📚 Year 11 CCEA Physics: Quick-Reference Handbook of Formulas and Theorems | Year 11 CCEA 物理：公式定理速查手册
This quick-reference handbook brings together the essential formulas and theorems covered in the Year 11 CCEA Physics course, primarily from Unit 1 (Motion, Forces, Energy, Density, Radioactivity) and introductory electricity. Use it to revise key relationships, check units, and reinforce your understanding ahead of assessments.
本速查手册汇集了 Year 11 CCEA 物理课程中的核心公式与定理，主要来自 Unit 1（运动、力、能量、密度、放射性）以及电学基础。可用作复习关键关系式、核对单位、巩固理解的快速参考。
1. Equations of Motion | 运动学公式
For an object moving in a straight line with uniform acceleration, the following three equations connect initial velocity (u), final velocity (v), acceleration (a), displacement (s), and time (t).
对于沿直线作匀加速运动的物体，以下三个公式将初速度（u）、末速度（v）、加速度（a）、位移（s）和时间（t）联系起来。
v = u + at
This is the definition of acceleration rearranged, often used when time is given and displacement is not needed.
这是加速度定义式的变形，常用于已知时间但不需要求位移的情形。
s = ut + ½at²
Use this relation when acceleration is constant and time is known.
当加速度恒定且时间已知时，使用此关系式。
v² = u² + 2as
Use this equation when time is not involved.
当时间未知时，使用此公式。
The average velocity can be found using s = ½(u+v)t when acceleration is uniform. All quantities are in SI units: v, u in m/s; a in m/s²; s in m; t in s.
在匀加速运动中，平均速度可用 s = ½(u+v)t 求出。所有物理量均为国际单位制：v、u 的单位是 m/s，a 的单位是 m/s²，s 的单位是 m，t 的单位是 s。
2. Newton's Second Law of Motion | 牛顿第二运动定律
The net force acting on an object is equal to the product of its mass and acceleration.
作用在物体上的净力等于其质量与加速度的乘积。
F = m a
Force is measured in newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²). A resultant force of 1 N gives a mass of 1 kg an acceleration of 1 m/s².
力的单位是牛顿（N），质量的单位是千克（kg），加速度的单位是米每二次方秒（m/s²）。1 N 的合力使 1 kg 的物体产生 1 m/s² 的加速度。
Always remember that F represents the resultant balanced) force. If multiple forces act, you must find the vector sum before using F = ma.
切记 F 表示合（非平衡）力。如果多个力同时作用，必须先求矢量和再代入 F = ma。
3. Weight and Mass | 重量与质量
Weight is the gravitational force acting on an object's mass. It is not the same as mass, which is a measure of the amount of matter.
重量是作用在物体质量上的引力，它与质量不同，质量是物体所含物质的量度。
W = m g
On Earth, the gravitational field strength g is taken as 9.8 N/kg (or approximately 10 N/kg for estimation questions in CCEA exams). Weight is a force, so its unit is the newton (N).
在地球表面，引力场强度 g 取 9.8 N/kg（CCEA 考试中估算题常用 10 N/kg）。重量是力的一种，因此单位是牛顿（N）。
The mass of an object remains constant everywhere, but its weight changes if g alters, such as on the Moon.
物体的质量处处相同，但若 g 改变（如在月球上），其重量将随之变化。
4. Moments and Equilibrium | 力矩与平衡
The moment of a force is a measure of its turning effect about a pivot.
力矩是力对支点产生的转动效应的量度。
M = F × d
Here, d is the perpendicular distance from the pivot to the line of action of the force. The unit of moment is newton-metre (N m).
式中 d 为从支点到力作用线的垂直距离。力矩的单位是牛·米（N m）。
For an object in equilibrium, the sum of the clockwise moments equals the sum of the anticlockwise moments about any pivot.
物体处于平衡时，对任意支点，所有顺时针力矩之和等于所有逆时针力矩之和。
If a beam is balanced, you can apply the principle: total clockwise moment = total anticlockwise moment.
若横梁平衡，可运用该原理：总顺时针力矩 = 总逆时针力矩。
5. Density | 密度
Density describes how much mass is packed into a given volume.
密度描述了单位体积内含有多少质量。
ρ = m / V
The Greek letter ρ (rho) stands for density in kg/m³, mass m is in kg, and volume V is in m³. For irregular solids, volume can be found by displacement of water.
希腊字母 ρ（rho）表示密度，单位是 kg/m³；质量 m 单位是 kg；体积 V 单位是 m³。不规则固体的体积可用排水法测得。
Remember that 1 g/cm³ = 1000 kg/m³. When converting, multiply by 1000.
注意 1 g/cm³ = 1000 kg/m³。换算时需乘以 1000。
6. Pressure | 压强
Pressure is the force acting per unit area. For a force acting perpendicularly on a surface:
压强是单位面积上所受的力。当力垂直作用于表面时：
p = F / A
p is in pascals (Pa), where 1 Pa = 1 N/m². Force F is in newtons, area A in square metres.
压强 p 的单位是帕斯卡（Pa），1 Pa = 1 N/m²。力 F 单位是牛顿，面积 A 单位是平方米。
In a liquid, pressure increases with depth and density:
p = h ρ g
Where h is the depth (m), ρ is the density of the liquid (kg/m³), and g is the gravitational field strength. This formula only gives the pressure due to the liquid column; total pressure includes atmospheric pressure on the surface.
其中 h 为深度（m），ρ 为液体密度（kg/m³），g 为引力场强度。该式只给出液柱产生的压强；总压强还需加上液面的大气压强。
7. Hooke's Law | 胡克定律
For a spring or elastic material, the extension is directly proportional to the applied force, provided the elastic limit is not exceeded.
对于弹簧或弹性材料，只要不超过弹性极限，伸长量与所施加的力成正比。
F = k x
F is the force applied (N), x is the extension (m), and k is the spring constant (N/m), a measure of stiffness. A stiffer spring has a larger k.
F 为施加的力（N），x 为伸长量（m），k 为弹簧常数（N/m），它是弹簧刚度的量度，k 越大弹簧越硬。
The elastic limit is the point beyond which the spring becomes permanently deformed and no longer obeys Hooke's law.
弹性极限是超过后弹簧将发生永久形变并不再遵从胡克定律的点。
8. Work, Energy and Power | 功、能量与功率
Work is done when a force moves an object in the direction of the force.
当力使物体沿力的方向移动时，力对物体做功。
W = F d
the force (N), and d is the distance moved in the direction of the force (m). 1 J = 1 N m.
功 W 的单位是焦耳（J），F 是力（N），d 是沿力方向移动的距离（m）。1 J = 1 N m。
Gravitational potential energy (GPE) stored by an object raised to a height h:
物体被举高 h 后储存的重力势能（GPE）：
Eₚ = m g h
Kinetic energy (KE) of a moving object:
运动物体的动能（KE）：
Eₖ = ½ m v²
stem, total energy is constant. If air resistance is negligible, loss in GPE = gain in KE.
能量守恒：在孤立系统中，总能量不变。若空气阻力可忽略，重力势能的减少量等于动能的增加量。
Power is the rate of doing work or transferring energy:
P = W / t = E / t
Power is measured in watts (W), where 1 W = 1 J/s.
功率的单位是瓦特（W），1 W = 1 J/s。
9. Kinetic Theory and Gas Pressure | 动能理论与气体压强
Gas pressure is caused by the collisions of gas particles with the walls of the container. Increasing temperature raises the average kinetic energy of particles, leading to more frequent and forceful collisions.
气体压强由气体粒子与容器壁的碰撞引起。温度升高使粒子的平均动能增大，碰撞更频繁、更有力。
For a fixed mass of gas at constant temperature, pressure and volume are inversely proportional (Boyle's Law):
对于一定质量、温度恒定的气体，压强与体积成反比（波义耳定律）：
pV = constant
p₁ V₁ = p₂ V₂
Pressure p must be in the same units on both sides; volume V can be in any unit provided it is consistent. If volume decreases, pressure increases provided temperature remains unchanged.
压强 p 在等式两边须使用相同单位；体积 V 只要前后一致可用任意单位。若温度不变，体积减小则压强增大。
Absolute zero (0 K = – erature at which particle kinetic energy is theoretically zero and pressure would be zero.
绝对零度（0 K = –273 °C）是粒子动能理论上为零、压强为零的温度。
10. Radioactive Decay and Half-Life | 放射性衰变与半衰期
Radioactive decay is a random process. The half‑life (T₁/₂) is the time taken for half the nuclei in a sample to decay, or for the activity to fall to half its initial value.
放射性衰变是一个随机过程。半衰期（T₁/₂）是指样品中一半的原子核发生衰变，或活度降到初始值一半所需的时间。
The number of undecayed nuclei N after n half‑lives can be found from:
N = N₀ × (½)ⁿ
Where N₀ is the initial number of nuclei and n = time elapsed / half‑ife. The same expression works for mass or activity: mass remaining = initial mass × (½)ⁿ.
式中 N₀ 为初始原子核数，n = 经历时间 / 半衰期。同样的表达式也适用于质量或活度：剩余质量 = 初始质量 × (½)ⁿ。
The net decline is exponential, but for CCEA Year 11, you mainly use the halving approach with half‑life intervals.
衰变呈指数规律，但在 CCEA Year 11 阶段，主要采用半衰期间隔减半的方法进行计算。
11. Electrical Circuits and Power | 电路与电功率
Electric current is the rate of flow of charge. One coulomb (C) is the amount of charge passing a point when a current of 1 A flows for 1 s.
电流是电荷流动的速率。1 库仑（C）是 1 A 电流在 1 s 内通过某点的电荷量。
Q = I t
Charge Q in coulombs, current I in amperes, time t in seconds.
电荷 Q 的单位是库仑，电流 I 的单位是安培，时间 t 的单位是秒。
Ohm's law states that the current through a conductor is directly proportional to the potential difference across it, provided temperature is constant:
欧姆定律指出，在温度不变的条件下，通过导体的电流与其两端电势差成正比：
V = I R
Resistance R is in ohms (Ω). The resistance of a wire depends on its length, cross-sectional area, and material.
电阻 R 的单位是欧姆（Ω）。导线的电阻取决于其长度、横截面积和材料。
For resistors in series: total resistance is the sum of individual resistances.
串联电阻：总电阻等于各电阻之和。
Rₛ = R₁ + R₂ + ...
For resistors in parallel: the reciprocal of the total resistance is the sum of the reciprocals.
并联电阻：总电阻的倒数等于各电阻倒数之和。
1/Rₚ = 1/R₁ + 1/R₂ + ...
Electrical power and energy are given by:
P = V I P = I² R P = V² / R
E = P t = V I t
Power P is in watts (W), energy E in joules (J). For appliances, a larger power rating means more energy transferred per second.
功率 P 的单位是瓦特（W），能量 E 的单位是焦耳（J）。对用电器而言，额定功率越大，每秒转化的能量越多。
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