📚 Year 10 OCR Physics Formula & Theorem Quick Reference Guide | Year 10 OCR 物理公式定理速查手册
Welcome to your ultimate quick reference for Year 10 OCR Physics. This guide compiles every essential formula and theorem you need to master mechanics, energy, waves, electricity, materials and thermal physics. Each section pairs the equation with its definition, its units and the exam traps that cost marks, so you can use it both to build understanding during the year and for last-minute revision before a test.
欢迎使用 Year 10 OCR 物理终极速查手册。本指南汇编了力学、能量、波、电学、材料和热物理中所有你必须掌握的核心公式与定理。每个小节都把公式与定义、单位以及考场上最容易丢分的陷阱配对讲解，因此它既能在学年中帮助你建立理解，也能在考试前用于最后的冲刺复习。
1. Motion: Speed, Velocity and Acceleration | 运动：速率、速度与加速度
Average speed is the total distance travelled divided by the time taken. It is a scalar quantity, which means it has size but no direction. Average velocity uses displacement instead of distance, so it is a vector and can be negative if the object ends up behind its starting point.
平均速率是总行程距离除以所用时间。它是标量，只有大小没有方向。平均速度用位移代替距离，因此是矢量；如果物体最终停在出发点后方，速度可以为负值。
v = d / t
ere v = speed (m/s), d = distance (m) and t = time (s). Rearranged: d = v t and t = d / v.
其中 v = 速率（米/秒），d = 距离（米），t = 时间（秒）。变形可得：d = v t，t = d / v。
Acceleration is the rate of change of velocity, measured in metres per second squared (m/s²). A negative acceleration simply means the object is slowing down or moving in the opposite direction to its velocity.
加速度是速度的变化率，单位是米每二次方秒（m/s²）。负加速度只表示物体在减速，或加速度方向与速度方向相反。
a = (v − u) / t
ation (m/s²), v = final velocity (m/s), u = initial velocity (m/s) and t = time taken (s).
其中 a = 加速度（米/秒²），v = 末速度（米/秒），u = 初速度（米/秒），t = 所用时间（秒）。
Graph skills are examined almost every year, so learn these three rules:
图像技能几乎每年必考，请牢记以下三条规则：
- Gradient of a distance-time graph = speed. | 距离—时间图像的斜率 = 速率。
- Gradient of a velocity-time graph = acceleration. | 速度—时间图像的斜率 = 加速度。
- Area under a velocity-time graph = displacement travelled. | 速度—时间图像下方的面积 = 位移。
2. Equations of Uniform Acceleration (SUVAT) | 匀加速运动方程（SUVAT）
velocity, v = final velocity, a = acceleration, t = time. Choose the equation that contains the three quantities you know and the one you want.
对于匀加速运动，可以使用以下方程，通常以 SUVAT 助记：s = 位移，u = 初速度，v = 末速度，a = 加速度，t = 时间。解题时挑选包含已知三个量和所求量的那一条方程即可。
v = u + a t
Final velocity after time t. | 经过时间 t 后的末速度。
s = ½ (u + v) t
Displacement s using average velocity. | 利用平均速度求位移 s。
s = u t + ½ a t²
Displacement from initial velocity and acceleration over time. | 由初速度、加速度和时间求位移。
v² = u² + 2 a s
Links velocities, acceleration and displacement without time. | 联立速度、加速度和位移，不含时间。
s as positive, so a = −9.8 m/s². For free fall near the Earth, g ≈ 9.8 m/s², so a falling object accelerates at about 9.8 m/s² downwards and air resistance is ignored unless the question mentions it.
符号约定很重要：先选定一个方向为正，并在整道题中保持一致。对于向上抛出的物体，取向上为正，则 a = −9.8 m/s²。在地球表面附近的自由落体，g ≈ 9.8 m/s²，因此下落物体的加速度约为 9.8 m/s² 且方向向下；除非题目提到空气阻力，否则一律忽略。
3. Forces and Newton's Laws | 力与牛顿定律
Newton's first law states that an object stays at rest or moves at constant velocity unless a resultant force acts on it. This is why a book on a desk stays still: the weight downwards and the normal contact force upwards cancel exactly.
牛顿第一定律指出：若无合力作用，物体保持静止或做匀速直线运动。这就是桌上的书保持静止的原因——向下的重力和向上的支持力恰好相互抵消。
Newton's second law ties force, mass and acceleration together: the resultant force equals mass times acceleration.
牛顿第二定律将力、质量和加速度联系起来：合力等于质量乘以加速度。
F = m a
Where F = resultant force (N), m = mass (kg) and a = acceleration (m/s²).
其中 F = 合力（牛顿），m = 质量（千克），a = 加速度（米/秒²）。
Weight is the gravitational force acting on an object and is measured in newtons, unlike mass which is measured in kilograms and does not change with location.
重量是作用在物体上的重力，单位为牛顿；这与质量不同，质量单位为千克，且不随所处位置改变。
W = m g
W = weight (N), m = mass (kg) and g = gravitational field strength (≈ 9.8 N/kg on Earth).
其中 W = 重量（牛顿），m = 质量（千克），g = 引力场强度（地球上约 9.8 牛/千克）。
Newton's third law states that for every action there is an equal and opposite reaction acting on a different object. In terminal velocity, the drag force grows until it equals the weight, the resultant force becomes zero and the object falls at constant speed.
牛顿第三定律指出：每一个作用力都有一个大小相等、方向相反的反作用力，作用在不同的物体上。在达到终端速度时，阻力增大到等于重力，合力为零，物体便匀速下落。
4. Work, Energy and Power | 功、能量与功率
Work done is the energy transferred when a force moves an object through a distance in the direction of the force, measured in joules (J).
功是力使物体沿力的方向移动一段距离时所转移的能量，单位为焦耳（J）。
W = F d
e W = work done (J), F = force (N) and d = distance moved along the line of the force (m).
其中 W = 功（焦耳），F = 力（牛顿），d = 沿力的方向移动的距离（米）。
Kinetic energy depends on mass and the square of speed, so doubling the speed quadruples the kinetic energy. Gravitational potential energy depends on height above a chosen reference level.
动能取决于质量和速度的平方，因此速度加倍会使动能变为原来的四倍。重力势能则取决于相对于所选参考高度的高度差。
Eₖ = ½ m v² Eₚ = m g h
v = speed (m/s); Eₚ = gravitational potential energy (J), g = 9.8 N/kg and h = height (m).
其中 Eₖ = 动能（焦耳），m = 质量（千克），v = 速率（米/秒）；Eₚ = 重力势能（焦耳），g = 9.8 牛/千克，h = 高度（米）。
Power is the rate of energy transfer, and efficiency compares useful output with total input. The principle of conservation of energy says energy cannot be created or destroyed, only transferred or dissipated, usually as heat to the surroundings.
功率是能量转移的速率，效率则比较有用输出与总输入。能量守恒定律指出能量既不能创生也不能消灭，只能转移或耗散，通常以热量形式散失到周围环境中。
P = E / t efficiency = useful output ÷ total input × 100%
Where P = power (W), E = energy transferred (J) and t = time (s).
其中 P = 功率（瓦），E = 转移的能量（焦耳），t = 时间（秒）。
5. Density, Pressure and Moments | 密度、压强与力矩
Density compares the mass of a material with the volume it occupies and is measured in kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³).
密度比较物质的质量与其所占体积，单位为千克每立方米（kg/m³）或克每立方厘米（g/cm³）。
ρ = m / V
Where ρ = density (kg/m³), m = mass (kg) and V = volume (m³).
其中 ρ = 密度（千克/米³），m = 质量（千克），V = 体积（米³）。
Pressure is the force acting normally per unit area. For a liquid, pressure increases with depth and with the density of the liquid, which is why dams are built thicker at the base.
压强是垂直作用在单位面积上的力。对液体而言，压强随深度和液体密度增大而增大，这就是水坝底部建得更厚的原因。
p = F / A p = h ρ g
rce (N), A = area (m²), h = depth (m), ρ = density of the liquid (kg/m³) and g = 9.8 N/kg.
其中 p = 压强（帕或牛/米²），F = 力（牛顿），A = 面积（米²），h = 深度（米），ρ = 液体密度（千克/米³），g = 9.8 牛/千克。
A moment is the turning effect of a force about a pivot, and the principle of moments states that for a body in equilibrium, the total clockwise moment equals the total anticlockwise moment.
力矩是力绕支点的转动效应；力矩平衡原理指出：处于平衡状态的物体，顺时针力矩总和等于逆时针力矩总和。
M = F d
(N) and d = perpendicular distance from the pivot to the line of action of the force (m).
其中 M = 力矩（牛·米），F = 力（牛顿），d = 从支点到力的作用线的垂直距离（米）。
6. Waves: The Wave Equation and Wave Properties | 波：波速方程与波的特性
A wave transfers energy without transferring matter. The wave equation links speed, frequency and wavelength, and frequency is the reciprocal of the period.
波传递能量而不传递物质。波速方程把波速、频率和波长联系起来，而频率是周期的倒数。
v = f λ f = 1 / T T = 1 / f
Where v = wave speed (m/s), f = frequency (Hz), λ = wavelength (m) and T = period (s).
其中 v = 波速（米/秒），f = 频率（赫兹），λ = 波长（米），T = 周期（秒）。
In a transverse wave the oscillations are perpendicular to the direction of energy transfer, for example light and water ripples. In a longitudinal wave the oscillations are parallel to the direction of travel, for example sound, which travels through air at roughly 340 m/s.
横波中振动方向垂直于能量传播方向，例如光和水的涟漪。纵波中振动方向平行于传播方向，例如声音；声音在空气中传播速度约为 340 米/秒。
Learn the wave behaviours and their definitions:
请掌握以下波的典型行为及其定义：
- Reflection: the wave bounces off a surface, at the same angle as it arrived. | 反射：波在表面反弹，入射角等于反射角。
- Refraction: the wave changes speed at a boundary and may change direction. | 折射：波在界面处改变速度，方向可能随之改变。
- Diffraction: the wave spreads out after passing a gap or an edge, most noticeable when the gap is about the same size as the wavelength. | 衍射：波通过狭缝或绕过障碍物后扩散，当缝宽接近波长时最明显。
- Frequency stays constant when a wave refracts; wavelength and speed change. | 波发生折射时频率不变，波长和波速改变。
7. Electricity: Charge, Current, Potential Difference and Resistance | 电学：电荷、电流、电压与电阻
Current is the rate of flow of charge. One ampere is one coulomb of charge passing a point each second. Conventional current flows from positive to negative, opposite to electron flow.
电流是电荷流动的速率。1 安培表示每秒有 1 库仑的电荷通过某一点。规定电流方向由正极流向负极，与电子流动方向相反。
Q = I t
Where Q = charge (C), I = current (A) and t = time (s).
其中 Q = 电荷量（库仑），I = 电流（安培），t = 时间（秒）。
Potential difference is the energy transferred per unit charge between two points, and resistance is a measure of how hard it is for current to flow.
电压（电势差）是两点之间每单位电荷所转移的能量，电阻则衡量电流通过的困难程度。
V = I R
Where V = potential difference (V), I = current (A) and R = resistance (Ω).
其中 V = 电压（伏特），I = 电流（安培），R = 电阻（欧姆）。
Electrical power and energy transferred are used constantly in questions about appliances and the cost of electricity.
电功率与电能转移频繁出现在家用电器和电费计算类题目中。
P = V I P = I² R E = P t E = Q V
Where P = power (W), E = energy (J), Q = charge (C) and V = potential difference (V).
其中 P = 功率（瓦），E = 能量（焦耳），Q = 电荷量（库仑），V = 电压（伏特）。
8. Circuit Rules: Series and Parallel | 电路规律：串联与并联
In a series circuit there is only one loop, so the current is the same at every point, the potential differences of the components add up to the supply voltage, and the total resistance is the sum of the individual resistances.
串联电路只有一个回路，所以各点电流相同，各元件的电压之和等于电源电压，总电阻为各电阻之和。
I = I₁ = I₂ V = V₁ + V₂ R = R₁ + R₂
In a parallel circuit the components are connected across the same two points. The potential difference is the same across each branch, the branch currents add up to the total current, and adding branches decreases the total resistance.
并联电路中各元件接在同样的两端点上。各支路电压相同，各支路电流之和等于总电流，增加支路会使总电阻减小。
V = V₁ = V₂ I = I₁ + I₂ 1 / R = 1 / R₁ + 1 / R₂
Remember the practical devices examined at this level:
请记住此阶段常考的实际元件：
| Component | 元件 | Behaviour | 特性 |
| Fixed resistor | 定值电阻 | Current ∝ potential difference; V-I graph is a straight line through the origin | 电流与电压成正比；伏安图是过原点的直线 |
| Filament lamp | 白炽灯 | Resistance rises as it heats up, so the graph curves | 灯丝发热后电阻增大，图像变弯 |
| Diode | 二极管 | Conducts in one direction only | 只允许单向导电 |
| Thermistor | 热敏电阻 | Resistance decreases as temperature rises | 温度升高时电阻减小 |
| LDR | 光敏电阻 | Resistance decreases as light intensity rises | 光照增强时电阻减小 |
9. Materials: Hooke's Law, Stress and Strain | 材料：胡克定律、应力与应变
Hooke's law states that the extension of a spring is directly proportional to the force applied, provided the elastic limit is not exceeded. The spring constant is a measure of stiffness: a larger value means a stiffer spring.
胡克定律指出：在不超过弹性限度时，弹簧的伸长量与所加的力成正比。劲度系数衡量弹簧的软硬程度：数值越大，弹簧越硬。
F = k x E = ½ F x
k = spring constant (N/m), x = extension (m) and E = elastic potential energy stored (J).
其中 F = 力（牛顿），k = 劲度系数（牛/米），x = 伸长量（米），E = 储存的弹性势能（焦耳）。
On a force-extension graph the gradient gives the spring constant, and the area under the straight-line region gives the energy stored. Beyond the limit of proportionality the graph curves and the material behaves plastically.
在力—伸长量图像中，斜率即劲度系数，直线部分下方的面积即储存的能量。超过正比极限后图像变弯，材料表现为塑性形变。
Stress is the force per unit cross-sectional area, strain is the fractional change in length, and the Young modulus is the ratio of stress to strain.
应力是单位横截面积上的力，应变是长度的相对变化量，杨氏模量是应力与应变的比值。
σ = F / A ε = x / L E = σ / ε
ional area (m²), ε = strain (no unit), L = original length (m) and E = Young modulus (Pa).
其中 σ = 应力（帕），A = 横截面积（米²），ε = 应变（无单位），L = 原长（米），E = 杨氏模量（帕）。
10. Thermal Physics: Specific Heat Capacity and Latent Heat | 热学：比热容与潜热
Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 °C. Water has a very high value of about 4200 J/kg °C, which is why it is used in heating systems and why coastal climates are mild.
比热容是使 1 千克物质温度升高 1 °C 所需的能量。水的比热容高达约 4200 焦/(千克·°C)，因此常被用作供暖介质，也使沿海气候更为温和。
ΔE = m c Δθ
(J), m = mass (kg), c = specific heat capacity (J/kg °C) and Δθ = temperature change (°C).
其中 ΔE = 转移的能量（焦耳），m = 质量（千克），c = 比热容（焦/(千克·°C)），Δθ = 温度变化（°C）。
Specific latent heat is the energy needed to change the state of 1 kg of a substance without changing its temperature. For melting and boiling the value is called the specific latent heat of fusion or vaporisation respectively.
比潜热是使 1 千克物质发生状态改变而温度不变所需的能量。熔化和沸腾对应的数值分别称为熔化比潜热和汽化比潜热。
E = m L
Where E = energy transferred (J), m = mass (kg) and L = specific latent heat (J/kg).
其中 E = 转移的能量（焦耳），m = 质量（千克），L = 比潜热（焦/千克）。
Heating and cooling curves are examined frequently: temperature rises while a substance is being heated, then stays flat while it changes state, because the energy supplied is being used to break bonds rather than to raise temperature.
加热与冷却曲线是高频考点：物质被加热时温度上升，而在状态改变期间温度保持不变，因为此时供给的能量用于破坏分子间作用力，而不是升高温度。
11. Units, Prefixes and Measurement | 单位、词头与测量
Always convert into SI base units before substituting into an equation. Marks are lost every year by mixing centimetres with metres, grams with kilograms, or minutes with seconds.
代入公式前务必转换成国际单位制基本单位。每年都有考生因为厘米与米、克与千克、分钟与秒混用而丢分。
| Prefix | 词头 | Symbol | 符号 | Factor | 倍数 |
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