Fill-in-the-Blanks Formula Sheet

Chapter 1: Measurements

Uncertainties

• Absolute Uncertainty:
• Fractional Uncertainty:
• Percentage Uncertainty:
• Percentage uncertainty =
• Uncertainty in timing experiment =

Algebra with Significant Figures

• Division and Multiplication Example:
• Addition and Subtraction Example 1:
• Addition and Subtraction Example 2:
• Addition and Subtraction Example 3:

Dimensional Analysis

• Velocity:
• Acceleration:
• Force:
• Work:
• Energy:
• Power:

Constants and Conversions

• 1 N =
• 1 Joule =
• 1 Watt =
• Example of power factor rule:

Chapter 2: Vectors and Equilibrium

Vector Properties and Operations

• Vector equality example:
• Vector rotation invariance:
• Full circle rotation:
• Unit vector:
• Position vector in two dimensions:
• Position vector in three dimensions:
• Multiplication of a Vector with a Scalar:
• Magnitude of new vector:

Rectangular Components of a Vector

• X-component:
• Y-component:
• Magnitude from components:
• Trigonometric Identity:
• Direction from components:
• When vector A makes angle θ with y-axis (Y-comp):
• When vector A makes angle θ with y-axis (X-comp):
• When vector A makes angle θ with y-axis (Direction):

Addition of Vectors by Rectangular Components

• Resultant magnitude:
• X-component of resultant:
• Y-component of resultant:
• Direction of resultant:
• For multiple vectors (magnitude):
• For multiple vectors (direction):

Parallelogram Law

• Final resultant magnitude:
• Final resultant magnitude (vector notation):
• Maximum resultant:
• Minimum resultant:
• For subtraction:

Scalar or Dot Products

• Definition:
• Commutative Law:
• Associative Law:
• Distributive Law:
• Perpendicular vectors:
• Parallel vectors:
• Anti-parallel vectors:
• Unit vector dot products (perpendicular):
• Unit vector dot products (parallel):
• Angle between two vectors:
• Self scalar product:

Vector or Cross Product

• Definition:
• Non-commutative:
• Parallel/Anti-parallel vectors:
• Unit vector cross products (cyclic):
• Scalar multiplication:
• Parallel/Anti-parallel vectors (zero product):
• Component form:
• Determinant form:
• Scalar triple product (expanded):
• Scalar triple product (determinant):

Torque

• Vector definition:
• Magnitude:
• Magnitude (perpendicular):
• Torque of a couple:

Conditions of Equilibrium

• First Condition (Translational):
• For coplanar forces:
• Example X-component sum:
• Example Y-component sum:
• Second Condition (Rotational):
• Example Clockwise torque:
• Example Anticlockwise torque:
• Example Sum of torques:

Chapter 3: Motion and Force

Acceleration

• Rate of change of velocity:
• Slope of velocity-time graph:

Average Speed/Acceleration

• Average speed (equal distance):
• Average speed (equal time):
• Average acceleration (two intervals):

Equations of Motion (Galileo)

• First Equation:
• Second Equation:
• Third Equation:
• Distance in nth second:

Newton's Laws of Motion

• Second Law (Proportionality):
• Second Law (Standard Form):
• Third Law:

Momentum and Impulse

• Linear Momentum:
• Zero Momentum:
• Impulse Definition (change in p):
• Impulse Definition (F and t):
• Law of Conservation of Linear Momentum:

Collisions (Elastic in One Dimension)

• Relative velocities 1:
• Relative velocities 2:
• Final velocity of m1:
• Final velocity of m2:

Force Due to Water Flow

• Force:

Momentum and Explosive Forces

• Recoil velocity:

Propulsion of Rocket

• Instantaneous acceleration:

Friction

• Coefficient of friction (words):
• Coefficient of friction (symbols):
• Limiting friction:
• Force for horizontal surface:
• Static friction force:
• Kinetic friction force:
• Angle of friction:
• Angle of static friction:
• Angle of kinetic friction:

Masses in Contact

• Newton's second law for m1:
• Newton's second law for m2:
• Force of reaction:
• Acceleration:

Masses Connected by Strings

• Tension (1 string 2 masses):
• Acceleration (1 string 2 masses):
• Acceleration (2 string 3 masses):
• Tension string1 (2 string 3 masses):
• Tension string2 (2 string 3 masses):

Tension and Acceleration in a String (Pulley)

• Acceleration:
• Tension:

Atwood Machine

• Acceleration due to gravity:
• Acceleration (one body vertical):
• Tension (one body vertical):

Mechanical Advantage

• Definition:
• Load:
• Effort:

Projectile Motion

• Horizontal coordinate:
• Vertical coordinate:
• Time to max height:
• Total time of flight:
• Maximum height:
• Range (horizontal):
• Maximum horizontal range (θ = 45°):
• Relation between Range and Height:

Chapter 4: Work and Energy

Work

• Dot product definition:
• Scalar definition:
• Work along closed path (conservative field):
• Work along closed path (non-conservative field):
• Spring force:
• Work done by variable force (integral):

Power

• Definition:
• Linear motion:
• Linear motion (vector):
• Angular motion:
• Average power:
• Instantaneous power:
• Unit conversion (W to J/s):
• Unit conversion (h.p to watt):
• Unit conversion (h.p to ft-lb/s):
• Unit conversion (kW h to J):

Energy

• Kinetic Energy:
• Kinetic Energy (momentum):
• Gravitational Potential Energy:
• Elastic Potential Energy:
• Electric Potential Energy:
• Work-Energy Principle:
• Absolute Gravitational P.E:
• Escape Velocity:
• Escape Velocity (g):
• Escape Velocity (numerical values):
• Interconversion of K.E and P.E:
• Velocity from P.E conversion:
• Einstein's Mass Energy:

Chapter 5: Rotational and Circular Motion

Angular Displacement

• Arc length:
• Degree to radian conversion:
• Numerical conversion (1 degree):
• Numerical conversion (1 radian):

Angular Velocity & Acceleration

• Average angular velocity:
• Instantaneous angular velocity:
• Tangential velocity relation:
• Tangential velocity (vector):
• Angular acceleration:
• Tangential acceleration (vector):

Centripetal Force & Acceleration

• Total acceleration:
• Centripetal force (vector, angular):
• Centripetal force (vector, linear):
• Centripetal acceleration (vector, angular):
• Centripetal acceleration (vector, linear):

Comparison of Linear and Rotatory Motion

• Linear velocity:
• Angular velocity:
• Linear displacement:
• Angular displacement:
• Linear acceleration:
• Angular acceleration:
• Mass:
• Moment of inertia:
• Linear momentum:
• Angular momentum:
• Linear impulse:
• Angular impulse:
• Force:
• Torque:
• Linear Work:
• Rotational Work:
• Linear Kinetic Energy:
• Rotational Kinetic Energy:
• Newton's First Law (Linear):
• Newton's Second Law (Linear):
• Newton's Third Law (Linear):
• Newton's First Law (Rotational):
• Newton's Second Law (Rotational):
• Newton's Third Law (Rotational):
• Linear Equation of Motion (i):
• Linear Equation of Motion (ii):
• Linear Equation of Motion (iii):
• Rotational Equation of Motion (i):
• Rotational Equation of Motion (ii):
• Rotational Equation of Motion (iii):
• Distance in nth second:
• Angle in nth second:
• Distance with constant velocity:
• Angle with constant angular velocity:
• Average linear velocity:
• Average angular velocity:

Moment of Inertia

• Definition:
• Rotational Analogue of Newton's Second Law:
• Hoop or cylindrical shell:
• Hollow cylinder:
• Solid cylinder or disk:
• Rectangular plate:
• Long thin rod:
• Solid sphere:
• Thin spherical shell:

Angular Momentum

• Linear momentum relation:
• Definition (scalar):
• Definition (vector):
• For circular orbit:
• Definition (rotational):
• Conservation Law:
• Conservation Law (simplified):

Rotational Kinetic Energy

• General:
• Disc:
• Hoop:
• Velocity of hoop (inclined plane):
• Velocity of disc (inclined plane):

Motion in a Vertical Circle

• Tension at highest point:
• Minimum tension at highest point:
• Minimum velocity at highest point (tension):
• Minimum velocity at highest point (formula):
• Critical speed:
• Tension at lowest point:
• Tension at lowest point (simplified):
• Velocity at lowest point:
• Velocity at horizontal points:

Banking of Curved Tracks

• Horizontal component of normal force:
• Vertical component of normal force:
• Angle of banking:
• Angle of banking (inverse tan):
• Maximum speed without skidding:
• Maximum speed without skidding (alt):

Universal Gravitation

• Newton's Law:
• Acceleration due to gravity:
• Mass of Earth (density):
• Acceleration due to gravity (density):

Variations in g

• Above surface:
• Above surface (approximate):
• With depth:
• At equator:
• At poles:
• Equator vs Poles:

Real and Apparent Weight

• Stationary/Constant velocity lift:
• Accelerating upward lift:
• Accelerating downward lift:

Artificial Satellites

• Critical velocity:
• Orbital velocity:
• Frequency for artificial gravity:
• Time period for artificial gravity:
• Radius of geo-stationary orbit:
• Kepler's Third Law:

Chapter 7: Fluid Dynamics

Density and Pressure

• Density:
• Pressure (definition):
• Pressure (fluid depth):
• Pascal's Law:
• Unit conversion (atm to Pa):
• Unit conversion (bar to Pa):
• Unit conversion (torr to N/m^2):
• Unit conversion (torr to mm of Hg):
• Thrust:

Buoyancy and Floatation

• Buoyant Force (Archimedes' Principle):

Viscous Drag and Stokes' Law

• Stokes' Law:

Terminal Velocity

• Terminal velocity (general):
• Terminal velocity (simplified):

Fluid Flow and Equation of Continuity

• Mass flow rate:
• Mass flow rate (simplified):
• Volume flow rate:
• Volume flow rate (simplified):

Bernoulli's Equation and Applications

• Bernoulli's Equation:
• Potential energy per unit volume:
• Kinetic energy per unit volume:
• Kinetic energy:
• Pressure energy:
• Pressure energy per unit volume:
• Torricelli's Theorem (Efflux Velocity):
• Venturimeter relation:

Chapter 8: Waves

Wave Properties

• Wave speed:
• Particles in phase (path difference):
• Particles out of phase (path difference):

Velocity of Sound in Air

• General Mechanical Wave:
• Newton's Formula (Isothermal):
• Laplace's Formula (Adiabatic):
• Temperature Dependence:
• Ratio of speeds with temperature:

Superposition and Interference

• Superposition Principle:
• Beat frequency:

Waves on Stretched Strings

• Speed of wave:
• Fundamental frequency (fixed both ends):
• Harmonics (fixed both ends):

Standing Waves in Air Columns

• Length of open pipe (harmonics):
• Length of closed pipe (harmonics):
• Fundamental frequency (open pipe):
• Fundamental frequency (closed pipe):

Doppler's Effect

• Source towards listener:
• Source away listener:
• Listener towards source:
• Listener away source:
• General (towards each other):
• General (away from each other):

Chapter 9: Physical Optics

Interference of Light (Young's Double Slit)

• Optical path:
• Bright fringes (constructive):
• Dark fringes (destructive):
• Position of m-th bright fringe:
• Position of m-th dark fringe:
• Wavelength from bright fringe:
• Wavelength from dark fringe:
• Fringe width:

Diffraction

• Minima for narrow slit:
• Diffraction Grating (maxima):
• Grating element:
• Resolving power (grating, lambda):
• Resolving power (grating, N and m):
• Bragg's Law:

Polarization

• Malus' Law (Intensity):

Chapter 10: Optical Instruments

Lenses and Magnification

• Power of a Lens (meters):
• Power of a Lens (cm):
• Combination of Lenses (Power):
• Combination of Lenses (Focal Length):
• Lens Formula:
• Linear magnification (q/p):
• Linear magnification (h_i/h_o):
• Angular magnification:

Resolving Power

• Angle of Resolution:
• Resolving power (lens):

Microscopes

• Simple Microscope Magnifying Power:
• Compound Microscope Magnification:

Refraction and Speed of Light

• Refractive index of prism:
• Michelson's Speed of Light:
• Index of Refraction:
• Snell's Law:

Chapter 11: Heat & Thermodynamics

Temperature and Heat Capacity

• Heat exchange:
• Specific Heat:

Temperature Conversions

• Celsius to Fahrenheit:
• Fahrenheit to Celsius:
• Celsius to Kelvin:
• Kelvin to Celsius:
• Relation between scales:

Kinetic Theory of Gases

• RMS speed of gas molecules:
• Pressure from KMT:
• Combined Gas Law:

Laws of Thermodynamics

• Thermodynamic work (constant pressure):
• First Law of Thermodynamics:
• Efficiency of Carnot Engine:
• Change in entropy:

Molar Specific Heats and Processes

• Heat supplied at constant volume:
• Heat supplied at constant pressure:
• Mayer's relation:
• Adiabatic index:
• Isothermal process equation:
• Adiabatic process equation:
• Isochoric process relation:
• Isobaric process relation:
• Slope of Isothermal P-V curve:
• Slope of Adiabatic P-V curve:
• Isothermal Elasticity:
• Adiabatic Elasticity:

Chapter 12: Electrostatics

Charge and Electric Field

• Charge per unit area:
• Acceleration of charged particle in electric field:
• Elementary charge:

Coulomb's Law

• Electrical Force:
• Coulomb's constant in vacuum:
• Permittivity of free space relation:
• Permittivity of free space value:
• Action-reaction pair:
• Force in medium (with F):
• Force in medium (with epsilon_r):
• Relative Permittivity:

Electric Field Intensity

• Definition:
• Due to point charge:
• Due to infinite sheet:
• Between parallel plates (vacuum):
• Between parallel plates (dielectric, epsilon_r):
• Between parallel plates (dielectric, K):

Electric Flux and Gauss's Law

• Definition (vector):
• Definition (scalar):
• Maximum flux:
• Minimum flux:
• Gauss's Law:
• Total flux:

Electric Potential

• Definition:
• Due to point charge:
• Relation between E and V:

Capacitance

• Definition:
• Parallel plate (vacuum):
• Parallel plate (dielectric, epsilon):
• Parallel plate (dielectric, K):
• Energy stored (Q, V):
• Energy stored (C, V):
• Energy stored (Q, C):
• Series combination:
• Parallel combination:
• RC Time Constant:

Millikan's Oil Drop Experiment

• Balanced forces:
• Charge on oil drop:

Chapter 13: Current Electricity

Current and Resistance

• Current:
• Ohm's Law:
• Resistance:

Resistor Combinations

• Series:
• Parallel:

Power Dissipation

• Power (V, I):
• Power (I, R):
• Power (V, R):

Kirchhoff's Rules

• First Rule (Junction Rule):
• Second Rule (Loop Rule):

Wheatstone Bridge and Potentiometer

• Wheatstone Bridge (balance condition):
• Potentiometer (voltage measurement):

Chapter 14: Electromagnetism

Magnetic Force

• On current-carrying conductor (vector):
• On current-carrying conductor (magnitude):
• On moving charge (Lorentz Force, vector):
• On moving charge (Lorentz Force, magnitude):

Motion of Charge in Magnetic Field

• Radius of circular path:
• Frequency of revolution (cyclotron):

Magnetic Field and Ampere's Law

• Magnetic Flux (vector):
• Magnetic Flux (scalar):
• Ampere's Law:
• Magnetic field (long straight wire):
• Magnetic field (inside solenoid):
• Magnetic field (inside toroid):
• Force per unit length (parallel wires):

Torque on Current Loop and Galvanometer

• Torque on current loop (vector):
• Torque on current loop (magnitude):
• Magnetic dipole moment:
• Shunt resistance (ammeter):
• Multiplier resistance (voltmeter):

Chapter 15: Electromagnetic Induction

Magnetic Flux and Faraday's Law

• Magnetic Flux (vector):
• Magnetic Flux (scalar):
• Faraday's Law of Induction:
• Motional EMF:

Inductance

• Self-induced EMF:
• Self-inductance (solenoid):
• Energy stored in inductor:
• Mutually induced EMF:
• Mutual inductance (coaxial solenoids):

AC Generators and Transformers

• AC Generator EMF:
• Maximum AC Generator EMF:
• Transformer voltage ratio:
• Transformer current ratio:
• Transformer efficiency:
• Transformer efficiency (power):

Chapter 16: Alternating Current

AC Quantities

• Instantaneous AC current:
• Instantaneous AC voltage:
• RMS current:
• RMS voltage:

Reactance and Impedance

• Ohm's Law for Resistor:
• Inductive Reactance:
• Ohm's Law for Inductor:
• Capacitive Reactance:
• Ohm's Law for Capacitor:
• Impedance (RC series):
• Phase angle (RC series):
• Impedance (RL series):
• Phase angle (RL series):
• Impedance (RLC series):
• Phase angle (RLC series):

Resonance and Power

• Resonant frequency (RLC series):
• Quality Factor (Q-factor, L):
• Quality Factor (Q-factor, C):
• Quality Factor (Q-factor, L/C):
• Power (Resistor, I):
• Power (Resistor, V, I):
• Average Power (AC):
• Power Factor:
• Wattless Current:

Chapter 17: Physics of Solids

Stress and Strain

• Stress:
• Longitudinal Strain:
• Volumetric Strain:
• Shear Strain:
• Shear Strain (approximate):

Moduli of Elasticity

• Hooke's Law:
• Young's Modulus (definition):
• Young's Modulus (formula):
• Young's Modulus (simplified):
• Bulk Modulus (definition):
• Bulk Modulus (formula):
• Compressibility:
• Shear Modulus (definition):
• Shear Modulus (formula):

Chapter 18: Electronics

Transistors and Amplifiers

• Current gain (β for common emitter):
• Voltage gain (transistor):
• Inverting Amplifier Gain:
• Non-Inverting Amplifier Gain:
• Adder/Summing Amplifier Output:

Logic Gates (Boolean Algebra)

• AND Gate:
• OR Gate:
• NOT Gate:
• NAND Gate:
• NOR Gate:
• XOR Gate:
• XOR Gate (expanded):
• XNOR Gate:
• XNOR Gate (expanded):

Chapter 19: Dawn of Modern Physics

Relativity

• Mass-Energy relation:
• Relativistic Mass:
• Lorentz Contraction (Length):
• Time Dilation:

Black Body Radiation

• Wien's Displacement Law:
• Stefan-Boltzmann Law:

Photoelectric Effect

• Photon energy (f):
• Photon energy (λ):
• Photon momentum (λ):
• Photon momentum (m,c):
• Photon momentum (h,f,c):
• Einstein's Photoelectric Equation (phi):
• Einstein's Photoelectric Equation (f_o):
• Einstein's Photoelectric Equation (f-f_o):
• Stopping potential relation (K.E.):
• Stopping potential relation (v_max):
• Work function (f_o):
• Work function (λ_o):

Compton Effect

• Compton shift (delta lambda):
• Compton shift (formula):
• Compton wavelength:

Pair Production and Annihilation

• Pair production energy:
• Rest mass energy of electron/positron:

De-Broglie Wavelength and Uncertainty Principle

• De-Broglie wavelength (v):
• De-Broglie wavelength (p):
• Davisson and Germer wavelength:
• Heisenberg's Uncertainty Principle (Position-Momentum):
• Heisenberg's Uncertainty Principle (Energy-Time):

Chapter 20: Atomic Spectra

Hydrogen Spectrum

• General formula:
• Rydberg's constant:
• Lyman Series (longest wavelength):
• Lyman Series (shortest wavelength):
• Balmer Series (longest wavelength):
• Balmer Series (shortest wavelength):
• Paschen Series (longest wavelength):
• Paschen Series (shortest wavelength):
• Bracket Series (longest wavelength):
• Bracket Series (shortest wavelength):
• Pfund Series (longest wavelength):
• Pfund Series (shortest wavelength):

Bohr's Model

• Angular momentum quantization:
• Radius of n-th orbit:
• Radius of n-th orbit (simplified):
• Bohr's Radius (n=1):
• Energy of electron in n-th orbit (KE+PE):
• Energy of electron in n-th orbit (r_n):
• Energy of electron in n-th orbit (E_o):
• Ground state energy (formula):
• Ground state energy (value):
• Energy transition (delta E):
• Energy transition (hf):

X-Rays

• Characteristic X-ray energy (K-alpha):
• Characteristic X-ray energy (M-alpha):
• Continuous X-ray maximum frequency:

Chapter 21: Nuclear Physics

Nuclear Composition and Properties

• Number of neutrons:
• Mass of electron:
• Mass of proton:
• Mass of neutron:
• Mass of deuteron:
• Mass of helium nucleus:
• Atomic mass unit to MeV:
• Mass defect:
• Mass defect for deuterium:
• Binding Energy:
• Binding Energy (expanded):
• Binding Energy for deuterium:

Nuclear Forces

• Coulomb's repulsive force:
• Newton's attraction force:

Radioactive Decay

• α-decay:
• β⁻-decay:
• β⁺-decay:
• γ-decay:
• Radioactive decay law:
• Radioactive decay (activity):
• Half-life:
• Mean life:

Radiation Exposure and Units

• Absorbed Dose:
• Equivalent Dose:
• Becquerel (unit of activity):
• Curie (unit of activity):

Nuclear Fission and Fusion

• D-D Reaction:
• D-T Reaction:
• Energy from 1 atom of U-235:
• Energy from 1 kg of U-235:
• Time for one fission:
• Time for 60 fissions:
• Efficiency of petrol engine:
• Efficiency of diesel engine:

Mass Spectrograph

• Radius of path: