Catalog / Physics Fundamentals Cheatsheet
Physics Fundamentals Cheatsheet
A concise reference guide to fundamental concepts, formulas, and principles in Physics. Ideal for students and professionals seeking a quick review.
Mechanics
Kinematics
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Displacement (\Delta x) |
\Delta x = x_f - x_i (final position - initial position) |
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Average Velocity (v_{avg}) |
v_{avg} = \frac{\Delta x}{\Delta t} (displacement / time) |
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Average Acceleration (a_{avg}) |
a_{avg} = \frac{\Delta v}{\Delta t} (change in velocity / time) |
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Final Velocity (v_f) (constant acceleration) |
v_f = v_i + at (initial velocity + acceleration * time) |
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Displacement (\Delta x) (constant acceleration) |
\Delta x = v_i t + \frac{1}{2}at^2 |
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Final Velocity Squared (v_f^2) (constant acceleration) |
v_f^2 = v_i^2 + 2a\Delta x |
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Position (x) as a function of time (t) |
x(t) = x_0 + v_0t + (1/2)at^2 |
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Average Speed |
Total distance traveled / Total time |
Dynamics
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Newton’s First Law (Inertia) |
An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by a force. |
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Newton’s Second Law |
F = ma (Force = mass * acceleration) |
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Newton’s Third Law |
For every action, there is an equal and opposite reaction. |
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Weight (W) |
W = mg (mass * acceleration due to gravity) |
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Frictional Force (F_f) |
F_f = \mu F_N (coefficient of friction * normal force) |
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Static Friction |
F_s \le \mu_s F_N |
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Kinetic Friction |
F_k = \mu_k F_N |
Work and Energy
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Work (W) |
W = Fd \cos(\theta) (force * distance * cosine of the angle between them) |
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Kinetic Energy (KE) |
KE = \frac{1}{2}mv^2 (1/2 * mass * velocity squared) |
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Potential Energy (PE) - Gravitational |
PE = mgh (mass * gravity * height) |
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Potential Energy (PE) - Spring |
PE = \frac{1}{2}kx^2 (1/2 * spring constant * displacement squared) |
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Power (P) |
P = \frac{W}{\Delta t} (work / time) |
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Work-Energy Theorem |
W_{net} = \Delta KE |
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Conservation of Mechanical Energy (no non-conservative forces) |
KE_i + PE_i = KE_f + PE_f |
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Efficiency |
\frac{W_{out}}{W_{in}} |
Thermodynamics
Thermodynamic Definitions
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Temperature (T) |
A measure of the average kinetic energy of the particles in a system. |
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Heat (Q) |
The transfer of energy between objects due to a temperature difference. |
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Internal Energy (U) |
The total energy of all the molecules within a substance. |
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Specific Heat (c) |
The amount of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius. |
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Latent Heat (L) |
The heat required to cause a phase change (e.g., solid to liquid). |
Laws of Thermodynamics
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Zeroth Law |
If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. |
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First Law |
\Delta U = Q - W (change in internal energy = heat added - work done by the system) |
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Second Law |
The entropy of an isolated system always increases or remains constant. Heat cannot spontaneously flow from a cold body to a hot body. |
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Third Law |
The entropy of a system approaches a constant value as the temperature approaches absolute zero. |
Heat Transfer
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Conduction |
Q = \frac{kA\Delta T t}{L} (heat transfer through a material) |
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Convection |
Heat transfer by the movement of a fluid. |
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Radiation |
Q = \epsilon \sigma A T^4 t (heat transfer by electromagnetic radiation) |
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Stefan-Boltzmann Constant |
\sigma = 5.67 \times 10^{-8} W/m^2K^4 |
Electromagnetism
Electrostatics
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Coulomb’s Law |
F = k \frac{|q_1 q_2|}{r^2} (force between two point charges) |
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Electric Field (E) |
E = \frac{F}{q} (force per unit charge) |
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Electric Potential (V) |
V = \frac{PE}{q} (potential energy per unit charge) |
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Electric Potential Energy (PE) |
PE = qV |
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Capacitance (C) |
C = \frac{Q}{V} (charge / voltage) |
Magnetism
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Magnetic Force on a Moving Charge |
F = qvB \sin(\theta) (charge * velocity * magnetic field * sine of the angle) |
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Magnetic Force on a Current-Carrying Wire |
F = ILB \sin(\theta) (current * length * magnetic field * sine of the angle) |
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Magnetic Field due to a Long Straight Wire |
B = \frac{\mu_0 I}{2 \pi r} |
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Permeability of Free Space |
\mu_0 = 4\pi \times 10^{-7} T \cdot m/A |
Electromagnetic Induction
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Faraday’s Law |
\mathcal{E} = -N \frac{\Delta \Phi_B}{\Delta t} (induced emf = -number of turns * change in magnetic flux / time) |
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Magnetic Flux (\Phi_B) |
\Phi_B = BA \cos(\theta) (magnetic field * area * cosine of the angle) |
Waves and Optics
Wave Properties
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Wave Speed (v) |
v = f\lambda (frequency * wavelength) |
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Period (T) |
T = \frac{1}{f} (1 / frequency) |
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Wave Number (k) |
k = \frac{2\pi}{\lambda} |
Optics
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Snell’s Law |
n_1 \sin(\theta_1) = n_2 \sin(\theta_2) (refractive index * sine of the angle) |
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Index of Refraction (n) |
n = \frac{c}{v} (speed of light in vacuum / speed of light in the medium) |
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Critical Angle (\theta_c) |
\sin(\theta_c) = \frac{n_2}{n_1} (for total internal reflection, n_1 > n_2) |
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Lens Equation |
\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} (focal length, object distance, image distance) |
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Magnification (M) |
M = - \frac{d_i}{d_o} |
Interference and Diffraction
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Constructive Interference (Double Slit) |
d \sin(\theta) = m \lambda (path difference = integer * wavelength) |
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Destructive Interference (Double Slit) |
d \sin(\theta) = (m + \frac{1}{2}) \lambda |