📚 Year 10 CCEA Physics: Formula and Theorem Quick Reference Guide | Year 10 CCEA 物理：公式定理速查手册
This quick reference guide brings together the essential formulas and theorems for the Year 10 CCEA Physics syllabus. Use it for revision, homework and exam preparation to build confidence with the quantitative side of physics.
本速查手册汇集了 Year 10 CCEA 物理课程中最关键的公式和定理。你可以用它进行复习、完成作业和备考，从而更自信地应对物理中的定量计算。
1. Speed, Distance and Time | 速率、距离与时间
Speed is a measure of how far an object travels in a given time. The fundamental equation links distance (s), speed (v) and time (t): v = s / t. Speed is a scalar; the direction is not included. The SI unit is metre per second (m s⁻¹).
速率衡量物体在一定时间内移动的距离。基本公式将距离 (s)、速率 (v) 和时间 (t) 联系在一起：v = s / t。速率是标量，不包含方向。国际单位是米每秒 (m s⁻¹)。
The distance travelled at constant speed is given by rearranging the formula: s = v × t. Time taken can be found from t = s / v.
匀速运动时通过的距离由公式变形得出：s = v × t。所需时间则用 t = s / v 求得。
2. Acceleration | 加速度
Acceleration is the rate of change of velocity. It is a vector quantity, meaning direction matters. The formula for constant acceleration is: a = (v − u) / t, where u is initial velocity, v is final velocity and t is the time taken.
加速度是速度变化的快慢，属于矢量，方向很重要。匀加速度的公式为：a = (v − u) / t，其中 u 为初速度，v 为末速度，t 为所用时间。
Acceleration is measured in metres per second squared (m s⁻²). If the acceleration is negative, the object is decelerating or slowing down.
加速度的单位是米每二次方秒 (m s⁻²)。如果加速度为负值，表示物体正在减速。
A positive acceleration means the velocity is increasing in the positive direction; a negative acceleration can mean slowing down or speeding up in the opposite direction.
正加速度意味着速度向正方向增加；负加速度可能表示减速或向相反方向加速。
3. Newton’s Second Law and Weight | 牛顿第二定律与重量
Newton’s second law states that the resultant force acting on an object is equal to the mass of the object multiplied by its acceleration: F = m a. Force is measured in newtons (N), mass in kilograms (kg) and acceleration in m s⁻².
牛顿第二定律指出，作用在物体上的合力等于物体的质量乘以其加速度：F = m a。力的单位是牛顿 (N)，质量是千克 (kg)，加速度是 m s⁻²。
Weight is the force of gravity on an object. It is calculated using W = m g, where g is the gravitational field strength. On Earth, g ≈ 9.8 N/kg (or 10 N/kg for estimation). Weight is a force and is also measured in newtons.
重量是重力作用在物体上的力。计算公式为 W = m g，其中 g 是重力场强度。在地球表面，g ≈ 9.8 N/kg（估算时常用 10 N/kg）。重量也是一种力，单位同样是牛顿。
4. Hooke’s Law | 胡克定律
Hooke’s law describes the extension of a spring when a force is applied, as long as the elastic limit is not exceeded. The formula is F = k x, where F is the applied force (N), k is the spring constant (N m⁻¹) and x is the extension (m).
胡克定律描述在弹性限度内，弹簧受力后的伸长量。公式为 F = k x，其中 F 是施加的力 (N)，k 是弹簧常数 (N m⁻¹)，x 是伸长量 (m)。
The spring constant k indicates how stiff the spring is; a larger k means a stiffer spring that is harder to stretch or compress.
弹簧常数 k 反映了弹簧的刚度；k 值越大，弹簧越硬，越难以拉伸或压缩。
If a force-extension graph is a straight line through the origin, the material obeys Hooke’s law and the gradient equals the spring constant.
如果力-伸长量图像是一条过原点的直线，说明材料遵守胡克定律，且斜率等于弹簧常数。
5. Moments | 力矩
A moment is the turning effect of a force about a pivot. It is calculated by M = F d, where F is the force (N) and d is the perpendicular distance from the pivot to the line of action of the force (m). The unit is newton metre (N m).
力矩是力绕支点产生的转动效果。计算公式为 M = F d，其中 F 是力 (N)，d 是支点到力的作用线的垂直距离 (m)。单位是牛顿·米 (N m)。
The principle of moments states that for an object in equilibrium, the sum of the clockwise moments about any pivot equals the sum of the anticlockwise moments: Σ clockwise moments = Σ anticlockwise moments.
力矩原理指出，对于一个处于平衡状态的物体，绕任一支点的顺时针力矩之和等于逆时针力矩之和：Σ 顺时针力矩 = Σ 逆时针力矩。
This principle is used to solve problems involving levers, seesaws and other balanced systems.
这一原理常用于解决杠杆、跷跷板和其他平衡系统的问题。
6. Work and Power | 功与功率
Work is done when a force moves an object in the direction of the force. It is given by W = F s (or W = F d), where W is work (J), F is force (N) and s is the distance moved in the direction of the force (m).
当一个力使物体沿力的方向移动时，该力做了功。公式为 W = F s（或 W = F d），其中 W 是功 (J)，F 是力 (N)，s 是沿力方向移动的距离 (m)。
One joule of work is done when a force of 1 newton moves an object 1 metre in the direction of the force.
1 焦耳的功相当于 1 牛顿的力使物体沿力的方向移动 1 米。
Power is the rate of doing work or transferring energy. The formula is P = W / t (or P = E / t), where P is power (W), W is work done (J) and t is time (s). The unit watt (W) is equivalent to J s⁻¹.
功率是做功或能量转化的快慢。公式为 P = W / t（或 P = E / t），其中 P 是功率 (W)，W 是做功 (J)，t 是时间 (s)。单位瓦特 (W) 等同于 J s⁻¹。
7. Kinetic Energy and Gravitational Potential Energy | 动能与重力势能
Kinetic energy (KE) is the energy stored in a moving object. It depends on mass and speed: KE = ½ m v². Mass m is in kg, speed v in m s⁻¹, and energy in joules (J).
动能 (KE) 是运动物体所具有的能量，取决于质量和速率：KE = ½ m v²。质量 m 单位为 kg，速率 v 单位为 m s⁻¹，能量单位为焦耳 (J)。
Gravitational potential energy (GPE) is the energy stored in an object due to its height above the ground. It is calculated by GPE = m g h, where h is the vertical height (m) and g is the gravitational field strength (N/kg).
重力势能 (GPE) 是物体由于距离地面有一定高度而储存的能量。计算公式为 GPE = m g h，其中 h 是垂直高度 (m)，g 是重力场强度 (N/kg)。
The change in GPE depends only on the change in height, not the path taken.
重力势能的变化只取决于高度的改变，与路径无关。
8. Conservation of Energy | 能量守恒
The principle of conservation of energy states that energy cannot be created or destroyed; it can only be transferred, stored or dissipated. In any process, total energy before = total energy after.
能量守恒定律指出，能量既不能被创造也不能被消灭，只能被转移、储存或耗散。在任何过程中，初始总能量等于最终总能量。
For a falling object with no air resistance, the loss in GPE equals the gain in KE: m g h = ½ m v². This allows the final speed v to be found as v = √(2 g h).
对于无空气阻力下落的物体，减少的重力势能等于增加的动能：m g h = ½ m v²。由此可求出末速度 v = √(2 g h)。
In real situations, some energy is dissipated as thermal energy due to friction or air resistance, so the useful energy output is always less than the total input.
在实际情况中，由于摩擦或空气阻力，部分能量会以热能的形式耗散，因此有用能量输出总是小于总输入。
9. Density | 密度
Density is mass per unit volume. It is a property of a material and can be used to identify substances. The formula is ρ = m / V, where ρ is density (kg m⁻³ or g cm⁻³), m is mass (kg or g) and V is volume (m³ or cm³).
密度是单位体积的质量，是材料的一种属性，可用于鉴别物质。公式为 ρ = m / V，其中 ρ 是密度 (kg m⁻³ 或 g cm⁻³)，m 是质量 (kg 或 g)，V 是体积 (m³ 或 cm³)。
To find the density of an irregular solid, measure its mass with a balance and its volume by displacement of water using a measuring cylinder. Density is then calculated from the formula.
测量不规则固体的密度时，先用天平测质量，再用量筒通过排水法测体积，最后用公式计算密度。
Objects with density less than the fluid they are placed in will float; those with greater density will sink.
密度小于所在流体的物体会上浮；密度大于流体的物体则会下沉。
10. Specific Heat Capacity | 比热容
Specific heat capacity (c) is the amount of energy needed to raise the temperature of 1 kg of a substance by 1 °C. The energy transferred is given by Q = m c Δθ, where Q is heat energy (J), m is mass (kg), c is specific heat capacity (J kg⁻¹ °C⁻¹) and Δθ is the temperature change (°C).
比热容 (c) 是使 1 kg 物质温度升高 1 °C 所需的能量。能量转移公式为 Q = m c Δθ，其中 Q 为热能 (J)，m 为质量 (kg)，c 为比热容 (J kg⁻¹ °C⁻¹)，Δθ 为温度变化 (°C)。
Water has a high specific heat capacity (about 4200 J kg⁻¹ °C⁻¹), meaning it can store a lot of thermal energy with a small temperature rise. This is why it is used in central heating and cooling systems.
水的比热容很高（约 4200 J kg⁻¹ °C⁻¹），意味着它可以在温度升高不多的情况下储存大量热能，因此常用于中央供暖和冷却系统。
11. Ohm’s Law and Electrical Resistance | 欧姆定律与电阻
Ohm’s law states that, at constant temperature, the current through a conductor is directly proportional to the potential difference (voltage) across it. The relationship is written as V = I R, where V is voltage (V), I is current (A) and R is resistance (Ω).
欧姆定律指出，在温度不变时，通过导体的电流与导体两端的电势差（电压）成正比。关系式为 V = I R，其中 V 是电压 (V)，I 是电流 (A)，R 是电阻 (Ω)。
Resistance is measured in ohms (Ω). A component that obeys Ohm’s law has a constant resistance and its I–V graph is a straight line through the origin.
电阻的单位是欧姆 (Ω)。遵守欧姆定律的元件具有恒定的电阻，其 I–V 图像是一条过原点的直线。
Factors affecting resistance include the material, length, cross-sectional area and temperature of the conductor.
影响电阻的因素包括导体的材料、长度、横截面积和温度。
12. Wave Speed, Frequency and Wavelength | 波速、频率与波长
All waves obey the wave equation: v = f λ, where v is wave speed (m s⁻¹), f is frequency (Hz) and λ (lambda) is wavelength (m).
所有波都遵守波动方程：v = f λ，其中 v 是波速 (m s⁻¹)，f 是频率 (Hz)，λ（拉姆达）是波长 (m)。
Frequency is the number of complete waves passing a point per second; it is related to the period T by f = 1 / T. The period is the time for one complete wave.
频率是每秒通过某点的完整波的数量；它与周期 T 的关系为 f = 1 / T。周期是一个完整波所需的时间。
When a wave moves from one medium to another, its speed and wavelength may change, but its frequency stays the same.
当波从一种介质进入另一种介质时，波速和波长可能改变，但频率保持不变。
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