📚 Year 10 OCR Physics Formula and Theorem Quick Reference Handbook | Year 10 OCR 物理：公式定理速查手册
Welcome to your one‑stop rapid revision guide for Year 10 OCR Physics. This handbook gathers all the essential equations, laws and definitions you need, pairing every statement in English with its Chinese equivalent so that you can cross‑check your understanding instantly. Work through each section, practise the rearrangements, and build confidence for your end‑of‑topic tests and final examinations.
欢迎使用这份 Year 10 OCR 物理一站式速查手册。本手册汇集了所有关键公式、定律和定义，每一条先提供英文表述，再附上中文对应，让你能立即交叉检验自己的理解。请逐一学习各章节，练习公式变形，为主题测试和期末考试建立信心。
1. Speed, Velocity and Acceleration | 速率、速度与加速度
Average speed is the total distance travelled divided by the total time taken. It is a scalar quantity measured in metres per second (m/s).
平均速率等于总路程除以总时间。它是一个标量，单位是米每秒（m/s）。
speed = distance / time v = s / t
Velocity is speed in a given direction; it is a vector. Acceleration is the rate of change of velocity. If an object speeds up, acceleration is positive; if it slows down, acceleration is negative (deceleration).
速度是带有方向的速率；它是一个矢量。加速度是速度变化的快慢。物体加速时加速度为正，减速时加速度为负（即减速）。
acceleration = change in velocity / time taken a = (v − u) / t
acceleration is constant: v² = u² + 2 a s. Make sure you can rearrange it for any unknown.
在加速度恒定时，可使用联系末速度、初速度、加速度和位移的运动学公式：v² = u² + 2 a s。务必能针对任意未知量进行变形。
2. Forces and Newton's Laws | 力与牛顿定律
Newton’s First Law states that an object remains at rest or in uniform motion unless acted upon by a resultant force. This explains why a stationary book stays still and why a moving spacecraft continues in a straight line at constant speed in deep space.
牛顿第一定律：除非受到合外力作用，否则物体将保持静止或匀速直线运动状态。这解释了为何静止的书本保持静止，也为何深空中的航天器沿直线恒速运动。
a. Here force is measured in newtons (N), mass in kilograms (kg) and acceleration in m/s².
牛顿第二定律将合外力、质量与加速度联系起来：F = m a。力的单位是牛顿（N），质量单位是千克（kg），加速度单位是米每二次方秒。
F = m a
Newton’s Third Law says that for every action force there is an equal and opposite reaction force. These two forces act on different objects and are of the same type.
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。这两个力作用在不同物体上，且性质相同。
ue to gravity: W = m g, where g is the gravitational field strength (≈ 9.8 N/kg on Earth).
重力是由引力产生的力：W = m g，其中 g 是引力场强度（地球上约为 9.8 N/kg）。
W = m g
3. Motion Graphs and Terminal Velocity | 运动图像与终端速度
A distance–time graph shows how distance changes with time. The gradient of the line gives the speed. A horizontal line means the object is stationary; a steeper gradient means greater speed.
距离‑时间图显示距离随时间的变化。线的斜率代表速率。水平线表示物体静止；斜率越大，速率越大。
A velocity–time graph shows how velocity changes with time. The gradient gives acceleration, and the area under the graph gives the displacement. A negative gradient indicates deceleration.
速度‑时间图显示速度随时间的变化。斜率代表加速度，图线下的面积代表位移。负斜率表示减速。
Terminal velocity occurs when the air resistance (drag) acting on a falling object becomes equal to its weight. The resultant force is zero, so the object falls at constant speed. Skydivers experience this before opening their parachute.
当作用在落体上的空气阻力（拖拽力）等于其重力时，达到终端速度。此时合外力为零，物体以恒定速率下落。跳伞运动员在打开降落伞前会经历这一过程。
4. Energy Stores and Transfers | 能量储存与传递
Energy is measured in joules (J). The main stores are kinetic, gravitational potential, elastic potential, thermal, chemical, nuclear and electromagnetic. Energy can be transferred mechanically, electrically, by heating or by radiation.
能量以焦耳（J）为单位。主要的能量储存形式包括动能、重力势能、弹性势能、热能、化学能、核能和电磁能。能量可以通过做功、电流、加热或辐射的方式传递。
kinetic energy = ½ m v² Eₖ = ½ m v²
gravitational potential energy = m g h Eₚ = m g h
The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or stored. In a closed system, total energy remains constant.
能量守恒定律指出：能量不能被创造或消灭，只能被传递或储存。在封闭系统中，总能量保持不变。
noring air resistance, m g h = ½ m v², which allows you to calculate the impact speed: v = √2 g h.
物体下落时，重力势能转化为动能。忽略空气阻力时，m g h = ½ m v²，从而可以计算撞击速度：v = √2 g h。
5. Work, Power and Efficiency | 功、功率与效率
Work is done when a force moves an object in the direction of the force. Work is also a measure of energy transferred.
当力使物体沿力的方向移动时，就说力做了功。功也是能量传递的量度。
work done = force × distance W = F d
doing work or the rate of energy transfer. It is measured in watts (W), where 1 W = 1 J/s.
功率是做功的速率或能量传递的速率，单位是瓦特（W），1 W = 1 J/s。
power = work done / time P = W / t or P = E / t
Efficiency is the ratio of useful output energy (or power) to total input energy (or power). It can be expressed as a decimal or a percentage. No device can be 100 % efficient because some energy is always dissipated as thermal energy.
效率是有用输出能量（或功率）与总输入能量（或功率）的比值，可以用小数或百分数表示。任何装置都不可能达到 100% 的效率，因为总有一部分能量以热能形式散失。
efficiency = useful output energy / total input energy
6. Density, Pressure and States of Matter | 密度、压强与物态
Density is mass per unit volume and is measured in kg/m³. The formula is:
密度是单位体积的质量，单位是千克每立方米。公式为：
density = mass / volume ρ = m / V
t). For an irregular solid, use a displacement can or a measuring cylinder to find volume.
测量规则固体的密度时，用天平称质量，用几何计算得出体积（如长×宽×高）。对于不规则固体，使用溢水罐或量筒测量体积。
force per unit area acting on a surface. The unit is the pascal (Pa), where 1 Pa = 1 N/m².
压强是作用在表面上单位面积的力，单位是帕斯卡（Pa），1 Pa = 1 N/m²。
pressure = force / area P = F / A
e depth, ρ is the liquid density and g is the gravitational field strength. This explains why dam walls are thicker at the bottom.
液体内部的压强随深度和密度增大而增大：P = h ρ g，其中 h 为深度，ρ 为液体密度，g 为引力场强度。这解释了为何水坝底部更厚。
7. Hooke's Law and Elastic Behaviour | 胡克定律与弹性行为
Hooke’s Law states that the extension of an elastic object is directly proportional to the applied force, provided the limit of proportionality is not exceeded.
胡克定律指出：在比例极限内，弹性物体的伸长量与所施加的力成正比。
force = spring constant × extension F = k x
The spring constant k is a measure of the stiffness of the spring. A stiffer spring has a larger k. On a force–extension graph, the initial linear region represents Hooke’s Law; the gradient equals k.
弹簧常数 k 是弹簧刚度的量度。弹簧越硬，k 越大。在力‑伸长量图上，初始线性区域代表胡克定律；斜率等于 k。
Elastic deformation is reversed when the force is removed; plastic deformation is permanent. The elastic limit is the point beyond which the material no longer returns to its original shape.
弹性形变在撤去外力后能恢复原状；塑性形变则是永久的。弹性极限是材料不再能恢复原状的临界点。
stored in a stretched or compressed spring can be calculated from the area under the force–extension graph: E = ½ F x = ½ k x² (for Hooke’s Law region).
拉伸或压缩弹簧储存的弹性势能可通过力‑伸长量图下的面积计算：E = ½ F x = ½ k x²（在遵守胡克定律的区域内）。
8. Waves: Properties and the Wave Equation | 波：特性与波动方程
Waves transfer energy without transferring matter. Transverse waves (e.g., light, water waves) oscillate perpendicular to the direction of energy transfer; longitudinal waves (e.g., sound) oscillate parallel to it.
波传递能量而不传递物质。横波（如光、水波）的振动方向与能量传递方向垂直；纵波（如声波）的振动方向与能量传递方向平行。
The amplitude is the maximum displacement from the equilibrium position. The wavelength λ is the distance between two consecutive points in phase (e.g., crest to crest). The frequency f is the number of complete waves passing a point per second, measured in hertz (Hz).
振幅是离开平衡位置的最大位移。波长 λ 是相邻两个同相位点（如波峰到波峰）之间的距离。频率 f 是每秒通过某点的完整波的数量，单位是赫兹（Hz）。
The period T is the time taken for one complete wave to pass a point: T = 1 / f.
周期 T 是一个完整波通过某点所需的时间：T = 1 / f。
wave speed = frequency × wavelength v = f λ
.0 × 10⁸ m/s. This equation is often used to relate frequency and wavelength for EM waves.
所有电磁波在真空中的传播速度相同：c = 3.0 × 10⁸ m/s。常用此方程关联电磁波的频率和波长。
9. Reflection, Refraction and the EM Spectrum | 反射、折射与电磁波谱
The law of reflection states that the angle of incidence equals the angle of reflection, measured from the normal (an imaginary line perpendicular to the surface).
反射定律指出：入射角等于反射角，均从法线（垂直于表面的假想线）量起。
Refraction is the bending of light as it passes from one medium into another due to a change in speed. When light enters a denser medium, it slows down and bends towards the normal.
折射是光从一种介质进入另一种介质时因速度变化而发生的弯曲。光进入光密介质时速度减小，向法线偏折。
The electromagnetic spectrum, in order of decreasing wavelength and increasing frequency, is: radio waves, microwaves, infrared, visible light, ultraviolet, X‑rays and gamma rays. Each region has distinct uses and dangers.
电磁波谱按波长递减、频率递增的顺序为：无线电波、微波、红外线、可见光、紫外线、X 射线和伽马射线。每一频段都有独特的用途和危害。
10. Electric Circuits: Current, Voltage and Resistance | 电路：电流、电压与电阻
Electric current is the rate of flow of charge. It is measured in amperes (A). One ampere is one coulomb per second.
电流是电荷流动的速率，单位是安培（A）。1 安培等于 1 库仑每秒。
charge = current × time Q = I t
Potential difference (voltage) is the energy transferred per unit charge. It is measured in volts (V). One volt means one joule per coulomb.
电势差（电压）是每单位电荷所传递的能量，单位是伏特（V）。1 伏特表示每库仑电荷传递 1 焦耳的能量。
energy = charge × voltage E = Q V
Resistance is a measure of how much a component opposes the flow of current. Ohm’s Law states that for a resistor at constant temperature, current is directly proportional to voltage.
电阻是衡量元件阻碍电流流动程度的物理量。欧姆定律指出：对于温度恒定的电阻，电流与电压成正比。
voltage = current × resistance V = I R
rywhere; the total resistance is the sum of the individual resistances: Rₜₒₜₐₗ = R₁ + R₂ + … ltage across each branch is the same; the total current is the sum of the branch currents.
在串联电路中，各处电流相等；总电阻等于各电阻之和：Rₜₒₜₐₗ = R₁ + R₂ + … 。在并联电路中，各支路电压相等；总电流等于各支路电流之和。
11. Electrical Power and Energy in Circuits | 电功率与电路中的电能
Power in an electrical circuit is the rate at which energy is transferred. It can be calculated using any of these equivalent forms:
电路中的电功率是能量传递的速率，可用以下任一等价公式计算：
P = I V P = I² R P = V² / R
t. Since P = I V, we also have E = I V t. Electricity companies measure energy in kilowatt‑hours (kWh) for domestic billing.
用电器传递的能量等于功率乘以时间：E = P t。又因 P = I V，故 E = I V t。家庭用电计费以千瓦时（kWh）为能量单位。
energy transferred = power × time E = P t
if power is in watts and time in seconds, energy is in joules. For kWh, power must be in kilowatts and time in hours.
务必注意单位：使用 E = P t 时，若功率以瓦特、时间以秒为单位，能量即为焦耳。若要以千瓦时为单位，功率须用千瓦、时间须用小时。
12. Radioactivity and Nuclear Equations | 放射性衰变与核方程
Radioactive decay is a random process where unstable atomic nuclei emit radiation to become more stable. Three main types of nuclear radiation exist: alpha (α), beta (β) and gamma (γ).
放射性衰变是一个随机过程，不稳定原子核通过发射辐射变得更稳定。主要存在三种核辐射：α 粒子、β 粒子和 γ 射线。
An alpha particle consists of 2 protons and 2 neutrons; it is a helium nucleus, represented as ⁴₂He. Beta decay involves a neutron turning into a proton and emitting a high‑speed electron, represented as ⁰₋₁e. Gamma radiation is electromagnetic and has no mass or charge.
α 粒子由 2 个质子和 2 个中子组成，即氦原子核，表示为 ⁴₂He。β 衰变中一个中子转变为一个质子并发射一个高速电子，表示为 ⁰₋₁e。γ 辐射是电磁波，无质量也无电荷。
Nuclear equations must balance the total mass number (top) and the total atomic number (bottom) on both sides. For example:
核方程必须确保两边质量数（左上标）和电荷数（左下标）守恒。例如：
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He (alpha decay)
¹⁴₆C → ¹⁴₇N + ⁰₋₁e (beta decay)
The activity of a radioactive source is the number of decays per second, measured in becquerels (Bq). Half‑life is the time taken for the activity (or the number of unstable nuclei) to halve.
放射源的活度是每秒钟衰变的次数，单位是贝克勒尔（Bq）。半衰期是活度（或不稳定原子核数量）减半所需的时间。
Understanding half‑life allows us to date archaeological samples using carbon‑14 and to manage radioactive waste safely.
理解半衰期使我们能利用碳‑14 测定考古样品年代，并能安全管理放射性废物。
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