📚 A-Level Edexcel Physics Formula Summary Handbook | A-Level Edexcel 物理公式汇总手册
This handbook compiles the essential equations needed to master the Edexcel A-Level Physics specification. Each formula is presented with a brief explanation of its variables and typical applications, helping you build a robust mental toolkit for problem-solving and examinations.
本手册汇集了掌握 Edexcel A-Level 物理大纲所需的核心方程。每个公式都配有其变量和典型应用的简要说明，帮助你构建起解决问题和应对考试所需的强大思维工具箱。
1. Kinematics | 运动学
v = u + at – lied by time. Useful for calculating motion under uniform acceleration when time is known.
v = u + at —— 末速度等于初速度加上加速度乘以时间。用于已知时间时计算匀加速运动。
s = ut + ½at² – the acceleration times the square of time. This equation does not require final velocity.
s = ut + ½at² —— 位移等于初速度乘以时间加上加速度乘以时间平方的一半。该方程不需要末速度。
v² = u² + 2as – to initial velocity squared, acceleration, and displacement. Ideal when time is not given.
v² = u² + 2as —— 将末速度的平方与初速度的平方、加速度和位移联系起来。适用于没有给出时间的情况。
s = ((u + v)/2) × t – lacement equals average velocity multiplied by time, valid only for constant acceleration.
s = ((u + v)/2) × t —— 位移等于平均速度乘以时间，仅适用于加速度不变的情况。
2. Dynamics | 动力学
F = ma – Newton' rce equals mass times acceleration. The cornerstone of mechanics linking force and motion.
F = ma —— 牛顿第二定律：合外力等于质量乘以加速度。这是连接力与运动的力学基石。
W = mg – Weight is mass times gravitational field strength (g ≈ 9.81 N/kg on Earth).
W = mg —— 重量等于质量乘以引力场强（地球上 g ≈ 9.81 N/kg）。
p = mv – ntum is the product of mass and velocity, a vector quantity conserved in isolated systems.
p = mv —— 动量是质量与速度的乘积，是孤立系统中守恒的矢量。
Impulse = Δp = FΔt – Impulse equals change in momentum and equals average force times time interval.
冲量 = Δp = FΔt —— 冲量等于动量的变化，也等于平均力乘以时间间隔。
3. Work, Energy and Power | 功、能和功率
W = Fd cosθ – ne by a constant force is force times displacement times cosine of the angle between them.
W = Fd cosθ —— 恒力所做的功等于力乘以位移再乘以力与位移夹角的余弦。
Eₖ = ½mv² – Kinetic energy depends on mass and the square of speed. Always non‑negative.
Eₖ = ½mv² —— 动能取决于质量和速度的平方，始终非负。
ΔEₚ = mgΔh – Change in gravitational potential energy near Earth's surface.
ΔEₚ = mgΔh —— 近地面重力势能的变化。
P = W/t = Fv – work; for constant force and motion in the same direction, it equals force times velocity.
P = W/t = Fv —— 功率是做功的速率；当力与运动方向相同时，等于力乘以速度。
Efficiency = (useful output / total input) × 100% – Represents the percentage of energy converted usefully.
效率 = （有用输出 / 总输入）× 100% —— 表示有用转化的能量百分比。
4. Circular Motion | 圆周运动
ω = θ/t = 2πf – ular velocity is the rate of change of angular displacement, also expressed via frequency.
ω = θ/t = 2πf —— 角速度是角位移变化的速率，也可通过频率表示。
v = ωr – Linear speed relates to angular velocity and radius for circular motion.
v = ωr —— 圆周运动中，线速度与角速度和半径相关。
a = v²/r = ω²r – Centripetal acceleration directed towards the centre of the circle.
a = v²/r = ω²r —— 指向圆心的向心加速度。
F = mv²/r = mω²r – d to maintain circular motion; not a separate force but provided by tension, gravity, etc.
F = mv²/r = mω²r —— 维持圆周运动所需的向心力；不是独立存在的力，而是由张力、引力等提供。
5. Oscillations and Waves | 振动与波
T = 1/f – Period is the reciprocal of frequency. For a mass‑spring system, T = 2π√m/k.
T = 1/f —— 周期是频率的倒数。对于弹簧振子系统，T = 2π√m/k。
v = fλ – Wave speed equals frequency times wavelength; applies to all periodic waves.
v = fλ —— 波速等于频率乘以波长；适用于所有周期波。
n₁ sin θ₁ = n₂ sin θ₂ – Snell's law of refraction, where n is the refractive index of each medium.
n₁ sin θ₁ = n₂ sin θ₂ —— 斯涅尔折射定律，其中 n 是各介质的折射率。
d sinθ = nλ – for maxima, grating spacing d times sine of angle equals integer multiples of wavelength.
d sinθ = nλ —— 光栅方程：极大值处，光栅间距 d 乘以 sinθ 等于波长的整数倍。
6. Electricity | 电学
I = ΔQ/Δt – Current is the rate of flow of charge, measured in amperes.
I = ΔQ/Δt —— 电流是电荷流动的速率，单位为安培。
V = W/Q – Potential difference is work done per unit charge.
V = W/Q —— 电势差是每单位电荷所做的功。
V = IR – Ohm's law for an ohmic conductor at constant temperature.
V = IR —— 恒定温度下欧姆导体的欧姆定律。
P = IV = I²R = V²/R – Power dissipated in a resistor, derived from combinations of Ohm's law and the power definition.
P = IV = I²R = V²/R —— 电阻消耗的功率，通过欧姆定律和功率定义推导得出。
R = ρL/A – Resistance depends on resistivity, length, and cross‑sectional area.
R = ρL/A —— 电阻取决于电阻率、长度和横截面积。
ε = I(R + r) – Emf equals terminal potential difference plus lost volts across internal resistance r.
ε = I(R + r) —— 电动势等于路端电压加上内阻 r 上的损耗电压。
7. Capacitance | 电容
C = Q/V – Capacitance is stored charge per unit potential difference; unit farad (F).
C = Q/V —— 电容是单位电势差下储存的电荷量；单位为法拉（F）。
E = ½QV = ½CV² = ½Q²/C – Energy stored in a charged capacitor.
E = ½QV = ½CV² = ½Q²/C —— 充电电容器储存的能量。
τ = RC – stant for capacitor discharge; in one time constant, charge falls to 1/e of initial value.
τ = RC —— 电容放电的时间常数；在一个时间常数内，电荷降至初始值的 1/e。
Q = Q₀ e⁻ᵗ/ᴿᶜ – Exponential decay of charge during discharge. Similar equations for current and voltage.
Q = Q₀ e⁻ᵗ/ᴿᶜ —— 放电过程中电荷的指数衰减。电流和电压也有类似形式。
8. Magnetic Fields | 磁场
F = BIL sinθ – Force on a current‑arrying conductor in a uniform magnetic field, with θ the angle between current and field.
F = BIL sinθ —— 匀强磁场中通电导体所受的安培力，θ 为电流与磁场间的夹角。
F = Bqv sinθ – Lorentz force on a moving charged particle; perpendicular to both velocity and field.
F = Bqv sinθ —— 运动电荷受到的洛伦兹力；与速度和磁场均垂直。
r = mv/(Bq) – rcular path in a magnetic field derived from centripetal force and Lorentz force equality.
r = mv/(Bq) —— 在磁场中圆周运动的轨迹半径，由向心力和洛伦兹力相等推得。
Φ = BA cosθ – gh a loop of area A, with B uniform and θ the angle between field and normal to the plane.
Φ = BA cosθ —— 穿过面积为 A 的线圈的磁通量，B 均匀，θ 为磁场与平面法线的夹角。
ε = -N ΔΦ/Δt – Faraday‑ ortional to rate of change of flux linkage; minus sign indicates direction opposes change.
ε = -N ΔΦ/Δt —— 法拉第‑楞次定律：感应电动势与磁链变化率成正比；负号表示其方向阻碍变化。
9. Gravitational Fields & Space | 引力场与空间
F = Gm₁m₂/r² – Newton' ctly proportional to product of masses and inversely proportional to square of separation.
F = Gm₁m₂/r² —— 牛顿万有引力定律：力与两质量乘积成正比，与距离平方成反比。
g = F/m = GM/r² – Gravitational field strength at a distance r from a point mass or spherical body.
g = F/m = GM/r² —— 距离点质量或球体 r 处的引力场强。
V = -GM/r – ial; work done per unit mass to bring a mass from infinity to that point. Always negative.
V = -GM/r —— 引力势；将单位质量从无穷远移到该点所做的功。始终为负值。
v = √GM/r – Orbital speed for a circular orbit derived from gravitational force providing centripetal force.
v = √GM/r —— 圆轨道运行速度，由引力提供向心力推得。
T² ∝ r³ – Kepler's third law: the square of the orbital period is proportional to the cube of the semi‑major axis.
T² ∝ r³ —— 开普勒第三定律：轨道周期的平方与半长轴的立方成正比。
10. Nuclear & Particle Physics | 核与粒子物理
E = mc² – Mass–energy equivalence; a mass m can be converted into energy E, with c the speed of light.
E = mc² —— 质能方程；质量 m 可以转化为能量 E，c 为光速。
ΔE = Δmc² – Energy released in nuclear reactions corresponds to the mass defect.
ΔE = Δmc² —— 核反应中释放的能量与质量亏损对应。
N = N₀ e⁻⁴ – Exponential decay law; λ is the decay constant, linked to half‑life by T₁/₂ = ln2/λ.
N = N₀ e⁻⁴ —— 指数衰变律；λ 为衰变常数，与半衰期关系为 T₁/₂ = ln2/λ。
A = λN – Activity is the number of decays per second; unit becquerel (Bq).
A = λN —— 活度是每秒衰变次数；单位为贝克勒尔（Bq）。
11. Thermal Physics | 热物理
pV = nRT – equation linking pressure, volume, amount (moles), gas constant and absolute temperature.
pV = nRT —— 理想气体状态方程，联系压强、体积、摩尔数、气体常数和绝对温度。
pV = NkT – The same law expressed with number of molecules N and Boltzmann constant k.
pV = NkT —— 用分子数 N 和玻尔兹曼常数 k 表达的同一规律。
pV = ⅓ Nm
pV = ⅓ Nm
Everage kinetic energy per molecule = ³/₂ kT – Average translational kinetic energy for a monatomic ideal gas.
每个分子的平均动能 = ³/₂ kT —— 单原子理想气体的平均平动动能。
ΔQ = mcΔθ – Heat transferred equals mass times specific heat capacity times temperature change.
ΔQ = mcΔθ —— 传递的热量等于质量乘以比热容乘以温度变化。
ΔQ = mL – heat: energy required for phase change at constant temperature (L = specific latent heat).
ΔQ = mL —— 潜热：恒定温度下相变所需的能量（L 为比潜热）。
12. Astrophysics (Optional Topic) | 天体物理（选修专题）
L = 4πd²b – Luminosity of a star relates to its distance d and apparent brightness b (inverse‑square law).
L = 4πd²b —— 恒星的光度与其距离 d 和视亮度 b 相关（平方反比律）。
λₘₐₓ T = 2.898 × 10⁻³ m K – Wien's displacement law: peak wavelength of black‑body radiation inversely proportional to temperature.
λₘₐₓ T = 2.898 × 10⁻³ m K —— 维恩位移定律：黑体辐射峰值波长与温度成反比。
P = σAT⁴ – Stefan‑ann law: total power radiated per unit area by a black body, with σ = 5.67×10⁻⁸ W m⁻² K⁻⁴.
P = σAT⁴ —— 斯特藩‑玻尔兹曼定律：黑体单位面积辐射的总功率，σ = 5.67×10⁻⁸ W m⁻² K⁻⁴。
z = Δλ/λ ≈ v/c – dshift for speeds much less than c; links spectral shift to recessional velocity in Hubble's law: v = H₀ d.
z = Δλ/λ ≈ v/c —— 适用于速度远小于 c 的红移；将谱线移动与哈勃定律中的退行速度联系起来：v = H₀ d。
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