circuits with multiple loops or voltage
sources.

• Junction Rule: A restatement of conservation of charge;
the current going into a junction must equal the current
going out of the junction.

• Loop Rule: A restatement of conservation of energy; the
sum of all voltages in the elements of a loop is zero.

• V=IR Ohm’s law
• P=IV=I2R
• RS=R1+R2+R3+…
• RP=1/R1+1/R2+1/R3+…

glass

air

glassglass

air

normalnormalangle of incidence
angle of

incidence

Refracted
beam
Refracted
beamangle of

refraction
angle of
refraction

“unrefracted”
beam

Note how the
beam bends to
the normal
when entering
the more dense
glass medium.
Then it bends
away from the
normal when re
entering air.

-

In this series
circuit the
current flow
would be
equal
throughout.

2
batteries

switch

Light
bulb

resistor

In this parallel
circuit the
voltage to each
resistor would
be equal.

2
batteries