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17 Verified Equations

CSCA Physics Formula Catalog

CSCA 物理定律与模型公式库

Exhaustive guide to all 17 CSCA Physics equations: kinematics, momentum conservation, thermodynamics, electrodynamics, circuits, and wave optics.

Mechanics

6 Formulas

Kinematics Equations under Constant Acceleration

匀变速直线运动规律与位移公式

Calculates displacement (s) and final velocity (v) under constant linear acceleration (a) starting with initial velocity (v₀).

$\[ v = v_0 + at, \quad s = v_0 t + \frac{1}{2} a t^2, \quad v^2 - v_0^2 = 2as \]$
Proof

Newton's Second Law of Motion

牛顿第二运动定律

States that the net external force vector acting on an object is equal to its inertial mass (m) multiplied by its acceleration vector (a).

$\[ \sum \mathbf{F} = m\mathbf{a} \]$
Proof

Momentum, Impulse & Law of Conservation of Momentum

动量定理与动量守恒定律

Relates impulse (FΔt) to change in linear momentum (Δp). In an isolated system with zero net external force, total momentum is strictly conserved.

$\[ \mathbf{I} = \mathbf{F}\Delta t = \Delta \mathbf{p}, \quad m_1 \mathbf{v}_1 + m_2 \mathbf{v}_2 = m_1 \mathbf{v}_1' + m_2 \mathbf{v}_2' \]$
Proof

Work-Energy Theorem & Conservation of Mechanical Energy

动能定理与机械能守恒定律

The net work done on an object equals the change in kinetic energy. When only conservative forces (gravity/elasticity) do work, total mechanical energy is conserved.

$\[ W_{\text{net}} = \Delta E_k = \frac{1}{2}mv_2^2 - \frac{1}{2}mv_1^2, \quad E_{k1} + E_{p1} = E_{k2} + E_{p2} \]$
Proof

Uniform Circular Motion & Law of Universal Gravitation

匀速圆周运动与万有引力定律

Centripetal force provides centripetal acceleration in circular motion. For celestial orbital motion, universal gravitation acts as the sole centripetal force.

$\[ F_c = m\frac{v^2}{r} = m\omega^2 r, \quad F_g = G\frac{Mm}{r^2} = m\frac{v^2}{r} \implies v = \sqrt{\frac{GM}{r}} \]$
Proof

Simple Harmonic Motion & Mechanical Wave Speed

简谐运动周期与机械波传播公式

The period (T) of a simple pendulum of length L under small angles, and the fundamental relation linking wave propagation speed (v), wavelength (λ), and frequency (f).

$\[ T = 2\pi \sqrt{\frac{L}{g}}, \quad v = \frac{\lambda}{T} = \lambda f \]$
Proof

Electromagnetism

6 Formulas

Coulomb's Law & Electric Field Strength

库仑定律与电场强度公式

Calculates the electrostatic force (F) between point charges, electric field strength (E), and potential difference (U = Ed) in a uniform field.

$\[ F = k_e \frac{|q_1 q_2|}{r^2}, \quad E = \frac{F}{q} = k_e \frac{Q}{r^2}, \quad U = Ed \]$
Proof

Ohm's Law & Closed Circuit EMF Equation

闭合电路欧姆定律与电功率公式

Relates current (I) in a closed circuit to source EMF (E), external resistance (R), and internal resistance (r). Terminal voltage U decreases linearly with current.

$\[ I = \frac{E}{R + r}, \quad U = E - Ir, \quad P = UI = I^2 R \]$
Proof

Lorentz Force & Magnetic Ampere Force

安培力与洛伦兹力公式

Magnetic force on a current-carrying conductor (Ampere) and on a moving charged particle (Lorentz). Lorentz force acts as centripetal force resulting in circular orbit radius r = mv/(qB).

$\[ F_{\text{Ampere}} = BIL\sin\theta, \quad F_{\text{Lorentz}} = qvB\sin\theta, \quad r = \frac{mv}{qB} \]$
Proof

Faraday's Law of Induction & Motional EMF

法拉第电磁感应定律与动生电动势

Calculates induced electromotive force from magnetic flux rate of change (ΔΦ/Δt) or conductor rod cutting magnetic field lines with velocity v.

$\[ E = n\frac{\Delta \Phi}{\Delta t}, \quad E = BLv\sin\theta \]$
Proof

AC Series RLC Circuit Impedance & Phasor

交变电流RLC串联电路阻抗与相量公式

Calculates total AC impedance (Z) in a series RLC circuit. XL = ωL is inductive reactance, XC = 1/(ωC) is capacitive reactance, and θ is the phase difference between voltage and current.

$\[ Z = \sqrt{R^2 + (X_L - X_C)^2}, \quad \tan\theta = \frac{X_L - X_C}{R} \]$
Proof

AC Active Power & Power Factor Formula

交流电路有功功率与功率因数公式

Active (real) power P is the rate of energy dissipation by the resistive component in an AC circuit. cos φ is the power factor, representing the ratio of active power to apparent power S = UI.

$\[ P = UI\cos\varphi, \quad \cos\varphi = \frac{R}{Z} = \frac{R}{\sqrt{R^2 + (X_L - X_C)^2}} \]$
Proof

Thermodynamics

1 Formula

First Law of Thermodynamics & Ideal Gas Law

热力学第一定律与理想气体状态方程

Conservation of energy for thermal systems: internal energy change (ΔU) equals heat absorbed (Q) plus work done ON the system (W). For ideal gases, PV/T is invariant.

$\[ \Delta U = Q + W, \quad \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]$
Proof

Optics

2 Formulas

Snell's Law of Refraction & Total Internal Reflection

光的折射定律与全反射临界角公式

Relates angles of incidence and refraction across medium boundaries. Total internal reflection (TIR) occurs when light travels from optically denser to rarer medium with angle θ ≥ C.

$\[ n = \frac{c}{v} = \frac{\sin\theta_1}{\sin\theta_2}, \quad \sin C = \frac{1}{n} \]$
Proof

Young's Double-Slit Interference Fringe Spacing

双缝干涉条纹间距公式

Calculates the spacing (Δx) between adjacent bright (or dark) interference fringes, where L is screen distance, d is slit separation, and λ is light wavelength.

$\[ \Delta x = \frac{L}{d}\lambda \]$
Proof

Modern Physics

2 Formulas

Einstein's Photoelectric Effect & Photon Energy

光电效应方程与光子能量公式

Einstein's equation for photoelectric emission. Maximum kinetic energy depends linearly on frequency ν above threshold ν₀. Stopping potential U_c measures E_kmax.

$\[ E_{\text{photon}} = h\nu, \quad E_{k\max} = h\nu - W_0 = eU_c \]$
Proof

Bohr Hydrogen Energy Levels & Mass-Energy Equivalence

玻尔氢原子能级跃迁与质能方程

Bohr's quantization condition for atomic transitions: emitted/absorbed photon energy equals the difference between orbital energy states. Mass defect Δm yields binding energy ΔE.

$\[ E_n = \frac{E_1}{n^2} \quad (E_1 = -13.6\text{ eV}), \quad h\nu = E_m - E_n, \quad \Delta E = \Delta m c^2 \]$
Proof