📚 Year 9 Cambridge Physics: Formula & Theorem Quick Reference | 剑桥9年级物理公式定理速查手册
This handbook compiles the essential formulas and theorems you will encounter in the Year 9 Cambridge Physics curriculum. It is designed as a rapid revision tool to help you recall key relationships quickly. Every section presents a concept in English immediately followed by its Chinese translation, with key equations displayed prominently in the centre.
本手册汇总了 Year 9 剑桥物理课程中所有的核心公式与定理。它是一本快速复习工具，帮助你迅速回忆关键关系。每一节都采用英中双语对照的形式，重要方程以醒目的居中方式展示。
1. Speed and Acceleration | 速度与加速度
Speed is a measure of how fast an object moves. Average speed can be found by dividing the total distance travelled by the time taken. The SI unit is metres per second (m/s).
速度是物体运动快慢的量度。平均速度等于总路程除以所用时间，国际单位是米每秒 (m/s)。
speed = distance ÷ time
v = d / t
Acceleration tells us how quickly the velocity of an object changes. It is calculated using the initial velocity u, final velocity v, and the time t for the change.
加速度描述物体速度变化的快慢。它由初速度 u、末速度 v 以及变化所用的时间 t 计算得出。
acceleration = (final velocity – initial velocity) ÷ time
a = (v – u) / t
The unit of acceleration is metres per second squared (m/s²). If the acceleration is negative, the object is decelerating.
加速度的单位是米每二次方秒 (m/s²)。如果加速度为负值，表示物体在减速。
2. Forces and Newton’s Second Law | 力与牛顿第二定律
A force can change an object’s speed, direction or shape. The resultant (net) force acting on an object is directly proportional to the product of its mass and acceleration. This relationship is Newton’s Second Law of Motion.
力可以改变物体的速度、方向或形状。作用在物体上的合力与其质量和加速度的乘积成正比，这就是牛顿第二运动定律。
resultant force = mass × acceleration
F = m a
Force is measured in newtons (N), mass in kilograms (kg), and acceleration in m/s². 1 N is the force needed to accelerate a 1 kg mass by 1 m/s².
力的单位是牛顿 (N)，质量单位是千克 (kg)，加速度单位是 m/s²。1 N 就是使 1 kg 的物体获得 1 m/s² 加速度所需的力。
When forces on an object are balanced, the resultant force is zero and the object either stays at rest or moves at a constant velocity.
当物体受到的力平衡时，合力为零，物体要么保持静止，要么做匀速直线运动。
3. Weight and Gravitational Field Strength | 重量与引力场强度
Weight is the gravitational force exerted on an object. It is different from mass; mass is the amount of matter and does not change with location, whereas weight depends on the gravitational field strength g.
重量是作用在物体上的引力。它不同于质量；质量是物质的多少，不随位置变化，而重量取决于引力场强度 g。
weight = mass × gravitational field strength
W = m g
On Earth, g ≈ 10 N/kg (more precisely 9.8 N/kg). Weight is measured in newtons.
在地球表面，g 约等于 10 N/kg（更精确为 9.8 N/kg）。重量单位是牛顿。
4. Hooke’s Law | 胡克定律
Hooke’s Law describes the behaviour of many elastic materials, such as springs. It states that the extension of a spring is directly proportional to the force applied, provided the elastic limit is not exceeded.
胡克定律描述了许多弹性材料（如弹簧）的特性。它指出在弹性限度内，弹簧的伸长量与施加的力成正比。
force = spring constant × extension
F = k x
Here, x is the extension (in metres), and k is the spring constant (N/m), which measures the stiffness of the spring.
其中 x 是伸长量（米），k 是弹簧常数（N/m），表示弹簧的刚度。
5. Moments | 力矩
A moment is the turning effect of a force about a pivot. It depends on the size of the force and the perpendicular distance from the pivot to the line of action of the force.
力矩是力对支点的转动效应。它取决于力的大小以及从支点到力作用线的垂直距离。
moment = force × perpendicular distance from pivot
M = F d
The unit of a moment is newton-metre (N m). For an object to be in equilibrium, the total clockwise moment must equal the total anticlockwise moment (principle of moments).
力矩的单位是牛顿·米 (N m)。物体要达到平衡，顺时针力矩之和必须等于逆时针力矩之和（力矩原理）。
6. 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. Energy is the capacity to do work. Kinetic energy (KE) is the energy an object possesses due to its motion, and gravitational potential energy (GPE) is the energy stored because of an object’s height above a reference point.
当力使物体在力的方向上移动时，便做了功。能量是做功的本领。动能 (KE) 是物体因运动而具有的能量，重力势能 (GPE) 是物体因被举高而储存的能量。
work done = force × distance moved in direction of force
W = F d
kinetic energy = ½ × mass × (speed)²
KE = ½ m v²
gravitational potential energy = mass × g × height
GPE = m g h
rk is done or energy is transferred. The unit of power is the watt (W), where 1 W = 1 J/s.
功率是做功或能量转换的速率。功率的单位是瓦特 (W)，1 W = 1 J/s。
power = work done ÷ time or power = energy transferred ÷ time
P = W / t
All forms of energy obey the law of conservation of energy: energy cannot be created or destroyed, only converted from one form to another.
各种能量都遵句能量守恒定律：能量不会凭空产生或消失，只会从一种形式转换为另一种形式。
7. Pressure | 压强
Pressure is the force acting per unit area. It explains why a sharp knife cuts more easily than a blunt one – a smaller area produces a larger pressure for the same force.
压强是单位面积上受到的压力。这解释了为何锋利的刀比钝刀更容易切割——同样的力下，面积越小，压强越大。
pressure = force ÷ area
P = F / A
In liquids, pressure increases with depth and density, and acts equally in all directions.
压强的单位是帕斯卡 (Pa) 或 N/m²，1 Pa = 1 N/m²。液体中压强随深度和密度增加而增大，且向各个方向均匀传递。
8. Density | 密度
Density describes how much mass is packed into a given volume. It helps to identify materials and predict whether an object will float or sink.
密度表示单位体积内所含物质的质量。它可以用来鉴别材料，也能预测物体会浮起还是下沉。
density = mass ÷ volume
ρ = m / V
The SI unit of density is kilograms per cubic metre (kg/m³), but grams per cubic centimetre (g/cm³) is also common. Fresh water has a density of about 1.0 g/cm³ or 1000 kg/m³.
密度的国际单位是千克每立方米 (kg/m³)，也常用克每立方厘米 (g/cm³)。淡水的密度约为 1.0 g/cm³ 或 1000 kg/m³。
9. Electrical Circuits: Ohm’s Law and Charge | 电路：欧姆定律与电荷
Ohm’s Law links voltage (potential difference), current, and resistance in a conductor at constant temperature. Current is the flow of electric charge, and charge itself can be calculated from current and time.
欧姆定律描述了在恒温下导体两端电压（电势差）、电流与电阻之间的关系。电流是电荷的流动，电荷量可通过电流和时间计算。
voltage = current × resistance
V = I R
charge = current × time
Q = I t
Voltage is measured in volts (V), current in amperes (A), resistance in ohms (Ω), and charge in coulombs (C). For resistors connected in series, the total resistance is the sum of individual resistances.
电压单位是伏特 (V)，电流单位是安培 (A)，电阻单位是欧姆 (Ω)，电荷量单位是库仑 (C)。对于串联的电阻，总电阻等于各电阻之和。
Rtotal = R₁ + R₂ + R₃ + …
10. Waves and Optics | 波与光学
The speed of a wave is determined by its frequency and wavelength. This relationship applies to sound, water waves, and electromagnetic waves. Frequency is the number of complete waves passing a point per second, measured in hertz (Hz).
波速由频率和波长决定。这个关系适用于声波、水波和电磁波。频率是每秒通过某点的完整波的数量，单位是赫兹 (Hz)。
wave speed = frequency × wavelength
v = f λ
For light and sound, reflection obeys the law of reflection: the angle of incidence equals the angle of reflection, both measured from the normal (an imaginary line perpendicular to the surface).
对于光和声波，反射遵守反射定律：入射角等于反射角，都是从法线（垂直于界面的虚线）量起。
i = r
When light passes from one transparent medium to another, it changes speed and bends; this is refraction. Although Snell’s Law is introduced formally later, Year 9 recognises that the ray bends towards the normal when entering a denser medium and away from the normal when entering a less dense medium.
当光从一种透明介质斜射入另一种介质时，速度改变并发生弯折，这就是折射。虽然斯涅尔定律的定量关系会在后续学习，但 Year 9 要认识到光线进入光密介质时向法线靠拢，进入光疏介质时则远离法线。
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