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High School Physics - Core Concept Master Cheat Sheet O1: Basic Skills in Physics
03: Solving Physics Problems
• 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 reading the measurement. • Significant Figures: Digits that were actually measured and have physical significance. (Also called “significant digits”)
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 Step 5: Review the answer
The metric system uses prefixes to indicate multiples of 10
K = Known U = Unknown D = Definition O = Output S = Substantiation
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.
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 Watch your time Free-Response tips: Show partial work Don’t forget units Don’t be fooled by blank space
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 Æ “milli” means 0.001 Æ 0.00125 L 87.5 kg Æ “kilo” means 1000 Æ 87500 g
04: Motion in One Dimension
02: A Mathematical Toolkit If a # is … to a variable, Added
then … the # to solve for the variable Subtract
Use the KUDOS method for solving word problems.
• 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.
5=x+2 -2 -2 5-2 = x 3=x–6 +6 +6 3-6 = x 2 = 4x 1. 4 2/4 = x 2·6=x·2 2 2·6=x
• • • • •
On Your Calculator: • 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.
v=d/t a = Δv/Δt=(vf-vi)/t d=vit+at2/2 vf2=vi2+2ad 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.
sinθ = cosθ =
opposite hypotenuse adjacent hypotenuse
− b ± b − 4ac 2a 2
• 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.
• 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. • Vector Addition: The process of combining vectors; added tip to tail.
• 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.
Velocity of a projectile
Horizontal component • • • • • • • • • •
v=d/t a = Δv/Δt=(vf-vi)/t d=vit+at2/2 vf2=vi2+2ad Pythagorean Theorem: c2=a2+b2 Sin θ = opp/hyp Cos θ = adj/hyp Tan θ = opp/adj 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.
• • • • • • •
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.
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. An inclined plane showing all the forces acting on the object:
• 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
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
Ball A strikes motionless ball B. After the collision they move off as shown.
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.
• 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.
• 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
• • • •
Fg=Gm1m2/d G=6.67x10-11Nm2/kg2 ac=v2/r Fc=mv2/r
• Thermal expansion:
(L − L0 ) = α (T − T0 )
= ρgh Buoyancy (Archimedes’ principle): B = ρgV
• Pressure variation with depth: P •
• Bernoulli’s equation (along any streamline):
• 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.
1 2 ρv + ρgh = const 2 Applied force = Loaded area P+
12: Temperature and Heat
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 equals 2 ∏ radians.
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 D
C + 273 = K
Fahrenheit: The Fahrenheit scale is set such that water freezes at 0°F and boils at 212°F. D
9 F = DC + 32 5
For changes in temperature:
• I=Σmr2 • L=Iω
Qheat = m × C p × ΔT
• Ƭ=F l Linear motion formula v=
∆ω α= ∆t
∆v a= ∆t
d = v i t + at /2
θ = ωi t + αt /2
v = v + 2ad
ω2f = ωi2 + 2αθ
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.
Rotational motion formula ω=
ΔQ fus = m × L fus
Qfus = heat of fusion
ΔQvap = m × Lvap
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.
U = Q +W
• 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.
m = mass; ΔT = T2 – T1
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.
• 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.
ΔU = ΔQ + W
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 Solid Liquid Solute Crystals in Solvent Simple molecules Less molecules
Has more entropy Liquid Gas Dissolved Solution Large, complex molecules More molecules
• 2nd Law of Thermodynamics: The total entropy of the universe can never decrease.
ΔS total ≥ 0 Note that the entropy of the system may decrease so long as the entropy of the surroundings increases by an equal or greater amount.
ΔS system + ΔS surroundings ≥ 0
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: Period of a mass on a spring: Wave speed equation: f = 1/T
T = 2π√(l/g) T = 2π√(M/K) v=fλ
• 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.
• 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 Here a polarizing filter changes random unpolarized light into a wave that vibrates in only Polarizing Unpolarized Polarized one direction. light
• 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.
• 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 additional capacitance gained by adding a dielectric material between the plates of a capacitor. • R=ρ L/A • q=CV • C= kε o A/d
• • • •
1/f=1/do+1/di m=hi/ho=-di/do n=c/v n1sinθ1=n2sinθ2 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.
• • • •
angle of incidence
angle of refraction
• Uc=qV/2=CV2/2 • V=PE/q
“unrefracted” Factors that determine the resistance of a wire: beam • Resistivity of wire material • Length of wire 18: Electric Forces and Fields • Cross sectional area of wire Charge: A fundamental intrinsic property of matter that • Temperature of wire gives rise to the attractions and repulsions between 20: Circuits electrons and protons. • Series Circuit: A circuit where the components form one Charging by Contact: The transfer of electric charge from continuous loop. The current is constant throughout. one object to another by simple contact or conduction. • Parallel Circuit: A circuit where each component is Charging by Induction: Redistribution or charging or an connects to form its own separate independent branch. The object by bringing a charged item in close proximity to, but voltage is constant throughout. not touching, an uncharged object. • Internal Resistance: Resistance from the processes inside Coulomb’s Law: Mathematical relationship between a voltage source; resistance due to the battery itself. electric force, charge, and distance. The electric force • Kirchhoff’s Laws: Two laws, the junction and loop rule, varies directly with the product of the charges, and that help describe circuits with multiple loops or voltage inversely to the square of the distance between the sources. charges. • Junction Rule: A restatement of conservation of charge; Polarized: Separation or alignment of the charges in a the current going into a junction must equal the current neutral body so that like charges are grouped together, going out of the junction. resulting in a positive and a negative region. • Loop Rule: A restatement of conservation of energy; the Electric Field: A force field that fills the space near any sum of all voltages in the elements of a loop is zero. 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=1/4π ε o ε o =8.85x10-12C2/Nm2 1 Coulomb = 6.25x1018 electrons E=F/q V=PE/q V=kq/r
• • • •
V=IR Ohm’s law P=IV=I2R RS=R1+R2+R3+… RP=1/R1+1/R2+1/R3+… sw itch
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.
In this parallel circuit the voltage to each resistor would be equal.
In this series circuit the current flow would be equal throughout.
21: Magnetic Fields
23: Atomic Physics
• Magnetic Domains: Microscopic areas of atoms where the magnetic fields are aligned. • Ferromagnetic: A naturally magnetic class of materials where the magnetic domains are ordered and do not cancel out. • Magnetic Field Lines: Lines showing the shape and extent of a magnetic field around a permanent magnet or a moving charged object. • Mass Spectrometer: A device that magnetically separates charged ions according to their mass. A magnetic field is used to accomplish this separation. • FB=BIL sinθ • FB=qvBsinθ • B = μ o i / 2π r -7
• μ o=4π x10 Tm/A Right Hand Rule, RHR 1. The fingers extend or curl in the direction of the magnetic field. 2. The outstretched thumb points in the direction of conventional current, or the direction of a positively charged moving particle. 3. A line perpendicular to the palm indicates the direction of the magnetic force. X X X X X X
Heisenberg’s Uncertainty Principle If position is identified the momentum cannot be measured If momentum is measured the position is lost. Δx X Δp ≥ h / 4π
22: Electromagnetism • Electromotive Force, EMF: A voltage that gives rise to a current flow. This voltage can be induced or created by a changing magnetic field. • Induced current: The flow of charge in a conductor due to the changing magnetic flux near that conductor. • Lenz’s Law: The induced emf always gives rise to a current whose magnetic flux opposed the original change in magnetic flux. Thus, the induced current tries to maintain the level of magnetic flux. • Generator: A machine that produces electricity by a rotating coil of wire immersed in a stationary magnetic field. This rotating motion could be obtained from a variety of sources. • • • •
ΦB=BAcosθ Acircle=∏r2 ε=-NΔΦ/Δt ε=BLv X
• First postulate: An atom consists of a positively charged nucleus at the centre. The electrons move round the nucleus in certain stationary orbits of definite radii and not all possible radii. • Second postulate: The radius of the orbit is such that the angular momentum of the electron is an integral multiple of h/2p • Third postulate: Electron may jump from one orbit to the other, in which case the difference in energy between the two states of motion is radiated in the form of a light quantum. • Atomic Spectra Solids, liquids and diffused gases emit light when heated. This light produces ordered arrangement of lines or bands or continuous patch of light.
Bohr’s atom model - Proposed by Neil Bohr in 1913
Here the conducting loop begins to pass into the magnetic field that goes into the page. An induced emf, and current are created. The current flows so that the newly created B field opposes the change in the original B field. While totally immersed, no current would flow since there would be no change in the B field flux.
24: Nuclear Physics • Radioactivity: Emission of radiation as a consequence of a nuclear reaction, or directly from the breakdown of an unstable nucleus. • Half Life: The time required for half of the nuclei in a sample of a specific isotope to undergo radioactive decay. • Alpha Particle: A positively charged helium nucleus (consisting of two protons and two neutrons). • Beta Particle: An energetic electron produced as the result of a nuclear reaction or nuclear decay. • Gamma Particle/Ray: Very high frequency electromagnetic radiation emitted as a consequence of radioactivity. • Fission: The process whereby one item splits to become two. • Binding Energy: The energy needed to separate the constituent parts of an atom or nucleus • Mass Defect: The difference between the mass of an atom and the sum of the masses of its individual components. Half Life: The amount of time needed for half of the original nuclei to decay away into another element. Calculating Binding Energy: 1. Determine the masses of each of the particles individually. 2. Determine the mass of a whole nucleus. 3. The difference between the two provides “m”. 4. Use m in the equation E=mc2 to calculate E. • Nuclear power plants have provided energy for half a century. • Atomic bombs are based on fission and among the most destructive weapons ever created. Medical applications of radioactivity are commonplace in our society, and are seen in cancer therapy, tracers, tomography (PET scans), NMRs and MRIs.