📚 Year 11 WJEC Physics: Formulas & Theorems Quick Reference Handbook | WJEC 11年级物理公式定理速查手册
This quick reference handbook covers the essential formulas, theorems and relationships you need to master for Year 11 WJEC Physics. From mechanics to electricity, waves to radioactivity, these key equations appear in exams and classroom assessments. Keeping them at your fingertips will help you solve problems efficiently and deepen your understanding of physical principles.
本速查手册涵盖了 WJEC 11年级物理需要掌握的核心公式、定理和关系式。从力学到电学，从波到放射性，这些关键方程频繁出现在考试和课堂评估中。熟记这些公式有助于你高效解题，加深对物理原理的理解。
1. Motion and Speed | 运动与速度
The average speed (or velocity for straight‑line motion) of an object is the total distance travelled divided by the time taken. On a distance–time graph, the gradient of the line represents the speed of the object.
v = s / t
物体的平均速度（或直线运动速度）等于通过的总路程除以所用时间。在距离‑时间图中，图线的斜率表示物体的速度。
When an object moves at a constant speed, the distance–time graph is a straight line. A steeper gradient indicates a higher speed, while a horizontal line means the object is stationary. The instantaneous speed is the speed at a particular moment, which can be found from the gradient of a tangent to a curved distance–time graph.
当物体匀速运动时，距离‑时间图为一条直线。斜率越大表示速度越快，水平线则表示物体静止。瞬时速度是物体在某一时刻的速度，可通过曲线距离‑时间图的切线斜率求得。
2. Acceleration and Equations of Motion | 加速度与运动方程
Acceleration is the rate at which velocity changes. It is a vector quantity and can be calculated using the change in velocity over the time taken.
a = (v − u) / t
加速度是速度变化的速率，是矢量。可用速度变化量除以所用时间计算。
For objects moving with uniform (constant) acceleration, the final velocity v can be related to the initial velocity u, acceleration a and time t.
v = u + a t
对于匀加速运动的物体，末速度 v 与初速度 u、加速度 a 和时间 t 有如下关系。
The displacement s travelled in a straight line under uniform acceleration can be found using the average velocity multiplied by time. This leads to another useful equation.
s = ½ (u + v) t
匀加速直线运动的位移 s 可由平均速度乘以时间求得，由此得到另一个常用方程。
Two further equations of motion are provided on the WJEC equation sheet and may be used when suitable:
s = u t + ½ a t²
v² = u² + 2 a s
WJEC公式表中还提供另外两个运动方程，在条件合适时可以使用：
3. Forces and Newton’s Laws | 力与牛顿定律
Newton’s second law of motion states that the resultant force acting on an object is equal to the mass of the object multiplied by its acceleration. This can be written as an equation.
F = m a
牛顿第二运动定律指出，作用在物体上的合力等于物体的质量乘以其加速度。可写成公式。
The weight of an object is the gravitational force exerted on it by the Earth. It is directly proportional to the object’s mass and the gravitational field strength g.
W = m g
物体的重量是地球对它的引力，与物体的质量及引力场强度 g 成正比。
For a spring that obeys Hooke’s law, the extension is directly proportional to the applied force, provided the elastic limit is not exceeded. The constant k is the spring constant (stiffness).
F = k x
对于遵循胡克定律的弹簧，在不超过弹性限度时，伸长量与外加载力成正比。常数 k 为弹簧劲度系数。
4. Work, Energy and Power | 功、能与功率
Work is done when a force moves an object in the direction of the force. The work done is calculated by multiplying the force by the distance moved in the direction of the force.
W = F d
当力使物体沿力的方向移动时就做了功。功等于力乘以物体沿力方向移动的距离。
Power is the rate at which work is done or the rate at which energy is transferred. It is measured in watts (W).
P = W / t = E / t
功率是做功的速率或能量转换的速率，单位为瓦特 (W)。
Efficiency compares the useful output of a system to the total input. It can be expressed as a ratio or a percentage.
Efficiency = (useful power output) / (total power input)
效率是系统有用输出与总输入的比较，可用比值或百分比表示。
5. Kinetic and Gravitational Potential Energy | 动能与重力势能
The kinetic energy (KE) of a moving object depends on its mass and its speed. The faster it moves or the more massive it is, the greater its kinetic energy.
KE = ½ m v²
运动物体的动能取决于其质量和速度。速度越快或质量越大，动能越大。
Gravitational potential energy (GPE) is the energy an object possesses because of its position in a gravitational field. It depends on mass, gravitational field strength g, and height above a reference level.
GPE = m g h
重力势能是物体因在引力场中的位置而具有的能量。它取决于质量、引力场强度 g 和相对于参考平面的高度。
In a closed system, the total mechanical energy (KE + GPE) remains constant if no external work is done (principle of conservation of energy). This allows you to relate speed and height, for example in pendulum or roller‑coaster problems.
在封闭系统中，若无外力做功，总机械能（动能+重力势能）守恒（能量守恒原理）。借此可将速度和高度联系起来，如单摆或过山车问题。
6. Density and Pressure | 密度与压强
Density is the mass per unit volume of a substance. It is a characteristic property of materials and is measured in kg/m³.
ρ = m / V
密度是物质单位体积的质量，是材料的特征属性，单位为 kg/m³。
Pressure is defined as the normal force acting per unit area. A smaller area under the same force produces a higher pressure.
p = F / A
压强定义为单位面积上所受的法向力。相同力作用下，面积越小压强越大。
For a liquid column, the pressure at a certain depth depends on the density of the liquid, g and the height of the column. This is useful for understanding hydraulic systems and underwater pressure.
p = h ρ g
对于液柱，某一深处的压强取决于液体密度、g 和液柱高度。此式有助于理解液压系统和水下压强。
7. Electrical Quantities and Ohm’s Law | 电学量与欧姆定律
Electric current is the rate of flow of charge. The total charge transferred can be found from the current and the time for which it flows.
Q = I t
电流是电荷流动的速率。转移的总电荷量可由电流和通电时间求得。
Potential difference (voltage) is the energy transferred per unit charge between two points in a circuit. It is measured in volts (V).
V = W / Q
电势差（电压）是电路中两点间每单位电荷转移的能量，单位为伏特 (V)。
Ohm’s law states that, for a conductor at constant temperature, the current through it is directly proportional to the potential difference across it. The resistance R remains constant.
V = I R
欧姆定律指出，对于温度恒定的导体，通过其的电流与两端电势差成正比，电阻 R 保持不变。
Power in an electrical component is the product of the current and the potential difference. It can also be expressed in alternative forms using Ohm’s law.
P = I V
P = I² R
用电器的功率等于电流与电势差的乘积，也可以利用欧姆定律转换成其他形式。
Energy transferred by electricity is the product of power and time. This is important for calculating the cost of using appliances.
E = P t
电能等于功率乘以时间，这在计算电器耗电费用时很重要。
8. Series and Parallel Circuit Rules | 串并联电路规则
In a series circuit, the current is the same at all points. The total potential difference is shared across the components, and the total resistance is the sum of individual resistances.
I = I₁ = I₂ = ...
Vₜ = V₁ + V₂ + ...
Rₜ = R₁ + R₂ + ...
在串联电路中，各处电流相同；总电压在元件间分配；总电阻等于各电阻之和。
In a parallel circuit, the total current is the sum of the currents in the separate branches. Each branch receives the same potential difference, and the total resistance is found using the reciprocal formula.
Iₜ = I₁ + I₂ + ...
Vₜ = V₁ = V₂ = ...
1/Rₜ = 1/R₁ + 1/R₂ + ...
在并联电路中，总电流等于各支路电流之和；各支路两端电压相同；总电阻用倒数公式计算。
Combining these rules allows you to analyse more complex circuits and predict readings on ammeters and voltmeters.
综合这些规则可分析更复杂的电路，并预测电流表和电压表的读数。
9. Waves: Speed, Frequency and Wavelength | 波：波速、频率与波长
The speed of a wave is related to its frequency and wavelength. This wave equation applies to all types of waves, including sound, light and water waves.
v = f λ
波速与频率和波长有关。该波动
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