📚 IGCSE Edexcel Physics: Formula Compendium | IGCSE Edexcel 物理：公式汇总手册
This comprehensive guide brings together all the essential equations you need for the IGCSE Edexcel Physics examinations. Each formula is presented with clear explanations of the symbols used and their SI units, followed by a concise example of its application. Mastery of these relationships is key to tackling calculation questions confidently and systematically across the entire syllabus.
这份全面指南汇集了 IGCSE Edexcel 物理考试所需的所有基本方程。每个公式都对所用符号及其国际单位进行了清晰解释，并附有简要的应用示例。掌握这些关系式是在整个课程体系中自信、系统地解决计算题的关键。
1. Speed, Velocity and Acceleration | 速率、速度与加速度
Average speed is defined as the total distance travelled divided by the total time taken. It is a scalar quantity, so direction is not considered.
平均速率定义为运动的总距离除以总时间。它是标量，因此不考虑方向。
v = s / t
(v = speed in m/s, s = distance in m, t = time in s)
(v = 速率，单位 m/s；s = 距离，单位 m；t = 时间，单位 s)
When velocity changes, acceleration quantifies the rate of change. Acceleration is a vector; negative acceleration is often called deceleration.
当速度发生变化时，加速度表示变化的快慢。加速度是矢量；负加速度常被称为减速度。
a = (v − u) / t
(a = acceleration in m/s², v = final velocity in m/s, u = initial velocity in m/s, t = time in s)
(a = 加速度，单位 m/s²；v = 末速度，单位 m/s；u = 初速度，单位 m/s；t = 时间，单位 s)
For uniformly accelerated motion in a straight line, the final speed can be related to distance without using time.
对于匀加速直线运动，末速度可以与路程关联而无须时间。
v² = u² + 2 a s
(s = displacement in m)
(s = 位移，单位 m)
2. Forces and Momentum | 力与动量
Newton’s second law links resultant force, mass and acceleration. A resultant force causes an object to accelerate in its direction.
牛顿第二定律将合力、质量与加速度联系起来。有合力就会使物体沿其方向加速。
F = m a
(F = resultant force in N, m = mass in kg, a = acceleration in m/s²)
(F = 合力，单位 N；m = 质量，单位 kg；a = 加速度，单位 m/s²)
Weight is the gravitational force on an object and should not be confused with mass. The gravitational field strength g is taken as 9.8 N/kg (or 10 N/kg when specified).
重量是作用在物体上的引力，不可与质量混淆。重力场强度 g 取 9.8 N/kg（或指定时取 10 N/kg）。
W = m g
(W = weight in N, g = gravitational field strength in N/kg)
(W = 重量，单位 N；g = 重力场强度，单位 N/kg)
Momentum is a measure of ‘mass in motion’. In a closed system, total momentum before a collision equals total momentum after, a principle used extensively in collision and explosion problems.
动量是“运动中的质量”的度量。在封闭系统中，碰撞前的总动量等于碰撞后的总动量，这一原理广泛应用于碰撞和爆炸问题。
p = m v
(p = momentum in kg m/s, v = velocity in m/s)
(p = 动量，单位 kg m/s；v = 速度，单位 m/s)
3. Energy, Work and Power | 能量、功与功率
Work done equals the energy transferred when a force moves an object. The distance must be in the direction of the force.
功等于力使物体移动时传递的能量。距离必须沿力的方向。
W = F d
(W = work done in J, F = force in N, d = distance moved in m)
(W = 功，单位 J；F = 力，单位 N；d = 移动距离，单位 m)
Kinetic energy depends on mass and the square of speed. Gravitational potential energy stored in an elevated body is proportional to its height.
动能取决于质量和速度的平方。升高物体的重力势能与高度成正比。
KE = ½ m v²
GPE = m g h
(KE = kinetic energy, GPE = gravitational potential energy, both in J; h = height in m)
(KE = 动能，GPE = 重力势能，单位均为 J；h = 高度，单位 m)
Power is the rate of doing work or transferring energy. It can also be expressed as the product of force and average speed for a moving object under a constant force.
功率是做功或传递能量的速率。对于在恒力作用下运动的物体，也可表示为力与平均速度的乘积。
P = W / t = ΔE / t
P = F v
(P = power in W, ΔE = energy transferred in J, t = time in s, v = average speed in m/s)
(P = 功率，单位 W；ΔE = 传递的能量，单位 J；t = 时间，单位 s；v = 平均速率，单位 m/s)
Efficiency compares useful output to total input, commonly expressed as a percentage.
效率比较有用输出与总输入，通常以百分比表示。
Efficiency = (useful energy output / total energy input) × 100%
(无单位 or %)
(无量纲或 %)
4. Waves and Optics | 波与光学
The wave speed equation applies to all types of wave – sound, light, water and electromagnetic. Frequency stays constant when a wave enters a different medium.
波速方程适用于所有类型的波——声波、光波、水波和电磁波。波进入不同介质时频率保持不变。
v = f λ
(v = wave speed in m/s, f = frequency in Hz, λ = wavelength in m)
(v = 波速，单位 m/s；f = 频率，单位 Hz；λ = 波长，单位 m)
Period is the time for one complete oscillation and is the reciprocal of frequency.
周期是一次完整振动的时间，是频率的倒数。
T = 1 / f
(T = period in s)
(T = 周期，单位 s)
For reflection and refraction, the angle of incidence equals the angle of reflection. Snell’s law links refractive index to the sines of the angles. The critical angle occurs when the angle of refraction is 90°.
反射与折射中，入射角等于反射角。斯涅尔定律将折射率与角度的正弦关联。当折射角为 90°时出现临界角。
n = sin i / sin r
sin c = 1 / n
(n = refractive index, i = angle of incidence, r = angle of refraction, c = critical angle)
(n = 折射率；i = 入射角；r = 折射角；c = 临界角)
5. Electricity | 电学
Ohm’s law holds for components with constant resistance. The volt per coulomb definition of potential difference relates energy and charge.
欧姆定律适用于电阻不变的元件。电势差的伏特/库仑定义将能量与电荷联系起来。
V = I R
V = W / Q = E / Q
(V = potential difference in V, I = current in A, R = resistance in Ω, Q = charge in C, E = energy in J)
(V = 电压，单位 V；I = 电流，单位 A；R = 电阻，单位 Ω；Q = 电荷，单位 C；E = 能量，单位 J)
Charge moved in a circuit is the product of current and time. Electric power can be written in three useful forms based on Ohm’s law substitution.
电路中移动的电荷量为电流与时间的乘积。电功率可根据欧姆定律代换写成三种实用形式。
Q = I t
P = I V
P = I² R
P = V² / R
(P = power in W)
(P = 功率，单位 W)
Energy transferred in a resistor can thus be expressed simply.
因此，电阻中传递的能量可以简单表示。
E = I V t
(E = energy in J, t = time in s)
(E = 能量，单位 J；t = 时间，单位 s)
For series and parallel circuits, the rules for current, voltage and resistance are essential. For two resistors R₁ and R₂:
对于串联和并联电路，电流、电压和电阻的规则至关重要。对于两个电阻 R₁ 与 R₂：
-
Series: Rtotal = R₁ + R₂
串联：Rtotal = R₁ + R₂
-
Parallel: 1/Rtotal = 1/R₁ + 1/R₂ (use the reciprocal formula)
并联：1/Rtotal = 1/R₁ + 1/R₂ (使用倒数公式)
6. Magnetism and Electromagnetism | 磁学与电磁学
The voltage induced across a conductor moving through a magnetic field depends on the rate of flux cutting. For a transformer, the ratio of voltages equals the ratio of turns.
导体在磁场中运动时产生的感应电压取决于磁通量切割的速率。对于变压器，电压之比等于匝数之比。
Vₚ / Vₛ = Nₚ / Nₛ
(Vₚ, Vₛ = primary and secondary voltages in V; Nₚ, Nₛ = number of turns on primary and secondary coils)
(Vₚ、Vₛ = 初级与次级电压，单位 V；Nₚ、Nₛ = 初级与次级线圈匝数)
Assuming 100% efficiency, the input and output power are equal, allowing the current ratio to be found.
假设效率为 100%，输入与输出功率相等，可求得电流比。
Vₚ Iₚ = Vₛ Iₛ
(Iₚ, Iₛ = currents in A)
(Iₚ、Iₛ = 电流，单位 A)
The force on a current-carrying conductor in a magnetic field is given by Fleming’s left-hand rule.
载流导体在磁场中所受的力由弗莱明左手定则给出。
F = B I l
(F = force in N, B = magnetic flux density in T, I = current in A, l = length of conductor in the field in m)
(F = 力，单位 N；B = 磁通量密度，单位 T；I = 电流，单位 A；l = 导体处于磁场中的长度，单位 m)
7. Thermal Physics | 热物理
The energy required to raise the temperature of a substance depends on its mass, the temperature change and the specific heat capacity.
升高物质温度所需的能量取决于其质量、温度变化和比热容。
ΔQ = m c Δθ
(ΔQ = thermal energy in J, m = mass in kg, c = specific heat capacity in J/(kg °C), Δθ = temperature change in °C or K)
(ΔQ = 热能，单位 J；m = 质量，单位 kg；c = 比热容，单位 J/(kg °C)；Δθ = 温度变化，单位 °C 或 K)
During a change of state, the temperature remains constant, and the energy involved is called latent heat.
状态变化期间温度保持不变，所涉及的能量称为潜热。
Q = m L
(L = specific latent heat in J/kg; for fusion use Lf, for vaporisation use Lv)
(L = 比潜热，单位 J/kg；熔化用 Lf，汽化用 Lv)
The behaviour of a fixed mass of an ideal gas can be described by combining Boyle’s law and Charles’s law.
一定质量理想气体的行为可通过玻意耳定律与查理定律的组合来描述。
p V = constant (for constant temperature)
V / T = constant (for constant pressure)
p / T = constant (for constant volume)
(p = pressure in Pa, V = volume in m³, T = temperature in K)
(p = 压强，单位 Pa；V = 体积，单位 m³；T = 热力学温度，单位 K)
For any change, the combined gas law can be applied: p₁ V₁ / T₁ = p₂ V₂ / T₂.
对于任何变化，可使用组合气体定律：p₁ V₁ / T₁ = p₂ V₂ / T₂。
8. Radioactivity | 放射性
The activity of a radioactive sample decreases over time. The half-life is the time taken for the activity (or the number of undecayed nuclei) to halve. No single formula covers all decay curves, but the concept is expressed as:
放射性样品的活度随时间降低。半衰期是活度（或未衰变原子核数目）减半所需的时间。没有单一公式涵盖所有衰变曲线，但概念可表示为：
count rate after n half-lives = initial count rate × (1/2)ⁿ
(n = number of half-lives elapsed)
(n = 经过的半衰期个数)
Background radiation must be subtracted from readings. The net count rate is calculated as:
本底辐射必须从读数中扣除。净计数率计算如下：
net count rate = measured count rate − background count rate
净计数率 = 测量计数率 − 本底计数率
In nuclear equations, the total number of nucleons (mass number) and the total charge (atomic number) are conserved. The energy released can be related to mass defect, but students only need to balance equations symbolically.
在核反应方程中，核子总数（质量数）和总电荷（原子序数）守恒。释放的能量可与质量亏损关联，但学生只需会用符号配平方程。
9. Space Physics | 天体物理
The orbital speed of a planet or satellite moving in a nearly circular path can be found from the circumference of the orbit divided by the period.
在近似圆形轨道上运行的行星或卫星的轨道速度，可由轨道周长除以周期求得。
v = 2 π r / T
(v = orbital speed in m/s, r = radius of orbit in m, T = orbital period in s)
(v = 轨道速度，单位 m/s；r = 轨道半径，单位 m；T = 轨道周期，单位 s)
Hubble’s law describes the expansion of the Universe; distant galaxies are moving away with speeds proportional to their distance.
哈勃定律描述了宇宙的膨胀；遥远星系正以与其距离成正比的速度远离我们。
v = H₀ d
(H₀ = Hubble constant, approximately 2.2 × 10⁻¹⁸ s⁻¹ or 70 km s⁻¹ Mpc⁻¹; d = distance in m or Mpc)
(H₀ = 哈勃常数，约为 2.2 × 10⁻¹⁸ s⁻¹ 或 70 km s⁻¹ Mpc⁻¹；d = 距离，单位 m 或 Mpc)
Redshift z quantifies the fractional change in wavelength of light from a receding source.
红移 z 表示来自退行光源的光波波长变化分数。
z = (λobserved − λlaboratory) / λlaboratory
z = (λ观测 − λ实验室) / λ实验室
10. Density, Pressure and Moments | 密度、压强与力矩
Density describes how much mass is packed into a given volume. It is a characteristic property of a material at a given temperature and pressure.
密度描述单位体积内所含的质量。它是材料在特定温度和压强下的特征性质。
ρ = m / V
(ρ = density in kg/m³, m = mass in kg, V = volume in m³)
(ρ = 密度，单位 kg/m³；m = 质量，单位 kg；V = 体积，单位 m³)
Pressure is force per unit area. For fluids at rest, the pressure at a depth h depends on the density of the fluid and the gravitational field strength.
压强是单位面积上的力。对于静止流体，深度 h 处的压强取决于流体密度和重力场强度。
p = F / A
Δp = ρ g h
(p = pressure in Pa, A = area in m², Δp = pressure difference due to a column of fluid, h = height of fluid column in m)
(p = 压强，单位 Pa；A = 面积，单位 m²；Δp = 液柱产生的压强差；h = 液柱高度，单位 m)
The principle of moments states that for an object in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about any pivot.
力矩原理指出，对于转动平衡的物体，对任意支点的顺时针力矩总和等于逆时针力矩总和。
moment = F d
(d = perpendicular distance from the pivot to the line of action of the force in m; moment measured in N m)
(d = 施力作用线到支点的垂直距离，单位 m；力矩单位 N m)
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