Calcolatrici Online Gratuite e Strumenti IA

Core kinematics formulas. Velocity: v = d/t (distance over time) for constant velocity, or v = v_0 + at for accelerated motion. Acceleration: a = (v - v_0) / t or a = delta v / delta t, measured in m/s squared. Kinetic energy: KE = (1/2)mv squared, where m = mass in kg, v = velocity in m/s, result in joules (J). Example: a 1500 kg car traveling 25 m/s has KE = 0.5 x 1500 x 625 = 468,750 J (or 469 kJ). Doubling velocity quadruples kinetic energy — this explains why high-speed crashes are disproportionately devastating. Other kinematic equations (constant acceleration): v squared = v_0 squared + 2a x (distance), d = v_0 x t + 0.5 x a x t squared. Free fall (Earth surface, ignoring air resistance): a = g = 9.81 m/s squared. A object dropped from rest falls d = 0.5 x g x t squared; after 1 second, 4.9 m; after 2 seconds, 19.6 m; after 3 seconds, 44.1 m. Terminal velocity (for humans) reaches about 53 m/s (120 mph) after 12 seconds and 450 meters due to air resistance. Energy conservation: KE + PE = constant in isolated systems (PE = mgh, gravitational potential energy). This principle underlies roller coasters, pendulums, and projectile motion. For relativistic speeds (above about 10 percent speed of light), use E = mc squared / sqrt(1 - v squared / c squared).

Ohm's Law: V = IR, where V = voltage (volts), I = current (amperes), R = resistance (ohms). Derived forms: I = V/R and R = V/I. Power calculation: P = VI = I squared x R = V squared / R, measured in watts. Example: a 60-watt lightbulb on 120 V circuit: I = P/V = 60/120 = 0.5 amps. Resistance: R = V/I = 120/0.5 = 240 ohms. For series circuits: total resistance R_total = R_1 + R_2 + R_3... Current is the same through all components. Voltage divides: V_1 = I x R_1, etc. For parallel circuits: 1/R_total = 1/R_1 + 1/R_2 + 1/R_3... Voltage is the same across all branches. Current divides inversely with resistance. Common household references US: wall outlet 120 V, 15 to 20 amp circuits (1800 to 2400 watts maximum); large appliances 240 V (clothes dryer, electric range, EV charger). Circuit breaker trips when current exceeds rated amperage (safety mechanism against fires). AC power formula: P = VI x cos(phi), where phi is the phase angle between voltage and current (power factor). Resistive loads: power factor near 1.0; inductive loads (motors, transformers): power factor 0.7 to 0.95. Utilities charge commercial customers for poor power factor. For DC systems (batteries, solar): P = VI (no power factor). For battery life, use Wh (watt-hours): a 100 Wh battery powers a 10-watt device for 10 hours. Electric car batteries are typically 60 to 100+ kWh (60,000 to 100,000 Wh).

Newton's Law of Universal Gravitation: F = G x (m_1 x m_2) / r squared, where G = 6.674 x 10^-11 N x m squared / kg squared (gravitational constant), m_1 and m_2 are masses (kg), r is distance between centers (m). Gravity on planet surface: g = GM / R squared. Earth: g = 9.81 m/s squared (mass 5.97 x 10^24 kg, radius 6371 km). Moon: g = 1.62 m/s squared (1/6 Earth). Mars: g = 3.71 m/s squared. Jupiter: g = 24.79 m/s squared (if you could stand on the cloud tops). Orbital velocity: v = sqrt(GM/r). Low Earth Orbit (ISS at 400 km altitude): v = 7.66 km/s = 27,580 km/h, orbiting Earth every 90 minutes. Geosynchronous orbit (satellites): altitude 35,786 km, velocity 3.07 km/s, orbital period 24 hours (matches Earth rotation). Escape velocity: v_esc = sqrt(2GM/r). Earth escape: 11.2 km/s (40,320 km/h) from surface. Solar escape from Earth orbit: 16.7 km/s total. Kepler's Third Law: T squared proportional to a cubed, where T is orbital period, a is semi-major axis. Earth: a = 1 AU, T = 1 year. Mars: a = 1.524 AU, T = 1.881 years. Saturn: a = 9.537 AU, T = 29.46 years. The Hohmann transfer orbit is the minimum-energy two-burn trajectory between circular orbits — used for most interplanetary missions. A Hohmann transfer to Mars takes about 259 days.

Wave equation: v = f x lambda, where v = wave speed (m/s), f = frequency (Hz = cycles per second), lambda = wavelength (meters). For electromagnetic waves in vacuum: c = 3 x 10^8 m/s (speed of light). Example: 100 MHz FM radio: lambda = c/f = 3 x 10^8 / 10^8 = 3 meters wavelength. Visible light wavelengths: violet 380 to 450 nm, blue 450 to 495 nm, green 495 to 570 nm, yellow 570 to 590 nm, red 620 to 750 nm (where nm = 10^-9 m). Energy per photon: E = hf = hc/lambda, where h = 6.626 x 10^-34 J x s (Planck's constant). Electromagnetic spectrum complete range (low to high frequency/energy): radio waves (3 kHz to 300 GHz, mm to km wavelengths), microwaves (300 MHz to 300 GHz, mm to m), infrared (300 GHz to 430 THz, 700 nm to 1 mm), visible light (430 to 790 THz), ultraviolet (790 THz to 30 PHz, 10 to 400 nm), X-rays (30 PHz to 30 EHz, 0.01 to 10 nm), gamma rays (above 30 EHz, below 0.01 nm). Sound waves are mechanical (not EM), propagating through medium. Sound in air: v = 343 m/s at 20 C. Doppler effect: observed frequency changes with relative motion. For sound: f_observed = f_source x (v + v_observer) / (v - v_source). For a 1 kHz source and observer approaching at 34.3 m/s (100 mph): f_observed = 1000 x (343 + 34.3) / 343 = 1100 Hz (a full note higher). Used in radar speed guns, astronomy (redshift for distant galaxies), and medical imaging.

Heat transfer fundamentals. Specific heat equation: Q = mc x delta T, where Q = heat energy (J), m = mass (kg), c = specific heat capacity (J/kg x K), delta T = temperature change (K or C, same magnitude). Water c = 4186 J/kg x K — the highest common specific heat, explaining why oceans moderate climate. Air c = 1005 J/kg x K. Example: heating 500 g water from 20 C to 100 C: Q = 0.5 x 4186 x 80 = 167,440 J. With a 1500-watt kettle: time = Q/P = 167440 / 1500 = 112 seconds (typical). Latent heat: energy absorbed during phase change at constant temperature. L_fusion (ice to water) = 334 kJ/kg; L_vaporization (water to steam) = 2260 kJ/kg. To boil the same 500 g water from 100 C to steam requires additional 1130 kJ (vs 167 kJ just to heat it). First Law of Thermodynamics: delta U = Q - W (energy is conserved; change in internal energy equals heat added minus work done by system). Second Law: entropy of isolated systems tends to increase; heat flows from hot to cold naturally. Efficiency of heat engines (Carnot): eta = 1 - T_cold / T_hot (Kelvin). Power plant at 600 C input (873 K) to 25 C output (298 K): max theoretical efficiency = 1 - 298/873 = 66 percent; real plants achieve 35 to 45 percent. Heat transfer modes: conduction (Fourier's Law, solids), convection (natural or forced, fluids), radiation (Stefan-Boltzmann Law, all objects above 0 K radiate). Insulation R-value (US): R-13 to R-21 for walls, R-38 to R-60 for attics meets current codes. R-value represents thermal resistance — higher R means less heat flow.