📚 IB & Edexcel Physics: Formula Handbook | IB 与 Edexcel 物理公式汇总手册
This handbook compiles the essential formulas for IB Physics (both SL and HL) and Edexcel A Level Physics. It covers mechanics, thermal physics, waves, electricity, magnetism, quantum and nuclear physics. Each formula is paired with a brief explanation, first in English then in Chinese, to reinforce understanding and bilingual revision. All symbols follow standard notation and use Unicode characters for easy reading.
本手册汇集了IB物理（标准和高级课程）及爱德思A Level物理的核心公式，涵盖力学、热学、波动、电学、磁学、量子和核物理等领域。每条公式均配有简要说明，先英文后中文，以便巩固理解和双语复习。所有符号均遵循标准记法，并使用Unicode字符，便于阅读。
1. Kinematics | 运动学
Uniformly accelerated motion relates displacement, initial velocity, final velocity, acceleration and time. These equations apply when acceleration is constant.
匀变速运动将位移、初速度、末速度、加速度和时间关联起来。当加速度恒定时，可应用下列方程。
v = u + at
Final velocity v equals initial velocity u plus acceleration a multiplied by time t.
末速度 v 等于初速度 u 加上加速度 a 乘以时间 t。
s = ut + ½at²
Displacement s equals initial velocity times time plus half the acceleration times the square of time.
位移 s 等于初速度乘以时间加上加速度乘以时间平方的一半。
v² = u² + 2as
The square of the final velocity equals the square of the initial velocity plus twice the acceleration times displacement.
末速度的平方等于初速度的平方加上两倍加速度乘以位移。
s = ½(u + v)t
Displacement is the average velocity multiplied by time.
位移等于平均速度乘以时间。
For projectile motion, horizontal and vertical components are treated independently; vertical motion follows the constant acceleration formulae with a = g (acceleration due to gravity) downward.
对于抛体运动，水平与竖直分量独立处理；竖直方向遵循匀加速度公式，其中 a = g（重力加速度）向下。
2. Dynamics and Forces | 动力学与力
Newton’s Second Law states that the net force on an object is equal to the product of its mass and acceleration.
牛顿第二定律指出，物体所受合力等于其质量乘以加速度。
F = ma
F is net force (N), m is mass (kg), a is acceleration (m s⁻²).
F 为合力（牛顿），m 为质量（千克），a 为加速度（米每二次方秒）。
Weight is the gravitational force on a mass: W = mg, where g = 9.81 N kg⁻¹ on Earth’s surface.
重量是质量所受的重力：W = mg，地球表面 g 取 9.81 N kg⁻¹。
Fₖ = μₖR and Fₛ ≤ μₛR
Kinetic friction Fₖ equals coefficient of kinetic friction μₖ times normal reaction R. Static friction Fₛ is less than or equal to μₛR.
动摩擦力 Fₖ 等于动摩擦因数 μₖ 乘以支持力 R。静摩擦力 Fₛ 小于等于 μₛR。
Hooke’s Law for an ideal spring: F = kx, where k is the spring constant and x the extension.
理想弹簧的胡克定律：F = kx，k 为劲度系数，x 为伸长量。
3. Work, Energy and Power | 功、能和功率
Work done by a constant force is the product of the force, displacement and the cosine of the angle between them.
恒力做的功等于力、位移及两者夹角余弦的乘积。
W = Fd cosθ
Kinetic energy: Eₖ = ½mv². Gravitational potential energy near Earth’s surface: Eₚ = mgΔh.
动能：Eₖ = ½mv²。地球表面附近的重力势能：Eₚ = mgΔh。
Eₖ = ½mv²
ΔEₚ = mgΔh
Work–energy principle: net work done equals change in kinetic energy, W_net = ΔEₖ.
功能原理：合力做的功等于动能的变化，W_net = ΔEₖ。
Power P is the rate of doing work: P = W / t = Fv for constant force and velocity parallel.
功率 P 是做功的速率：P = W / t = Fv（力与速度平行时）。
P = W / t = Fv
Efficiency = (useful power output) / (total power input) × 100%.
效率 = （有用输出功率）/（总输入功率） × 100%。
4. Momentum and Impulse | 动量与冲量
Momentum p = mv. Impulse J = FΔt = Δp. The area under a force–time graph gives impulse.
动量 p = mv。冲量 J = FΔt = Δp。力–时间图下的面积表示冲量。
p = mv
J = FΔt = Δp
Principle of conservation of momentum: in a closed system, total momentum before collision equals total momentum after collision, provided no external force acts.
动量守恒定律：孤立系统中，只要不受外力，碰撞前的总动量等于碰撞后的总动量。
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Elastic collision: kinetic energy is conserved. Inelastic collision: kinetic energy is not conserved; objects may stick together.
弹性碰撞：动能守恒。非弹性碰撞：动能不守恒；物体可能粘在一起。
5. Circular Motion and Gravitation | 圆周运动与万有引力
Centripetal acceleration a = v²/r = ω²r. Centripetal force F = mv²/r = mω²r.
向心加速度 a = v²/r = ω²r。向心力 F = mv²/r = mω²r。
a = v²/r = ω²r
F = mv²/r = mω²r
Angular velocity ω = Δθ/Δt. Relationship with period T: ω = 2π/T, v = 2πr/T.
角速度 ω = Δθ/Δt。与周期 T 的关系：ω = 2π/T，v = 2πr/T。
Newton’s law of gravitation: F = G (Mm) / r². Gravitational field strength g = GM / r².
牛顿万有引力定律：F = G (Mm) / r²。引力场强 g = GM / r²。
F = G M m / r²
g = GM / r²
Gravitational potential V = – GM / r (HL). Escape velocity v_esc = √(2GM / r).
引力势 V = – GM / r（高级内容）。逃逸速度 v_esc = √(2GM / r)。
6. Thermal Physics and Gases | 热物理与气体
Heat transfer: Q = mcΔθ for temperature change, Q = mL for phase change.
热量传递：温度变化时 Q = mcΔθ，相变时 Q = mL。
Q = mcΔT
Q = mL
Ideal gas equation: pV = nRT = Nk_B T, where k_B = 1.38×10⁻²³ J K⁻¹.
理想气体状态方程：pV = nRT = Nk_B T，其中 k_B = 1.38×10⁻²³ J K⁻¹。
pV = nRT
Average kinetic energy of a molecule: E_k, avg = 3/2 k_B T (for a monatomic gas).
分子平均动能：E_k, avg = 3/2 k_B T（对于单原子气体）。
Internal energy ΔU = Q – W (First law of thermodynamics). Work done by gas: W = pΔV (constant pressure).
内能 ΔU = Q – W（热力学第一定律）。气体做功：W = pΔV（恒压过程）。
7. Oscillations and Waves | 振动与波
Simple harmonic motion: a = –ω²x. Displacement x = A sin(ωt) or x = A cos(ωt).
简谐运动：a = –ω²x。位移 x = A sin(ωt) 或 x = A cos(ωt)。
a = –ω²x
Period of a mass-spring system: T = 2π√(m/k). Period of a simple pendulum: T =2π√(L/g).
弹簧振子周期：T = 2π√(m/k)。单摆周期：T = 2π√(L/g)。
T = 2π √(m/k)
T = 2π √(L/g)
Wave speed v = fλ. Period T = 1/f. Intensity I ∝ A² (for a wave).
波速 v = fλ。周期 T = 1/f。波的强度 I ∝ A²（与振幅平方成正比）。
v = fλ
For two-source interference: path difference = nλ for constructive, (n + ½)λ for destructive.
双源干涉：波程差 = nλ 时加强，= (n + ½)λ 时减弱。
Diffraction grating: d sinθ = nλ. Snell’s law: n₁ sinθ₁ = n₂ sinθ₂. Critical angle sinθ_c = n₂/n₁ for n₂ < n₁.
衍射光栅：d sinθ = nλ。斯涅耳定律：n₁ sinθ₁ = n₂ sinθ₂。临界角 sinθ_c = n₂/n₁（当 n₂ < n₁）。
8. Electricity and Circuits | 电学与电路
Current I = ΔQ/Δt. Ohm’s Law: V = IR. Resistance R = ρL/A.
电流 I = ΔQ/Δt。欧姆定律：V = IR。电阻 R = ρL/A。
I = ΔQ/Δt
V = IR
R = ρL/A
Power in circuits: P = IV = I²R = V²/R.
电路功率：P = IV = I²R = V²/R。
P = IV = I²R = V²/R
Resistors in series: R_total = R₁ + R₂ + … . Resistors in parallel: 1/R_total = 1/R₁ + 1/R₂ + … .
电阻串联：R_total = R₁ + R₂ + … 。电阻并联：1/R_total = 1/R₁ + 1/R₂ + … 。
Internal resistance: terminal p.d. V = ε – Ir, where ε is emf and r internal resistance.
内电阻：端电压 V = ε – Ir，其中 ε 为电动势，r 为内电阻。
Potential divider: V_out = (R₂ / (R₁ + R₂)) × V_in.
分压电路：V_out = (R₂ / (R₁ + R₂)) × V_in。
9. Magnetism and Electromagnetic Induction | 磁学与电磁感应
Magnetic force on a moving charge: F = qvB sinθ. Force on a current-carrying wire: F = BIL sinθ.
运动电荷在磁场中的力：F = qvB sinθ。载流导线所受安培力：F = BIL sinθ。
F = qvB sinθ
F = BIL sinθ
Magnetic flux Φ = BA cosθ. Faraday’s law: induced emf ε = –N (ΔΦ/Δt).
磁通量 Φ = BA cosθ。法拉第电磁感应定律：感应电动势 ε = –N (ΔΦ/Δt)。
Φ = BA cosθ
ε = –N ΔΦ/Δt
Emf induced in a moving conductor: ε = B L v sinθ. Transformer equation: Vₚ/Vₛ = Nₚ/Nₛ. For an ideal transformer, Pₚ = Pₛ, so VₚIₚ = VₛIₛ.
动生电动势：ε = B L v sinθ。变压器公式：Vₚ/Vₛ = Nₚ/Nₛ。理想变压器中 Pₚ = Pₛ，因此 VₚIₚ = VₛIₛ。
10. Quantum and Nuclear Physics | 量子与核物理
Photon energy E = hf = hc/λ. Photoelectric equation: E_k max = hf – Φ.
光子能量 E = hf = hc/λ。光电效应方程：E_k max = hf – Φ。
E = hf
E_k = hf – Φ
De Broglie wavelength: λ = h/p. Energy levels in hydrogen: E_n = –13.6 eV / n².
德布罗意波长：λ = h/p。氢原子能级：E_n = –13.6 eV / n²。
λ = h / p
Nuclear reactions: mass–energy equivalence ΔE = Δm c². Radioactive decay: N = N₀ e⁻λt, half-life T_½ = ln2 / λ.
核反应：质能方程 ΔE = Δm c²。放射性衰变：N = N₀ e⁻λt，半衰期 T_½ = ln2 / λ。
ΔE = Δm c²
N = N₀ e⁻λt
T_½ = ln 2 / λ
Activity A = λN. Unified atomic mass unit u = 1.66 × 10⁻²⁷ kg; 1 u equivalent to 931.5 MeV/c².
放射性活度 A = λN。原子质量单位 u = 1.66 × 10⁻²⁷ kg；1 u 相当于 931.5 MeV/c²。
11. Optics and Wave Phenomena (Additional) | 光学与波动现象（补充）
Lens formula: 1/f = 1/u + 1/v. Magnification m = v/u = h_i/h_o.
透镜公式：1/f = 1/u + 1/v。放大率 m = v/u = h_i/h_o。
1/f = 1/u + 1/v
Single-slit diffraction: first minimum occurs at a sinθ = λ. Rayleigh criterion: θ = 1.22 λ / b.
单缝衍射：第一级暗纹在 a sinθ = λ 处。瑞利判据：θ = 1.22 λ / b。
Polarisation: Malus’s law I = I₀ cos²θ. Brewster’s angle tanθ_B = n₂/n₁.
偏振：马吕斯定律 I = I₀ cos²θ。布儒斯特角 tanθ_B = n₂/n₁。
12. Fields and Potentials (Advanced) | 场与势（进阶）
Electric field strength E = F/q for a point charge. For a uniform field, E = V/d.
电场强度对于点电荷为 E = F/q。对于匀强电场，E = V/d。
E = F / q and E = V / d
Coulomb’s law: F = k Q₁ Q₂ / r², where k = 1/(4πε₀). Electric potential V = k Q / r.
库仑定律：F = k Q₁ Q₂ / r²，其中 k = 1/(4πε₀)。电势 V = k Q / r。
F = k Q₁ Q₂ / r²
V = k Q / r
Capacitance C = Q/V. Energy stored in capacitor: E = ½ Q V = ½ C V² = ½ Q²/C. Time constant τ = RC.
电容 C = Q/V。电容器储存能量：E = ½ Q V = ½ C V² = ½ Q²/C。时间常数 τ = RC。
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