Mechanics, Kinematics, Dynamics, Energy, and Momentum
Mechanics comprises roughly half of every introductory physics course. These formulas and concepts form the bedrock for everything else you'll study.
Core Kinematics Equations
Average velocity divides displacement by time: v_avg = Δx / Δt. The three kinematic equations (v = v0 + at, x = v0t + 0.5at^2, v^2 = v0^2 + 2aΔx) solve motion under constant acceleration.
Free fall means motion under gravity alone with a = 9.8 m/s^2 downward, ignoring air resistance. In projectile motion, horizontal velocity stays constant while vertical motion follows free fall.
Newton's Laws and Forces
Newton's first law states objects at rest or in uniform motion remain that way unless a net external force acts. Newton's second law gives F_net = ma (net force equals mass times acceleration). Newton's third law says every action has an equal, opposite reaction.
Friction opposes motion: static friction f_s ≤ μ_s·N, kinetic friction f_k = μ_k·N. In circular motion, centripetal acceleration a_c = v^2/r always points toward the center.
Energy and Momentum
Work transfers energy: W = F·d·cos(θ). Kinetic energy KE = 0.5mv^2 measures motion. Gravitational potential energy PE = mgh near Earth's surface.
Conservation of energy holds in isolated systems without non-conservative forces. Linear momentum p = mv is conserved in collisions. Impulse J = FΔt equals the change in momentum.
Elastic collisions conserve both momentum and kinetic energy. Inelastic collisions conserve momentum only.
| Term | Meaning |
|---|---|
| Average velocity | v_avg = Δx / Δt. The displacement divided by time elapsed. |
| Kinematic equations (constant a) | v = v0 + at; x = v0·t + (1/2)at^2; v^2 = v0^2 + 2aΔx. |
| Free fall | Motion under gravity alone with a = g = 9.8 m/s^2 downward. Air resistance neglected. |
| Projectile motion | Horizontal velocity constant; vertical motion is free fall. Solve x and y components independently. |
| Newton's first law | An object at rest or in uniform motion stays that way unless acted on by a net external force. |
| Newton's second law | F_net = ma. Net force equals mass times acceleration. |
| Newton's third law | For every action force there is an equal and opposite reaction force. |
| Friction | f_s ≤ μ_s·N (static), f_k = μ_k·N (kinetic). Kinetic friction opposes motion. |
| Centripetal acceleration | a_c = v^2/r, directed toward the center of the circular path. |
| Work | W = F·d·cos(θ). Energy transferred by a force over a displacement. |
| Kinetic energy | KE = (1/2)mv^2. Energy of motion. |
| Gravitational potential energy | PE = mgh near Earth's surface. |
| Conservation of energy | In an isolated system, total mechanical energy is conserved unless non-conservative forces act. |
| Linear momentum | p = mv. A vector quantity. Conserved in isolated systems. |
| Impulse | J = FΔt = Δp. Change in momentum equals force times time. |
| Elastic vs inelastic collisions | Elastic collisions conserve both momentum and kinetic energy; inelastic collisions conserve momentum only. |
Waves, Thermodynamics, and Fluids
These three topics bridge mechanics and electromagnetism. Master the wave equation, thermodynamic laws, and fluid principles tested on every physics final.
Waves and Oscillations
Wave speed v = f·λ (frequency times wavelength). Period T = 1/f measures seconds per cycle; frequency measures cycles per second (Hz).
Simple harmonic motion has a restoring force proportional to displacement (F = -kx). Springs vibrate with period T = 2π·sqrt(m/k). A pendulum oscillates with period T = 2π·sqrt(L/g) for small angles, independent of mass.
Transverse waves (like light) oscillate perpendicular to motion direction. Longitudinal waves (like sound) oscillate parallel to motion direction. The Doppler effect shifts observed frequency when source and observer move relative to each other.
Standing waves form when waves travel in opposite directions, creating nodes and antinodes. Sound intensity I = P/A, measured in decibels: β = 10·log(I/I0) with I0 = 10^-12 W/m^2.
Thermodynamics
The ideal gas law PV = nRT relates pressure, volume, moles, and temperature. The first law of thermodynamics ΔU = Q - W says internal energy change equals heat added minus work done.
The second law states entropy always increases in isolated systems. Heat flows spontaneously from hot to cold. A heat engine has efficiency η = W/Q_h. Carnot efficiency gives the theoretical maximum: η_C = 1 - T_c/T_h.
Fluids
Pressure increases with depth: P = P0 + ρgh. Archimedes' principle says buoyant force F_b = ρ_fluid·V_displaced·g equals displaced fluid weight.
Bernoulli's equation P + 0.5ρv^2 + ρgh = constant describes ideal fluid flow along a streamline. The continuity equation A1·v1 = A2·v2 conserves mass in incompressible flow.
| Term | Meaning |
|---|---|
| Wave speed equation | v = f·λ. Wave speed equals frequency times wavelength. |
| Period and frequency | T = 1/f. Period is seconds per cycle; frequency is cycles per second (Hz). |
| Simple harmonic motion | Restoring force proportional to displacement (F = -kx). Period T = 2π·sqrt(m/k) for springs. |
| Pendulum period | T = 2π·sqrt(L/g) for small angles. Independent of mass. |
| Transverse vs longitudinal wave | Transverse oscillation is perpendicular to wave direction (light); longitudinal is parallel (sound). |
| Doppler effect | Observed frequency changes when source and observer move relative to each other. f_obs = f_src·(v ± v_obs)/(v ∓ v_src). |
| Standing waves | Interference of waves traveling in opposite directions produces stationary nodes and antinodes. |
| Intensity (sound) | I = P/A. Decibel level β = 10·log(I/I0), with I0 = 10^-12 W/m^2. |
| Ideal gas law | PV = nRT. Relates pressure, volume, moles, and temperature. |
| First law of thermodynamics | ΔU = Q - W. Internal energy change equals heat added minus work done by the system. |
| Second law of thermodynamics | Entropy of an isolated system always increases. Heat flows spontaneously from hot to cold. |
| Efficiency of a heat engine | η = W/Q_h. Carnot efficiency η_C = 1 - T_c/T_h. |
| Pressure in a fluid | P = P0 + ρgh. Pressure increases linearly with depth. |
| Archimedes' principle | Buoyant force equals the weight of fluid displaced. F_b = ρ_fluid·V_displaced·g. |
| Bernoulli's equation | P + (1/2)ρv^2 + ρgh = constant along a streamline for ideal fluid flow. |
| Continuity equation | A1·v1 = A2·v2 for incompressible fluid flow. Conservation of mass. |
Electricity, Magnetism, and Optics
Second-semester physics centers here. These formulas appear on every E&M exam and carry heavy weight on AP Physics C, MCAT, and engineering placement tests.
Electrostatics and Circuits
Coulomb's law F = k·|q1·q2|/r^2 gives force between charges, where k = 8.99 × 10^9 N·m^2/C^2. Electric field E = F/q points away from positive charges toward negative charges.
Electric potential V = kQ/r measures energy per unit charge in volts. Capacitance C = Q/V measures charge storage. A parallel plate capacitor has C = ε0·A/d.
Ohm's law V = IR relates voltage, current, and resistance. Power P = IV = I^2R = V^2/R. Resistors in series: R_eq = R1 + R2 + ... In parallel: 1/R_eq = 1/R1 + 1/R2 + ...
Kirchhoff's junction rule says current in equals current out. The loop rule states the sum of voltages around a closed loop equals zero.
Magnetism
Magnetic force on a moving charge: F = qv × B, perpendicular to velocity and field. Magnetic force on a current-carrying wire: F = IL × B.
Faraday's law EMF = -dΦ/dt shows changing magnetic flux induces an EMF. Lenz's law states the induced current opposes the change causing it.
Optics
Snell's law n1·sin(θ1) = n2·sin(θ2) relates angles of incidence and refraction to refractive indices. Total internal reflection occurs when light hits a boundary at angle greater than critical angle: sin(θ_c) = n2/n1.
The thin lens equation 1/f = 1/d_o + 1/d_i describes image formation. Magnification m = -d_i/d_o = h_i/h_o. Double-slit interference shows bright fringes where d·sin(θ) = mλ. Single-slit diffraction shows dark fringes at a·sin(θ) = mλ.
| Term | Meaning |
|---|---|
| Coulomb's law | F = k·|q1·q2|/r^2, where k = 8.99 × 10^9 N·m^2/C^2. Force between point charges. |
| Electric field | E = F/q. Force per unit charge. Points away from positive charges, toward negative. |
| Electric potential | V = U/q = kQ/r for a point charge. Scalar quantity measured in volts. |
| Capacitance | C = Q/V. Farads. Parallel plate: C = ε0·A/d. |
| Ohm's law | V = IR. Voltage equals current times resistance. |
| Power in circuits | P = IV = I^2R = V^2/R. |
| Resistors in series and parallel | Series: R_eq = R1 + R2 + …; parallel: 1/R_eq = 1/R1 + 1/R2 + …. |
| Kirchhoff's laws | Junction rule (current in = current out); loop rule (sum of voltages around a loop = 0). |
| Magnetic force on a charge | F = qv × B. Perpendicular to both velocity and magnetic field. |
| Magnetic force on a wire | F = IL × B. Force on a current-carrying wire in a magnetic field. |
| Faraday's law | EMF = -dΦ/dt. A changing magnetic flux induces an EMF. |
| Lenz's law | The induced current opposes the change in flux that caused it. |
| Snell's law | n1·sin(θ1) = n2·sin(θ2). Relates angles of incidence and refraction to refractive indices. |
| Total internal reflection | Occurs when light hits a boundary at an angle greater than the critical angle: sin(θ_c) = n2/n1. |
| Thin lens equation | 1/f = 1/d_o + 1/d_i. Magnification m = -d_i/d_o = h_i/h_o. |
| Diffraction and interference | Double-slit: d·sin(θ) = mλ for constructive interference; single-slit minima at a·sin(θ) = mλ. |
How to Study physics Effectively
Mastering physics requires the right study approach, not more hours. Research shows three techniques produce best learning outcomes: active recall (testing yourself), spaced repetition (reviewing at optimized intervals), and interleaving (mixing related topics).
FluentFlash builds on all three. Every term gets scheduled at the exact moment you're about to forget it, maximizing retention while minimizing study time.
Why Passive Review Fails
Re-reading notes, highlighting textbooks, and watching lectures feel productive but produce only 10-20% of the retention that active recall achieves. Flashcards force your brain to retrieve information, strengthening memory pathways far more than recognition alone.
Pair this with spaced repetition, and you can learn in 20 minutes daily what takes hours of passive review.
A Practical Study Plan
Start by creating 15-25 flashcards covering highest-priority concepts. Review them daily the first week using FSRS scheduling. As cards become easier, intervals expand from minutes to days to weeks.
You're always working on material at the edge of your knowledge. After 2-3 weeks of consistent practice, physics concepts become automatic rather than effortful.
Daily Study Steps
- Generate flashcards using FluentFlash AI or create manually from notes
- Study 15-20 new cards per day plus scheduled reviews
- Use multiple modes (flip, multiple choice, written) to strengthen recall
- Track progress and identify weak topics for focused review
- Review consistently daily, as this beats marathon sessions
- 1
Generate flashcards using FluentFlash AI or create them manually from your notes
- 2
Study 15-20 new cards per day, plus scheduled reviews
- 3
Use multiple study modes (flip, multiple choice, written) to strengthen recall
- 4
Track your progress and identify weak topics for focused review
- 5
Review consistently, daily practice beats marathon sessions
Why Flashcards Work Better Than Other Study Methods for physics
Flashcards aren't just for vocabulary. They're one of the most research-backed study tools for any subject, including physics. When you read textbook passages, your brain stores information in short-term memory. Without retrieval practice, it fades within hours.
Flashcards force retrieval, the mechanism that transfers information from short-term to long-term memory.
The Testing Effect
Hundreds of peer-reviewed studies document the testing effect: students using flashcards consistently outperform re-readers by 30-60% on delayed tests. This isn't because flashcards contain more information. It's because retrieval strengthens neural pathways in ways passive exposure cannot.
Every successful recall of a physics concept makes that concept easier to recall next time. You're building automatic, fluid knowledge.
FSRS Amplifies Results
FluentFlash amplifies this with the FSRS algorithm, a modern spaced repetition system scheduling reviews at mathematically-optimal intervals based on your actual performance. Cards you find easy move further into the future. Cards you struggle with return sooner.
Over time, this builds remarkable retention with minimal effort. Students using FSRS-based systems typically retain 85-95% of material after 30 days, compared to roughly 20% retention from passive review alone.