📚 Year 11 Eduqas Physics: Quick Reference Formulas & Theorems | Eduqas 物理 11 年级：公式定理速查手册
This handbook brings together the essential equations and principles you need for the Eduqas GCSE Physics course. Each section presents the key formulas with a clear explanation, followed by the corresponding Chinese translation to support bilingual learners. Use it as a quick revision tool to reinforce your understanding and build confidence for your exams.
本手册汇集了Eduqas GCSE物理课程中所有必备的公式和原理。每个部分都提供关键公式及清晰的解释，并附有对应的中文译文，以帮助双语学习者。请将其作为快速复习工具，巩固理解并增强考试信心。
1. Motion and Forces | 运动与力
The average speed of an object is the total distance travelled divided by the time taken. For motion with constant acceleration, the SUVAT equations link initial velocity, final velocity, acceleration, displacement and time.
物体的平均速度是行驶的总距离除以所用时间。对于匀加速直线运动，SUVAT 方程将初速度、末速度、加速度、位移和时间联系起来。
average speed = distance / time v = s / t
a = (v – u) / t
v² = u² + 2 a s
s = u t + ½ a t²
Newton’s Second Law states that the acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass. Weight is the force due to gravity acting on a mass.
牛顿第二定律指出，物体的加速度与作用在其上的合力成正比，与其质量成反比。重力是作用在质量上的引力。
F = m a
W = m g
On Earth, g ≈ 9.8 m/s² and is often taken as 10 m/s² in estimation questions. The stopping distance of a vehicle is the sum of the thinking distance and the braking distance.
地球上的 g 约等于 9.8 m/s²，估算题中常取 10 m/s²。车辆的停车距离是反应距离和制动距离之和。
2. Energy and Work | 能量与功
Work is done when a force moves an object through a distance. Energy cannot be created or destroyed, only transferred, stored or dissipated. Kinetic energy depends on mass and speed, while gravitational potential energy depends on mass, height and gravitational field strength.
当力使物体移动一段距离时，就做了功。能量既不能被创造也不能被消灭，只能被转移、储存或耗散。动能取决于质量和速度，而重力势能取决于质量、高度和引力场强。
W = F d
Eₖ = ½ m v²
Eₚ = m g h
Eₑ = ½ k e²
Power is the rate of energy transfer or the rate of doing work. Efficiency compares useful output energy or power with total input.
功率是能量转移或做功的速率。效率将有用的输出能量或功率与总输入进行比较。
P = E / t = W / t
efficiency = (useful output energy / total input energy) × 100%
In closed systems, total energy is conserved. Energy changes often appear as Sankey diagrams, where the width of the arrows represents the amount of energy.
在封闭系统中，总能量守恒。能量变化常以桑基图表示，其中箭头的宽度代表能量的大小。
3. Electricity | 电学
Electric charge, current, potential difference and resistance are linked by a set of fundamental equations. Ohm’s Law applies to components where the resistance remains constant as current changes.
电荷、电流、电压和电阻由一组基本方程联系在一起。对于电阻随电流保持不变的元件，欧姆定律成立。
Q = I t
V = I R
Power in an electrical circuit can be calculated using current and voltage, or current and resistance. Resistors in series add directly, while in parallel the reciprocal of the total resistance equals the sum of the reciprocals.
电路中的电功率可用电流和电压或电流和电阻计算。串联电阻直接相加，并联时总电阻的倒数等于各电阻倒数之和。
P = I V
P = I² R
R_total = R₁ + R₂ + …
1/R_total = 1/R₁ + 1/R₂ + …
The energy transferred by a component also depends on the charge and voltage across it. This leads to the equation E = Q V, which can be combined with Q = I t to give E = I V t.
元件转移的能量还取决于通过它的电荷量及两端电压。由此可得 E = Q V，再结合 Q = I t 可得到 E = I V t。
E = Q V
4. Waves | 波
All waves obey the wave equation, which relates wave speed, frequency and wavelength. For electromagnetic waves, the speed in a vacuum is the same for all types and is approximately 3.0 × 10⁸ m/s.
所有波都遵循波动方程，该方程将波速、频率和波长联系起来。对于电磁波，真空中所有类型的波速相同，约为 3.0 × 10⁸ m/s。
v = f λ
When a wave crosses a boundary between two media, it changes speed and direction unless it strikes along the normal. Snell’s law uses the refractive index n, and the critical angle c is the angle of incidence for which the angle of refraction is 90°.
当波穿过两种介质的边界时，除非沿法线入射，否则波速和方向会改变。斯涅尔定律使用折射率 n，临界角 c 是折射角为 90° 时的入射角。
n = sin i / sin r
sin c = 1 / n
The period of a wave is the time for one complete oscillation and is the reciprocal of the frequency. T = 1/f is commonly used in both mechanical and electromagnetic contexts.
波的周期是一次全振动的时间，是频率的倒数。T = 1/f 在机械波和电磁波中普遍使用。
T = 1 / f
5. Particle Model of Matter | 物质粒子模型
Density measures how much mass is packed into a given volume. The internal energy of a system is the total kinetic and potential energy of its particles. Heating a substance increases its temperature or changes its state.
密度衡量给定体积内含有多少质量。系统的内能是其粒子的总动能和势能之和。加热物质会使其温度升高或改变其状态。
ρ = m / V
The energy required to raise the temperature of a given mass depends on the specific heat capacity c. During a change of state, the temperature remains constant and the energy needed is given by the specific latent heat L.
升高给定质量物质的温度所需的能量取决于比热容 c。物态变化期间温度保持不变，所需的能量由比潜热 L 表示。
ΔE = m c Δθ
E = m L
For a fixed mass of gas at constant temperature, the product of pressure and volume is constant. This is often tested by describing the behaviour of particles inside a sealed container.
对于一定质量的气体，在恒温下压力和体积的乘积为常数。常通过描述密封容器内粒子的行为来考查此式。
p V = constant
6. Atomic Structure and Radioactivity | 原子结构与放射性
Atoms consist of a nucleus containing protons and neutrons, surrounded by electrons. Radioactive decay is a random process in which an unstable nucleus emits alpha, beta or gamma radiation. The activity of a source is the number of decays per second.
原子由含有质子和中子的原子核以及绕核运动的电子组成。放射性衰变是一个随机过程，不稳定的原子核会放出 α、β 或 γ 射线。源的活度是每秒衰变的次数。
A = ΔN / Δt
The half-life of an isotope is the time taken for half the radioactive nuclei in a sample to decay, or for the count rate to halve. The number of remaining nuclei after n half-lives can be calculated.
同位素的半衰期是样本中一半放射性原子核发生衰变，或计数率减半所需的时间。经过 n 个半衰期后剩余的原子核数目可用公式计算。
N = N₀ (1/2)ⁿ
Nuclear equations must balance the total atomic (proton) number and the total mass (nucleon) number. Alpha decay reduces the mass number by 4 and atomic number by 2; beta decay increases the atomic number by 1 with no change in mass number.
核反应方程必须使总原子序数（质子数）和总质量数（核子数）守恒。α 衰变质量数减 4、原子序数减 2；β 衰变原子序数加 1，质量数不变。
7. Forces and Pressure | 力与压强
Pressure is the force acting perpendicularly per unit area. It is a scalar quantity and has units of pascals (Pa), where 1 Pa = 1 N/m².
压强是垂直作用在单位面积上的力。它是一个标量，单位为帕斯卡 (Pa)，1 Pa = 1 N/m²。
p = F / A
Pressure in a liquid increases with depth and density, and acts equally in all directions at a given depth. The equation p = h ρ g can be used for a static column of liquid. In a hydraulic system, pressure is transmitted equally, allowing a small force applied to a small area to produce a large force on a larger area.
液体的压强随深度和密度增加而增大，并在同一深度向各个方向同等作用。公式 p = h ρ g 适用于静止液柱。在液压系统中，压强被等大地传递，使施加在小面积上的小力能在大面积上产生大力。
p = h ρ g
8. Magnetism and Electromagnetism | 磁与电磁
A current-carrying wire produces a magnetic field. When a conductor cuts through magnetic field lines, a potential difference is induced. Transformers change the voltage of an alternating current and rely on the principle of electromagnetic induction.
载流导线产生磁场。当导体切割磁力线时，会感应出电动势。变压器改变交流电的电压，依赖于电磁感应原理。
For an ideal transformer where all the magnetic flux links both coils, the ratio of the voltages equals the ratio of the number of turns in the coils. The input power equals the output power in a 100% efficient transformer.
对于理想变压器（所有磁通量均交链两个线圈），电压之比等于线圈匝数之比。在 100% 效率的变压器中，输入功率等于输出功率。
Vₚ / Vₛ = Nₚ / Nₛ
Vₚ Iₚ = Vₛ Iₛ
The motor effect describes the force experienced by a current-carrying wire in a magnetic field. The size of the force can be increased by using a stronger magnet, a larger current, or a longer length of wire within the field.
电动机效应描述了载流导线在磁场中受到的力。力的大小可通过使用更强的磁体、更大的电流或更长的导线在磁场中来增大。
9. Space Physics | 空间物理
Planets and satellites orbit in nearly circular paths. The orbital speed can be calculated using the circumference of the orbit and the orbital period. For an object in a stable orbit, the speed changes only if the radius changes.
行星和卫星以近似圆形的轨道运行。轨道速度可通过轨道周长和轨道周期计算。对于在稳定轨道上的物体，只有当半径改变时速度才会改变。
v = 2πr / T
Redshift provides evidence for the expanding universe. When a galaxy moves away from us, the wavelength of its light is stretched. The redshift z is the fractional change in wavelength and relates to the recessional velocity v and the speed of light c.
红移为宇宙膨胀提供了证据。当星系远离我们时，其光的波长被拉长。红移 z 是波长的分数变化，与退行速度 v 和光速 c 有关。
z = Δλ / λ₀ = v / c
Hubble’s law states that the recessional velocity of a galaxy is directly proportional to its distance from us. The constant of proportionality is the Hubble constant H₀.
哈勃定律指出，星系的退行速度与其距离成正比。比例常数是哈勃常数 H₀。
v = H₀ d
10. Key Constants and Unit Conversions | 重要常数与单位换算
Many calculations require using standard values or converting between units. This quick reference list will help you avoid common mistakes.
许多计算需要使用标准值或进行单位换算。这份快速参考清单将帮助你避免常见错误。
| Constant / 常数 | Value / 数值 |
|---|---|
| Acceleration of free fall, g | 9.8 m/s² (use 10 m/s² for estimation) |
| Speed of light in vacuum, c | 3.0 × 10⁸ m/s |
| Charge on an electron, e | 1.6 × 10⁻¹⁹ C |
| Planck constant, h | 6.63 × 10⁻³⁴ J s |
| 1 kilowatt-hour (kWh) | 3.6 × 10⁶ J |
Common unit prefixes include milli (m, 10⁻³), centi (c, 10⁻²), kilo (k, 10³), mega (M, 10⁶) and giga (G, 10⁹). When substituting into formulas, remember to convert all quantities to SI base units: metres, kilograms, seconds, amperes, etc.
常见的单位前缀包括毫（m, 10⁻³）、厘（c, 10⁻²）、千（k, 10³）、兆（M, 10⁶）和吉（G, 10⁹）。代入公式时，记得将所有量转换为国际单位制基本单位：米、千克、秒、安培等。
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