📚 Year 10 SQA Physics: Quick Reference Formula & Theorem Handbook | Year 10 SQA 物理：公式定理速查手册
This handbook brings together every essential formula, law and relationship you need to know for the SQA National 5 Physics course. It is designed for Year 10 learners following the Scottish curriculum board, covering Dynamics, Electricity, Waves, Radiation, Gas Laws and Energy. Each entry is presented with a clear English explanation immediately followed by its equivalent in Chinese, helping you master the concepts in both languages and feel confident in revision and exams.
本手册汇集了 SQA 国家五等物理课程中你必须掌握的每一个基本公式、定律和关系式。专为遵循苏格兰课程局的 Year 10 学生设计，覆盖动力学、电学、波、辐射、气体定律与能量。每个条目都以清晰的英文解释紧接中文对应段落，帮助你用两种语言掌握概念，并在复习和考试中充满信心。
1. Average Speed and Instantaneous Speed | 平均速度与瞬时速度
Average speed is the total distance travelled divided by the total time taken. It is a scalar quantity and does not involve direction. The formula is vavg = d / t, where d is distance in metres (m) and t is time in seconds (s).
平均速度是总路程除以总时间。它是一个标量，不涉及方向。公式为 vavg = d / t，其中 d 是距离（米），t 是时间（秒）。
Instantaneous speed is the speed of an object at a particular moment. On a distance–time graph, it is the gradient of the tangent at that point. The SQA requires you to understand the difference between average and instantaneous speed.
瞬时速度是物体在某一特定时刻的速度。在距离–时间图上，它是该点切线的斜率。SQA 要求你理解平均速度与瞬时速度之间的区别。
2. Acceleration and Motion Graphs | 加速度与运动图像
t, where v is final velocity, u is initial velocity and t is time. If the object slows down, acceleration is negative (deceleration).
加速度是每单位时间内速度的变化。它是一个矢量，单位为米每二次方秒（m/s²）。公式为 a = (v - u) / t，其中 v 是末速度，u 是初速度，t 是时间。如果物体减速，加速度为负（减速度）。
Velocity–time graphs give crucial information: gradient equals acceleration, the area under the line equals displacement. A straight sloping line represents constant acceleration, a horizontal line means constant velocity.
速度–时间图提供关键信息：斜率等于加速度，线下面积等于位移。倾斜直线表示匀加速度，水平线表示匀速。
3. Newton’s Laws of Motion | 牛顿运动定律
Newton’s First Law states that an object will remain at rest or move at constant velocity unless acted upon by an unbalanced force. This introduces the concept of inertia.
牛顿第一定律指出，除非受到非平衡力的作用，否则物体将保持静止或匀速直线运动。这引入了惯性的概念。
m a. Force is in newtons (N), mass in kilograms (kg), acceleration in m/s². This is the core equation for dynamics problems.
牛顿第二定律将非平衡力、质量和加速度联系起来：F = m a。力的单位是牛顿（N），质量单位是千克（kg），加速度单位是 m/s²。这是解决动力学问题的核心方程。
Newton’s Third Law states that for every action force there is an equal and opposite reaction force. These forces act on different objects and are of the same type.
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。这两个力作用在不同物体上，且属于同类型力。
4. Work Done, Potential Energy and Kinetic Energy | 功、势能与动能
W = F d, provided the force is in the direction of movement. It is measured in joules (J).
当力使物体移动一段距离时，力做功。功 = 力 × 距离，即 W = F d，前提是力与运动方向一致。单位是焦耳（J）。
Gravitational potential energy (GPE) is the energy stored due to an object’s height. It is given by Ep g is gravitational field strength (10 N/kg on Earth) and h is height. Kinetic energy is Ek = ½ m v², linking mass and speed.
重力势能（GPE）是因物体高度而储存的能量，由 Ep = m g h 给出，其中 m 是质量，g 是重力场强度（地球表面 10 N/kg），h 是高度。动能是 Ek = ½ m v²，将质量与速度联系起来。
5. Conservation of Energy and Power | 能量守恒与功率
Energy cannot be created or destroyed, only transformed from one form to another. In a closed system, total energy remains constant. This principle is used to solve problems involving energy transfers, such as a falling object converting GPE to kinetic energy.
能量不能被创造或消灭，只能从一种形式转化为另一种形式。在封闭系统中，总能量保持不变。这一原理用于解决能量转化问题，例如下落的物体将重力势能转化为动能。
is the watt (W). You may also see P = W / t. Electrical power will be treated separately.
功率是做功或转移能量的速率。P = E / t，其中 E 是能量（焦耳），t 是时间（秒）。功率的单位是瓦特（W）。也可以写作 P = W / t。电功率将单独处理。
6. Momentum and Impulse | 动量与冲量
, where p is momentum in kg m/s. An object at rest has zero momentum. The law of conservation of momentum states that in the absence of external forces, total momentum before a collision equals total momentum after.
动量是质量与速度的乘积。它是一个矢量：p = m v，其中 p 是动量，单位为 kg m/s。静止的物体动量为零。动量守恒定律指出，在没有外力作用时，碰撞前的总动量等于碰撞后的总动量。
it acts: F t = m v - m u. This is used to analyse car safety features and sports impacts.
冲量是动量的变化量。它等于平均力乘以作用时间：F t = m v - m u。这可用于分析汽车安全特性和运动中的撞击。
7. Gas Laws and the Kinetic Model | 气体定律与动力学模型
The behaviour of a fixed mass of gas can be described by three key relationships. (1) Boyle’s Law: at constant temperature, pressure is inversely proportional to volume, p ∝ 1/V, so p1V1 = p2V2. (2) Charles’ Law: at constant pressure, volume is directly proportional to absolute temperature (in kelvin), V ∝ T. (3) Pressure Law: at constant volume, pressure is directly proportional to absolute temperature.
一定质量气体的行为可以用三个关键关系描述。（1）玻意耳定律：温度不变时，压强与体积成反比，p ∝ 1/V，故 p₁V₁ = p₂V₂。（2）查理定律：压强不变时，体积与绝对温度（开尔文）成正比，V ∝ T。（3）压强定律：体积不变时，压强与绝对温度成正比。
plains these laws by describing gas particles in constant random motion; increasing temperature raises the average kinetic energy of the particles, leading to higher pressure or volume change.
必须使用绝对温度：T (K) = θ (°C) + 273。动力学模型通过描述气体粒子的无规则运动来解释这些定律：温度升高使粒子平均动能增加，导致压强升高或体积变化。
8. Ohm’s Law and Resistance | 欧姆定律与电阻
ce across it. The equation is V = I R, where V is voltage in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω).
欧姆定律指出，对于恒定温度下的金属导体，通过它的电流与它两端的电势差成正比。方程为 V = I R，其中 V 是电压（伏特），I 是电流（安培），R 是电阻（欧姆）。
Resistance is the opposition to current flow. In series circuits, total resistance is the sum of individual resistances: Rtotal n parallel circuits, the reciprocal of total resistance equals the sum of reciprocals: 1/Rtotal ₁ + 1/R₂ + ... . You must be able to calculate combined resistance for parallel resistors.
电阻是对电流的阻碍。串联电路总电阻等于各个电阻之和：R总 = R₁ + R₂ + ... 。并联电路中，总电阻的倒数等于各电阻倒数之和：1/R总 = 1/R₁ + 1/R₂ + ... 。你必须能够计算并联电阻的等效电阻。
9. Electrical Power and Energy Transfer | 电功率与能量转移
/ R. The SQA expects you to select the appropriate formula based on the given quantities.
电功率是电路中每秒转移的能量。可用 P = I V 计算，或结合欧姆定律得到 P = I² R 和 P = V² / R。SQA 希望你能根据已知量选择合适的公式。
= (V²/R) t. This energy often heats components and is linked to the concept of efficiency.
转移的能量由 E = P t 给出，其中 t 是时间（秒）。因此，E = I V t、E = I² R t 或 E = (V²/R) t。此能量通常使元件发热，并与效率概念相关。
10. Wave Speed, Frequency and Wavelength | 波速、频率与波长
λ, where v is wave speed (m/s), f is frequency (Hz) and λ (lambda) is wavelength (m). This applies to sound, light, water waves and all types of electromagnetic radiation.
所有波都遵循波动方程：v = f λ，其中 v 是波速（m/s），f 是频率（Hz），λ（拉姆达）是波长（m）。这适用于声波、光波、水波以及所有类型的电磁辐射。
aximum displacement from the rest position. Diffraction and refraction can be explained using the wave equation and changes in speed.
频率是每秒通过某点的完整波数。周期 T 是完成一个完整波所需的时间：T = 1/f。波的振幅是偏离平衡位置的最大位移。衍射和折射可以通过波动方程和速度变化来解释。
11. Specific Heat Capacity | 比热容
lta;θ is the temperature change in degrees Celsius or kelvin, m is mass in kg, and c has units J/kg °C. Water has a particularly high specific heat capacity (4180 J/kg °C).
物质受热时，其温度变化取决于其比热容 c。能量方程为 E = c m Δθ，其中 Δθ 是温度变化（摄氏度或开尔文），m 是质量（kg），c 的单位是 J/kg °C。水具有特别高的比热容（4180 J/kg °C）。
onservation of energy lets you equate electrical energy (E = P t) to the heat gained: P t = c m Δθ.
该公式常在能量转移情境中考查，例如电浸没式加热器升高水或金属块的温度。利用能量守恒，可将电能（E = P t）与获得的热量等同起来：P t = c m Δθ。
12. Radioactive Decay and Half-Life | 放射性衰变与半衰期
Radioactive decay is a random process in which an unstable nucleus emits radiation. Activity (measured in becquerels, Bq) is the number of decays per second. The half-life is the time taken for the activity (or the number of radioactive nuclei) to fall to half its original value.
放射性衰变是一个随机过程，不稳定的原子核放出辐射。活度（以贝克勒尔 Bq 测量）是每秒衰变数。半衰期是活度（或放射性核的数量）降低到其原始值一半所需的时间。
There is no single formula for half-life in N5, but you must interpret decay curves and use the halving concept. After n half-lives, the fraction remaining is (1/2)n. For example, after 3 half-lives, 1/8 of the original nuclei remain. Dose equivalent is measured in sieverts (Sv) and takes account of radiation type and biological effect.
国家五等中半衰期没有单一公式，但你必须会解读衰变曲线并使用减半概念。经过 n 个半衰期后，剩余分数为 (1/2)n。例如，3 个半衰期后，剩下原始核数量的 1/8。剂量当量以希沃特（Sv）测量，考虑了辐射类型和生物效应。
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