Physics Cheat Sheet
Essential Physics Formulas and Laws
Mechanics
Property/Formula | Formula | Description | Example |
---|---|---|---|
Newton's Second Law | F = ma | Force equals mass times acceleration. | Mass = 5 kg, acceleration = 2 m/s²: F = 5 × 2 = 10 N |
Kinetic Energy | KE = ½mv² | Kinetic energy equals one-half mass times velocity squared. | Mass = 2 kg, velocity = 3 m/s: KE = ½ × 2 × 3² = 9 J |
Gravitational Potential Energy | PE = mgh | Potential energy equals mass times gravity times height. | Mass = 1 kg, height = 10 m: PE = 1 × 9.8 × 10 = 98 J |
Work | W = Fd | Work equals force times distance. | Force = 10 N, distance = 5 m: W = 10 × 5 = 50 J |
Power | P = W/t = Fv | Power equals work divided by time or force times velocity. | Work = 100 J, time = 10 s: P = 100/10 = 10 W |
Momentum | p = mv | Momentum equals mass times velocity. | Mass = 3 kg, velocity = 4 m/s: p = 3 × 4 = 12 kg⋅m/s |
Velocity | v = Δx/Δt | Velocity equals change in position divided by change in time. | Distance = 20 m, time = 4 s: v = 20/4 = 5 m/s |
Acceleration | a = Δv/Δt | Acceleration equals change in velocity divided by change in time. | Velocity change = 10 m/s, time = 2 s: a = 10/2 = 5 m/s² |
Electricity
Property/Formula | Formula | Description | Example |
---|---|---|---|
Ohm's Law | V = IR | Voltage equals current times resistance. | Current = 2 A, resistance = 5 Ω: V = 2 × 5 = 10 V |
Electrical Power | P = VI = I²R = V²/R | Power equals voltage times current, or current squared times resistance. | Voltage = 12 V, current = 3 A: P = 12 × 3 = 36 W |
Electrical Energy | E = Pt = VIt | Energy equals power times time or voltage times current times time. | Power = 50 W, time = 2 h: E = 50 × 2 = 100 Wh |
Resistance in Series | R_total = R₁ + R₂ + R₃ + ... | Total resistance in series equals sum of individual resistances. | R₁ = 2 Ω, R₂ = 3 Ω, R₃ = 5 Ω: R_total = 2 + 3 + 5 = 10 Ω |
Resistance in Parallel | 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ... | Reciprocal of total resistance equals sum of reciprocals of individual resistances. | R₁ = 2 Ω, R₂ = 4 Ω: 1/R_total = 1/2 + 1/4 = 3/4, so R_total = 4/3 Ω |
Coulomb's Law | F = k(q₁q₂)/r² | Force between charges equals Coulomb constant times product of charges divided by distance squared. | q₁ = 2 C, q₂ = 3 C, r = 1 m: F = 9×10⁹ × (2×3)/1² = 5.4×10¹⁰ N |
Thermodynamics
Property/Formula | Formula | Description | Example |
---|---|---|---|
Heat Transfer | Q = mcΔT | Heat equals mass times specific heat times temperature change. | Mass = 1 kg, c = 4200 J/kg⋅K, ΔT = 10 K: Q = 1 × 4200 × 10 = 42,000 J |
Ideal Gas Law | PV = nRT | Pressure times volume equals moles times gas constant times temperature. | P = 101,325 Pa, V = 0.0224 m³, n = 1 mol: T = PV/(nR) = 273 K |
Efficiency | η = (W_out/W_in) × 100% | Efficiency equals useful work output divided by total work input times 100%. | W_out = 80 J, W_in = 100 J: η = (80/100) × 100% = 80% |
Waves
Property/Formula | Formula | Description | Example |
---|---|---|---|
Wave Speed | v = fλ | Wave speed equals frequency times wavelength. | Frequency = 50 Hz, wavelength = 2 m: v = 50 × 2 = 100 m/s |
Wave Frequency | f = 1/T | Frequency equals reciprocal of period. | Period = 0.02 s: f = 1/0.02 = 50 Hz |
Doppler Effect | f' = f(v ± v_obs)/(v ± v_source) | Observed frequency changes when source or observer moves relative to the medium. | Source moving toward observer: f' = f(v + v_source)/(v - v_source) |
Optics
Property/Formula | Formula | Description | Example |
---|---|---|---|
Snell's Law | n₁sinθ₁ = n₂sinθ₂ | Refraction law: product of refractive index and sine of angle is constant. | n₁ = 1, θ₁ = 30°, n₂ = 1.5: sinθ₂ = (1×sin30°)/1.5 = 0.333, so θ₂ = 19.5° |
Lens Formula | 1/f = 1/d_o + 1/d_i | Reciprocal of focal length equals sum of reciprocals of object and image distances. | f = 10 cm, d_o = 20 cm: 1/d_i = 1/10 - 1/20 = 1/20, so d_i = 20 cm |
Magnification | m = -d_i/d_o = h_i/h_o | Magnification equals negative image distance over object distance. | d_i = 15 cm, d_o = 30 cm: m = -15/30 = -0.5 (inverted, half size) |
Modern Physics
Property/Formula | Formula | Description | Example |
---|---|---|---|
Mass-Energy Equivalence | E = mc² | Energy equals mass times speed of light squared. | Mass = 1 kg: E = 1 × (3×10⁸)² = 9×10¹⁶ J |
Photoelectric Effect | KE = hf - φ | Kinetic energy of photoelectrons equals photon energy minus work function. | f = 6×10¹⁴ Hz, φ = 2 eV: KE = hf - φ = 2.48 eV - 2 eV = 0.48 eV |
De Broglie Wavelength | λ = h/p = h/(mv) | Wavelength equals Planck constant divided by momentum. | Mass = 9.11×10⁻³¹ kg, velocity = 10⁶ m/s: λ = h/(mv) = 7.28×10⁻¹⁰ m |
Physics Cheat Sheet
Physics: Unveiling the Fundamental Laws of Nature
Physics represents humanity's systematic attempt to understand the fundamental principles governing the universe, from subatomic particles to galactic superclusters. As the most foundational of natural sciences, physics seeks to discover and express the universal laws that describe matter, energy, space, and time. The word "physics" derives from the Greek "physika," meaning "natural things," reflecting its ancient roots in natural philosophy. Modern physics encompasses an extraordinary range—quantum mechanics describing atomic behavior, relativity explaining gravity and spacetime, thermodynamics governing energy and entropy, electromagnetism unifying electric and magnetic phenomena, and much more.
The Evolution of Physical Understanding
Physics has undergone revolutionary transformations throughout history. Classical mechanics, developed primarily by Isaac Newton in the 17th century, explained motion and forces with unprecedented precision, enabling predictions from projectile trajectories to planetary orbits. The 19th century brought thermodynamics, explaining heat and energy relationships, and electromagnetism, unifying previously separate electrical and magnetic phenomena through Maxwell's equations. The early 20th century witnessed quantum mechanics and relativity, overturning classical physics at extreme scales and revealing counterintuitive aspects of reality. Each revolution didn't invalidate previous physics but rather revealed its domain of applicability and embedded it within broader frameworks.
Major Domains of Physical Science
Physics organizes into interconnected branches studying different aspects of the physical world:
- Mechanics: Motion, forces, energy, and momentum in classical and quantum contexts
- Thermodynamics: Heat, temperature, entropy, and the statistical behavior of systems
- Electromagnetism: Electric and magnetic fields, electromagnetic waves, and their interactions with matter
- Optics: Light behavior, reflection, refraction, interference, and optical instruments
- Wave Physics: Oscillations, vibrations, sound waves, and wave phenomena generally
- Modern Physics: Quantum mechanics, relativity, particle physics, and cosmology
The Mathematical Language of Physical Laws
Physics formulas represent patterns discovered through careful observation and experiment, then refined through mathematical expression. These equations aren't merely calculation tools but profound statements about how nature behaves. Newton's F = ma connects force, mass, and acceleration in a simple relationship with vast implications. Einstein's E = mc² reveals the equivalence of mass and energy. Schrödinger's equation describes quantum wave functions. Maxwell's equations unify electricity and magnetism. These formulas achieve remarkable compression—expressing complex phenomena concisely while enabling quantitative prediction with extraordinary precision.
Experimental Foundation and Theoretical Structure
Physics uniquely combines experimental observation with theoretical framework construction. Experiments reveal nature's behavior under controlled conditions, providing data that theories must explain and predict. Theories organize observations into coherent frameworks, suggest new phenomena to investigate, and make testable predictions. This interplay between experiment and theory drives physics forward—discrepancies between prediction and observation lead to refined theories or revolutionary new frameworks. The requirement that theories make precise, testable predictions distinguishes physics from more qualitative sciences and philosophy.
Applications Transforming Modern Civilization
Physical principles underpin virtually all modern technology:
- Electronics and Computing: Semiconductor physics enabling microprocessors, displays, and sensors
- Energy Generation: Nuclear reactors, solar panels, wind turbines based on physical principles
- Medical Technology: MRI machines, radiation therapy, ultrasound imaging, laser surgery
- Communications: Fiber optics, radio transmission, satellite technology, wireless networks
- Transportation: Aerodynamics, propulsion systems, navigation technologies
- Materials Science: Understanding atomic structures to engineer novel materials with specific properties
Educational Value and Scientific Literacy
Studying physics develops quantitative reasoning, systematic problem-solving, and evidence-based thinking applicable across disciplines. Physics education teaches not just formulas but scientific methodology—how to frame questions, design experiments, analyze data, evaluate theories, and think critically about causal relationships. This scientific literacy proves essential for informed citizenship in a technological society where policy decisions increasingly involve scientific considerations. Beyond practical utility, physics provides profound insights into the nature of reality, addressing questions about the universe's structure, origin, and fundamental constituents.
The Unity and Beauty of Physical Laws
A remarkable feature of physics is the unity emerging from seemingly diverse phenomena. Electricity and magnetism, once thought separate, merged into electromagnetism. Quantum field theory unifies quantum mechanics and special relativity. Grand unified theories attempt to unify all fundamental forces. This quest for unification reflects a deep pattern in physics—diverse phenomena often spring from common underlying principles. The mathematical elegance of physical laws, their symmetries and conservation principles, exhibits an aesthetic beauty that attracts many physicists beyond practical applications alone.