📚 Year 11 OCR Physics: Formula & Theorem Quick Reference | 11 年级 OCR 物理：公式定理速查手册
This quick reference handbook covers all the essential formulas and theorems you need for the OCR GCSE (9-1) Physics syllabus, organised by topic. Whether you are revising for mocks or preparing for the final exams, having these relationships at your fingertips will save time and strengthen your understanding. Each entry is presented with both the equation and a brief note on when to apply it, followed by the standard units.
本速查手册涵盖了 OCR GCSE（9-1）物理大纲中所有必须掌握的公式和定理，并按主题分类。无论你是在准备模拟考试还是最终大考，熟记这些关系式都能帮你节省时间、加深理解。每一条都给出了方程和适用情境的简要说明，并附上了标准单位。
1. Forces and Motion | 力与运动
The core kinematic equation links final velocity, initial velocity, acceleration and time: v = u + at. This applies only when acceleration is constant. Remember that velocity and acceleration are vectors, so direction matters.
核心运动学方程联系了末速度、初速度、加速度和时间：v = u + at。该方程仅在加速度恒定时适用。注意速度和加速度是矢量，方向至关重要。
For distance travelled under constant acceleration from rest (u = 0), use s = ½ at². When the object already has an initial velocity, the full equation is s = ut + ½ at². In many exam questions, you will also need v² = u² + 2as.
在恒定加速度下，若从静止出发（u = 0），可用 s = ½ at²。当物体已有初速度时，完整方程为 s = ut + ½ at²。在许多试题中，你还会用到 v² = u² + 2as。
Newton’s second law is the cornerstone of mechanics: F = m × a. Force is measured in newtons (N), mass in kilograms (kg) and acceleration in metres per second squared (m/s²). The resultant force determines the acceleration of an object of fixed mass.
牛顿第二定律是力学的基石：F = m × a。力的单位是牛（N），质量单位是千克（kg），加速度单位是米每二次方秒（m/s²）。合外力决定一定质量物体的加速度。
Weight is the force due to gravity: W = m × g, where g is the gravitational field strength (∼9.8 N/kg on Earth). Weight and mass are often confused; mass is scalar and constant, while weight is a force in newtons.
重量是由重力产生的力：W = m × g，其中 g 为引力场强度（地球上约 9.8 N/kg）。重量和质量常被混淆；质量是标量且不变，重量是以牛为单位的力。
2. Momentum | 动量
Momentum is the product of mass and velocity: p = m × v. It is a vector quantity with unit kg m/s. In any collision or explosion, total momentum is conserved provided no external forces act.
动量是质量与速度的乘积：p = m × v。它是个矢量，单位是 kg·m/s。在任何碰撞或爆炸中，若无外力作用，总动量守恒。
Force and momentum are linked by the rate of change of momentum: F = Δp / Δt. This is a more general form of Newton’s second law. A large change in momentum over a short time produces a large force, which explains why crumple zones save lives.
力与动量通过动量变化率相联系：F = Δp / Δt。这是牛顿第二定律的更一般形式。短时间内发生大的动量变化会产生大的力，这解释了为何溃缩区能挽救生命。
3. Work, Energy and Power | 功、能与功率
Work done by a force is W = F × d (when force and displacement are in the same direction). Work is measured in joules (J), force in newtons and distance in metres. Work transfers energy mechanically.
力做的功为 W = F × d（当力与位移同向时）。功的单位是焦耳（J），力是牛，距离是米。功通过机械方式转移能量。
Gravitational potential energy gained when lifting an object is ΔEₚ = m × g × Δh. This assumes a uniform field. Elastic potential energy stored in a stretched spring is Eₑ = ½ k e², where k is the spring constant in N/m and e is extension in metres.
提升物体获得的重力势能是 ΔEₚ = m × g × Δh。这假设了均匀场。拉伸弹簧储存的弹性势能是 Eₑ = ½ k e²，其中 k 为劲度系数（N/m），e 为伸长量（m）。
Kinetic energy is given by Eₖ = ½ m v². This is a scalar quantity. The work–energy principle says that the net work done on an object equals its change in kinetic energy.
动能的表达式为 Eₖ = ½ m v²。这是标量。功能原理指出，对物体做的净功等于其动能的变化量。
Power is the rate of doing work or transferring energy: P = W / t or P = E / t. Its unit is the watt (W). You can also calculate power as P = F × v for an object moving at constant speed against a constant resistive force.
功率是做功或转移能量的速率：P = W / t 或 P = E / t。单位为瓦特（W）。你还可以用 P = F × v 计算物体恒速克服恒定阻力时的功率。
4. Density and Pressure | 密度与压强
Density is mass per unit volume: ρ = m / V. Typical units are kg/m³ or g/cm³. The density of water is 1000 kg/m³; objects with an average density less than this will float.
密度是单位体积的质量：ρ = m / V。常用单位是 kg/m³ 或 g/cm³。水的密度为 1000 kg/m³；平均密度小于此值的物体会漂浮。
Pressure in a fluid at rest is p = F / A (for a surface) and p = h ρ g for a column of liquid. In the liquid pressure equation, h is the depth, ρ the density of the liquid and g the gravitational field strength. Pressure increases with depth and does not depend on the shape of the container.
静止流体中的压强，针对表面是 p = F / A，对液柱则是 p = h ρ g。在液体压强公式中，h 为深度，ρ 为液体密度，g 为引力场强。压强随深度增加，与容器形状无关。
5. Electricity | 电学
Charge, current and time are related by Q = I × t. Charge is measured in coulombs (C), current in amperes (A) and time in seconds (s). In a series circuit the current is the same everywhere.
电荷量、电流和时间的关系是 Q = I × t。电荷单位是库仑（C），电流是安培（A），时间是秒（s）。在串联电路中，各处电流相等。
Potential difference (voltage) is the work done per unit charge: V = W / Q. Energy transferred in a circuit component is E = Q V. Combining these with the definition of current gives the power equations: P = I V and P = I² R.
电势差（电压）是单位电荷做的功：V = W / Q。电路元件中转移的能量是 E = Q V。将这些与电流的定义结合，可得到功率方程：P = I V 与 P = I² R。
Ohm’s law for a resistor at constant temperature: V = I × R, where R is resistance in ohms (Ω). Resistance of a wire depends on its length and cross-sectional area, but the simple form is enough for most GCSE calculations.
恒温下电阻器的欧姆定律：V = I × R，其中 R 是电阻，单位为欧姆（Ω）。导线的电阻取决于其长度与横截面积，但简单的形式足以应对大多数 GCSE 计算。
In a transformer, the turns ratio and voltage ratio are linked by Vₚ / Vₛ = Nₚ / Nₛ. For an ideal transformer (100% efficient), power in equals power out, so Vₚ Iₚ = Vₛ Iₛ. Transformers only work with alternating current.
变压器中，匝数比与电压比的关系是 Vₚ / Vₛ = Nₚ / Nₛ。对于理想变压器（效率 100%），输入功率等于输出功率，故 Vₚ Iₚ = Vₛ Iₛ。变压器仅对交流电有效。
6. Energy Transfers in Circuits | 电路中的能量转移
The energy transferred by an electrical component is E = P × t. Using P = I V and Q = I t, we also have E = I V t. These equations allow you to calculate heating effects or the energy stored in a battery.
电器元件转移的能量为 E = P × t。利用 P = I V 和 Q = I t，还可得到 E = I V t。这些方程能帮助你计算热效应或电池储存的能量。
When electricity is used for heating, the efficiency can be calculated as useful thermal energy output divided by electrical energy input. For a resistor, all electrical energy is converted to internal (thermal) energy; thus efficiency is 100% only if no light or sound is produced.
当电用于加热时，效率可计算为输出的有用热能除以输入的电能。对于电阻器，所有电能都转化为内能（热能）；因此若不产生光或声音，效率才是 100%。
7. Waves | 波
The wave speed equation links frequency, wavelength and speed: v = f λ. v is the wave speed in m/s, f is the frequency in hertz (Hz) and λ is the wavelength in metres. This applies to both transverse and longitudinal waves.
波速方程将频率、波长和波速联系起来：v = f λ。v 是波速（m/s），f 是频率（赫兹，Hz），λ 是波长（米）。这对横波和纵波均适用。
For reflection, the angle of incidence equals the angle of reflection, measured from the normal. In refraction, the change in speed leads to a change in direction unless the wave enters the medium along the normal.
反射时，入射角等于反射角，均从法线量起。折射时，速度的变化导致方向改变，除非波沿法线进入介质。
The period T of a wave is the reciprocal of the frequency: T = 1 / f. The time period is measured in seconds. For a wave of frequency 50 Hz, the period is 0.02 s.
波的周期 T 是频率的倒数：T = 1 / f。周期以秒为单位。频率为 50 Hz 的波，周期为 0.02 s。
8. Electromagnetic Spectrum | 电磁波谱
All electromagnetic waves travel at the same speed in a vacuum: c = 3.00 × 10⁸ m/s. The equation c = f λ still holds. As you go from radio waves to gamma rays, frequency increases and wavelength decreases, with corresponding changes in energy carried by each photon.
所有电磁波在真空中的传播速度相同：c = 3.00 × 10⁸ m/s。方程 c = f λ 依然成立。从无线电波到伽马射线，频率递增，波长递减，每个光子携带的能量也相应变化。
Photon energy is given by E = h f, where h is the Planck constant. Although this is used more in GCSE discussions of the photoelectric effect, it underscores why UV and X-rays are more damaging than radio waves.
光子能量由 E = h f 给出，其中 h 是普朗克常数。尽管这在 GCSE 中更多用于讨论光电效应，但它解释了为何紫外线和 X 射线比无线电波更具危害性。
9. Radioactivity | 放射性
. The number of radioactive nuclei remaining decreases exponentially, but GCSE calculations often involve half-life: the time taken for half the nuclei to decay, or for the activity to halve.
放射性衰变是随机的，由活度和计数率描述。活度 A 的单位是贝克勒尔（Bq），1 Bq = 每秒 1 次衰变。剩余放射性核的数量呈指数衰减，但 GCSE 计算常用半衰期：半数核衰变或活度减半所需的时间。
Alpha, beta and gamma radiation have different penetrating powers and ionising abilities. Alpha particles are helium nuclei, beta particles are fast electrons, and gamma rays are electromagnetic waves. Equations for nuclear decay must balance both atomic number and mass number.
α、β 和 γ 辐射具有不同的穿透能力和电离能力。α 粒子是氦核，β 粒子是高速电子，γ 射线是电磁波。核衰变方程必须同时平衡原子序数和质量数。
10. Energy Resources and Efficiency | 能源与效率
Efficiency is the ratio of useful output energy to total input energy, or useful power output to total power input: Efficiency = (useful output / total input) × 100%. No device can be 100% efficient because some energy is always dissipated as heat to the surroundings.
效率是有用输出能量与总输入能量（或有用输出功率与总输入功率）的比值：效率 = (有用输出 / 总输入) × 100%。任何装置都不可能达到 100% 的效率，因为总有部分能量以热的形式耗散到环境中。
In many energy transfer processes, the amount of energy stored or transferred can be calculated by combining the equations you already know. For example, a falling object converts gravitational potential energy into kinetic energy. If air resistance is negligible, m g h = ½ m v², allowing you to find speed.
在许多能量转移过程中，储存或转移的能量可以通过组合已知方程计算。例如，下落的物体会将重力势能转化为动能。若空气阻力可忽略，m g h = ½ m v²，可由此求出速度。
11. Units and Prefixes | 单位与词头
It is vital to use standard SI units when substituting into equations. Common prefixes tested at GCSE include milli (m, 10⁻³), kilo (k, 10³), mega (M, 10⁶), centi (c, 10⁻²) and micro (μ, 10⁻⁶). Convert all quantities to base units before calculating, otherwise you may be out by a factor of a thousand.
代入方程时务必使用标准国际单位制。GCSE 常考的词头包括毫（m, 10⁻³）、千（k, 10³）、兆（M, 10⁶）、厘（c, 10⁻²）和微（μ, 10⁻⁶）。计算前把所有量转换为基本单位，否则可能差出一千倍。
hange it to A (1 mA = 0.001 A). This habit prevents mistakes in equations like E = ½ k e².
例如，若弹簧伸长的单位是 cm，要先转换为米（1 cm = 0.01 m）。若电流单位是 mA，转换为安（1 mA = 0.001 A）。这个习惯能避免在 E = ½ k e² 等方程中出错。
12. Circuit Components and Characteristics | 电路元件与特性
The resistance of a filament lamp increases as the current increases because the metal filament gets hot. The I–V graph is a curve. For a diode, current only flows in one direction; its forward resistance is very low once the threshold voltage (about 0.6 V) is reached.
灯丝的电阻随电流增大而增大，因为金属灯丝变热。其 I–V 图是曲线。对于二极管，电流只能单向流动；一旦达到门槛电压（约 0.6 V），其正向电阻极低。
A thermistor’s resistance decreases as temperature increases (negative temperature coefficient). A light-dependent resistor (LDR) behaves similarly with light intensity: the brighter the light, the lower the resistance. These are used in sensing circuits.
热敏电阻的阻值随温度升高而降低（负温度系数）。光敏电阻（LDR）随光照强度表现类似：光越亮，电阻越低。它们常用于传感电路。
In a fixed resistor at constant temperature, current is directly proportional to potential difference. This is the only condition under which Ohm’s law is strictly obeyed. Circuit calculations often rely on rules for series and parallel:
- Series: current same, voltages add, total R = R₁ + R₂ + …
- Parallel: voltage same across branches, currents add, 1/Rtotal = 1/R₁ + 1/R₂ + …
在恒温固定电阻器中，电流与电势差成正比。只有在此条件下欧姆定律才严格成立。电路计算常依赖串并联规则：
- 串联：电流相同，电压相加，总电阻 R = R₁ + R₂ + …
- 并联：各支路电压相同，电流相加，1/Rtotal = 1/R₁ + 1/R₂ + …
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图