📚 Year 10 CCEA Physics: Formula & Theorem Quick Reference Handbook | Year 10 CCEA 物理：公式定理速查手册
This quick-reference handbook compiles all the essential formulas, definitions and key theorems you need for the Year 10 CCEA Physics course. Use it for revision, homework and exam preparation. Each section pairs an English explanation with a Chinese translation so you can master concepts in both languages.
本速查手册汇集了Year 10 CCEA物理课程所需的所有核心公式、定义和关键定理，可用于复习、作业和备考。每个要点均配有英文解释和中文翻译，助你双语掌握物理概念。
1. Speed, Velocity and Acceleration | 速率、速度与加速度
Speed is a scalar quantity that measures how fast an object moves, while velocity is a vector that also includes direction. The average speed v can be calculated using distance s and time t.
速率是标量，表示物体运动的快慢；速度是矢量，包含方向。平均速率 v 可用路程 s 和时间 t 计算。
v = s / t
Acceleration a is the rate of change of velocity. It is a vector quantity defined by the change in velocity Δv over time t. If an object speeds up, acceleration is positive; if it slows down, acceleration is negative (deceleration).
加速度 a 是速度的变化率，为矢量，定义为速度变化量 Δv 除以时间 t。物体加速时加速度为正，减速时为负（即减速度）。
a = (v − u) / t
where u is the initial velocity, v is the final velocity and t is the time taken. The units for speed and velocity are metres per second (m/s) and for acceleration are metres per second squared (m/s²).
其中 u 为初速度，v 为末速度，t 为所用时间。速率和速度的单位是米每秒（m/s），加速度的单位是米每二次方秒（m/s²）。
2. Equations of Motion | 运动方程
For objects moving with constant acceleration in a straight line, three key equations link displacement s, initial velocity u, final velocity v, acceleration a and time t. They are often called SUVAT equations.
对于匀加速直线运动的物体，三个关键方程将位移 s、初速度 u、末速度 v、加速度 a 和时间 t 联系起来，常称为 SUVAT 方程。
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
These equations apply only when acceleration is uniform. The displacement s is a vector, so you must consider direction. Remember to convert all units to SI (metres, seconds, m/s) before substituting.
这些方程仅适用于加速度恒定的情况。位移 s 是矢量，计算时需考虑方向。代入数值前，必须将所有单位转换为国际单位制（米、秒、米每秒）。
3. 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 introduces the concept of inertia.
牛顿第一定律指出，若物体不受合力作用，将保持静止或匀速直线运动状态，这引入了惯性的概念。
Newton’s second law defines the relationship between resultant force F, mass m and acceleration a. It is one of the most important equations in physics.
牛顿第二定律定义了合力 F、质量 m 和加速度 a 之间的关系，是物理学最重要的公式之一。
F = m a
The unit of force is the newton (N), where 1 N = 1 kg m/s². The mass m must be in kilograms. Newton’s third law states that for every action there is an equal and opposite reaction; forces always occur in pairs acting on different objects.
力的单位是牛顿（N），1 N = 1 kg m/s²。质量 m 必须用千克。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；力总是成对出现并作用在不同物体上。
When drawing free-body diagrams, draw all forces as arrows from a point, label them clearly, and remember that balanced forces mean constant velocity.
画受力分析图时，所有力以箭头从一点出发，清晰标注，且平衡力意味着物体速度不变。
4. Work, Energy and Power | 功、能量与功率
Work is done when a force moves an object through a distance in the direction of the force. The work done W is calculated by:
当力使物体沿力的方向移动一段距离时，力对物体做功。功 W 的计算公式为：
W = F d
where F is the force in newtons and d is the distance moved in metres. The unit of work is the joule (J).
其中 F 为力（牛），d 为移动距离（米）。功的单位是焦耳（J）。
Gravitational potential energy (GPE) is the energy stored due to an object’s height above ground. It is given by:
重力势能（GPE）是物体因高度而储存的能量，计算公式为：
Eₚ = m g h
Kinetic energy (KE) depends on mass and speed:
动能（KE）取决于质量和速度：
Eₖ = ½ m v²
Power P is the rate of doing work or transferring energy. It can be expressed using work done or energy transferred divided by time.
功率 P 是做功或能量转移的速率，可用做功或转移能量除以时间表示。
P = W / t = ΔE / t
The unit of power is the watt (W), equivalent to J/s. Always check that mass is in kg, height in m and speed in m/s.
功率的单位是瓦特（W），等同于 J/s。务必确保质量用 kg，高度用 m，速度用 m/s。
5. Density and Pressure | 密度与压强
Density ρ (rho) is mass per unit volume. It tells us how tightly packed the particles in a substance are.
密度 ρ 是单位体积的质量，反映物质内部粒子的紧密程度。
ρ = m / V
The SI unit of density is kg/m³, but you may also use g/cm³. Remember 1 g/cm³ = 1000 kg/m³.
密度的国际单位是 kg/m³，也可使用 g/cm³。注意 1 g/cm³ = 1000 kg/m³。
Pressure p is the force acting perpendicularly per unit area. It is a scalar quantity.
压强 p 是垂直于表面单位面积上的压力，为标量。
p = F / A
where F is force in newtons and A is area in m². The unit of pressure is the pascal (Pa); 1 Pa = 1 N/m². Pressure in liquids increases with depth and density, described by p = ρ g h, where h is the depth.
其中 F 为力（牛），A 为面积（米²）。压强单位是帕斯卡（Pa），1 Pa = 1 N/m²。液体压强随深度和密度增加，公式为 p = ρ g h，h 为深度。
6. Wave Equation and Properties | 波动方程与波的性质
Waves transfer energy without transferring matter. The key properties are frequency f (in hertz, Hz), wavelength λ (in metres, m) and wave speed v (in m/s).
波传递能量而不传递物质。关键属性有频率 f（赫兹 Hz）、波长 λ（米 m）和波速 v（米/秒 m/s）。
The wave equation links these three quantities:
波动方程将这三个量联系起来：
v = f λ
Frequency is the number of complete waves passing a point per second, and the period T is the time for one complete wave: T = 1 / f.
频率是每秒通过某点的完整波数，周期 T 是完成一个完整波的时间：T = 1 / f。
For all electromagnetic waves travelling in a vacuum, the speed is a constant c = 3.00 × 10⁸ m/s. In transverse waves, the oscillations are perpendicular to the direction of energy transfer; in longitudinal waves, they are parallel.
所有电磁波在真空中速度均为常数 c = 3.00 × 10⁸ m/s。横波的振动方向与能量传播方向垂直，纵波的振动方向则与之平行。
7. Electricity: Current, Voltage and Resistance | 电学：电流、电压与电阻
Electric current I is the rate of flow of charge. It is measured in amperes (A) using an ammeter connected in series.
电流 I 是电荷流动的速率，单位为安培（A），用串联的电流表测量。
I = Q / t
where Q is the charge in coulombs (C) and t is time in seconds. Voltage (potential difference) V is the energy transferred per unit charge, measured in volts (V) with a voltmeter connected in parallel.
其中 Q 为电荷量（库仑 C），t 为时间（秒）。电压（电势差）V 是单位电荷转移的能量，单位为伏特（V），用并联的电压表测量。
V = E / Q
Resistance R (in ohms, Ω) opposes current. Ohm’s law states that for a metallic conductor at constant temperature, V is directly proportional to I:
电阻 R（欧姆 Ω）阻碍电流。欧姆定律指出，在温度不变时，金属导体的电压 V 与电流 I 成正比：
V = I R
An I-V graph for a fixed resistor is a straight line through the origin; for a filament lamp, the line curves as resistance increases with temperature.
定值电阻的 I-V 图像是过原点的直线；灯丝的 I-V 图像弯曲，因为电阻随温度升高而增大。
8. Electrical Power and Energy Transfer | 电功率与能量转移
Electrical power P is the rate at which an appliance transfers energy. It can be calculated using current and voltage:
电功率 P 是用电器转移能量的速率，可通过电流和电压计算：
P = V I
Using Ohm’s law, two alternative forms can be derived for components that follow Ohm’s law:
结合欧姆定律，对遵循欧姆定律的元件，可推导出另两种形式：
P = I² R
P = V² / R
The unit of electrical power is the watt (W). The energy transferred E by a component over time t is:
电功率单位是瓦特（W）。元件在时间 t 内转移的能量 E 为：
E = P t = V I t
Energy is often measured in joules (J) or kilowatt-hours (kWh) for domestic electricity. 1 kWh = 3.6 × 10⁶ J.
能量常用焦耳（J）或家庭用电中的千瓦时（kWh）计量。1 kWh = 3.6 × 10⁶ J。
9. Circuit Rules (Series and Parallel) | 电路规则（串联与并联）
In a series circuit, the current is the same at all points. The total resistance Rₜ is the sum of individual resistances:
串联电路中，各处的电流相等。总电阻 Rₜ 等于各个电阻之和：
Rₜ = R₁ + R₂ + R₃ + …
The total voltage from the supply is shared across the components; the sum of the p.d.s across each component equals the supply voltage. If one component fails, the whole circuit is broken.
电源总电压由各元件分担；各元件两端电压之和等于电源电压。若某一元件损坏，整个电路断开。
In a parallel circuit, the voltage across each branch is the same as the supply voltage. The total current is the sum of the currents in each branch. The reciprocal formula for total resistance is:
并联电路中，各支路两端电压相等，等于电源电压。总电流等于各支路电流之和。总电阻的倒数公式为：
1 / Rₜ = 1 / R₁ + 1 / R₂ + …
Adding more resistors in parallel decreases the total resistance and increases the total current drawn from the supply.
并联更多电阻会减小总电阻，增大从电源取用的总电流。
10. Radioactivity and Half-life | 放射性与半衰期
Radioactive decay is a random process where unstable atomic nuclei emit radiation. There are three main types: alpha (α), beta (β) and gamma (γ). In nuclear equations, both mass number (A) and atomic number (Z) are conserved.
放射性衰变是不稳定原子核随机发射辐射的过程。主要辐射类型有 α、β 和 γ。在核反应方程中，质量数（A）和原子序数（Z）守恒。
An example of alpha decay: uranium-238 becomes thorium-234. Beta decay involves a neutron turning into a proton and emitting an electron. Gamma emission usually accompanies other decays without changing the mass or atomic number.
α 衰变实例：铀-238 变为钍-234。β 衰变涉及中子转变为质子并释放电子。γ 辐射常伴随其他衰变，不改变质量数或原子序数。
The half-life of a radioactive isotope is the time taken for half the unstable nuclei in a sample to decay, or for the count rate to halve. It is a constant for a given isotope and can be found from a decay curve.
放射性同位素的半衰期是样本中一半不稳定核发生衰变，或计数率减半所需的时间。对于给定同位素，半衰期是常数，可从衰变曲线上读出。
Activity is measured in becquerels (Bq), where 1 Bq = 1 decay per second. Background radiation must be subtracted from readings to obtain the corrected count rate.
活度单位为贝可勒尔（Bq），1 Bq 表示每秒衰变一次。测量时应扣除本底辐射，以获得修正后的计数率。
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