📚 Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This handbook gathers the essential equations and principles encountered in Year 9 SQA Physics. Each formula is stated clearly, accompanied by a definition of terms, units, and a short explanation of when to use it. Work through the sections one by one to build confidence in solving numerical problems and linking theoretical concepts. The dual-language format ensures you grasp both the English scientific vocabulary and the precise Chinese meaning.
本手册汇集了 Year 9 SQA 物理课程中遇到的核心方程和原理。每一条公式都清楚列出，附有术语定义、单位以及适用场景的简要说明。请逐节学习，逐步建立解答数值题的信心，并将理论概念串联起来。中英对照的格式，确保你既能掌握英文科学词汇，也能理解准确的中文含义。
1. Speed & Velocity | 速率与速度
Formula:
v = s / t
where v is speed (or magnitude of velocity) in metres per second (m/s), s is distance travelled in metres (m), and t is the time taken in seconds (s). This relationship applies to uniform motion where the speed is constant. In SQA questions, you will often be asked to calculate speed, distance, or time when the other two quantities are given. Remember that velocity is a vector; the same formula gives its magnitude when the direction is constant.
其中 v 是速率（或速度的大小），单位是米每秒（m/s），s 是经过的距离，单位是米（m），t 是所用的时间，单位是秒（s）。该关系适用于匀速运动的情形。在 SQA 考题中，通常会在已知其中两个量的情况下，要求你计算速率、距离或时间。要记住速度是矢量；当方向不变时，该公式同样给出速度的大小。
2. Acceleration | 加速度
Formula:
a = (v - u) / t
where a stands for acceleration in metres per second squared (m/s²), v is the final velocity (m/s), u is the initial velocity (m/s), and t is the time taken for the change in velocity (s). Acceleration describes how quickly the velocity changes. A positive value means the object is speeding up in the direction of motion; a negative value (deceleration) means it is slowing down. Use this formula when motion is uniformly accelerated, e.g. a car accelerating from rest.
其中 a 表示加速度，单位是米每二次方秒（m/s²），v 是末速度（m/s），u 是初速度（m/s），t 是速度变化所用的时间（s）。加速度描述速度变化的快慢。正值表示物体沿运动方向加速；负值（减速）表示物体在减速。当运动是匀加速时使用该公式，例如汽车从静止开始加速的情景。
3. Newton’s Second Law | 牛顿第二定律
Formula:
F = m a
Here F is the unbalanced (resultant) force acting on an object, measured in newtons (N); m is the mass of the object in kilograms (kg); and a is the acceleration produced in metres per second squared (m/s²). This law links force, mass and acceleration directly. If you know any two, you can find the third. It also tells us that for a given force, a larger mass results in a smaller acceleration. Always ensure mass is in kg, not grams.
其中 F 是作用在物体上的非平衡（合力）力，单位是牛顿（N）；m 是物体的质量，以千克（kg）为单位；a 是产生的加速度，单位是米每二次方秒（m/s²）。这一定律直接将力、质量和加速度联系起来。知道任意两个量，就可以求出第三个。它也告诉我们，在给定的力下，质量越大，加速度越小。务必保证质量的单位是千克，而不是克。
4. Weight & Gravitational Field Strength | 重量与重力场强度
Formula:
W = m g
), and g is the gravitational field strength. On Earth’s surface, g ≈ 9.8 N/kg, though SQA often uses 10 N/kg for simplicity. Weight should not be confused with mass – mass stays the same everywhere, but weight changes if g changes (e.g. on the Moon).
重量（W）是地球（或其他大质量天体）对物体施加的重力，单位是牛顿（N）。m 是物体的质量（kg），g 是重力场强度。在地球表面，g ≈ 9.8 N/kg，不过 SQA 考题中为简化常常取值 10 N/kg。重量不能与质量混淆——质量在任何地方都相同，但如果 g 改变（例如在月球上），重量就会改变。
5. Work Done | 做功
Formula:
W = F d
In physics, work is done when a force makes an object move. W represents work done in joules (J), F is the constant force applied in the direction of motion in newtons (N), and d is the distance moved by the object in metres (m). If the force is not parallel to the displacement, only the component of force in the direction of motion does work. On SQA papers, this formula often appears in questions about lifting objects or pushing them across a surface.
在物理学中，当力使物体移动时就做了功。W 代表做功，单位是焦耳（J）；F 是沿运动方向施加的恒力，单位是牛顿（N）；d 是物体移动的距离，单位是米（m）。如果力与位移不平行，则只有力在运动方向上的分量做功。在 SQA 试题中，这一公式常常出现在提举物体或推物体移动的题目中。
6. Kinetic Energy | 动能
Formula:
Ek = ½ m v²
Kinetic energy (Ek) is the energy an object possesses due to its motion, measured in joules (J). m is the mass (kg) and v is the speed (m/s). Notice the square dependence on speed: doubling the speed quadruples the kinetic energy. This relationship is vital when analysing car braking distances or energy conversions in roller coasters. Always check that v is in m/s, not km/h.
动能（Ek）是物体由于运动而具有的能量，单位是焦耳（J）。m 是质量（kg），v 是速率（m/s）。注意动能与速度的平方成正比关系：速率加倍，动能变为原来的四倍。在分析汽车刹车距离或过山车的能量转换时，这一关系至关重要。请务必检查速率单位是 m/s，而不是 km/h。
7. Gravitational Potential Energy | 重力势能
Formula:
Ep = m g h
Gravitational potential energy (Ep) is the energy stored in an object because of its height above the ground. It is measured in joules (J). m is mass (kg), g is gravitational field strength (N/kg), and h is the vertical height (m). This formula assumes g is constant. When an object falls, its Ep decreases while its kinetic energy increases, illustrating the principle of conservation of energy.
重力势能（Ep）是物体因位于地面以上高度而储存的能量，单位是焦耳（J）。m 是质量（kg），g 是重力场强度（N/kg），h 是垂直高度（m）。该公式假定 g 为常数。物体下落时，Ep 减小而动能增加，这体现了能量守恒定律。
8. Power | 功率
Formula:
P = W / t
s the work done or energy transferred (J), and t is the time taken (s). A more powerful engine does the same work in less time, or more work in the same time. In practical contexts, this formula links to electrical power as well, but here it is the mechanical definition.
功率（P）是做功（或能量转移）的速率。它的单位是瓦特（W），1 W = 1 J/s。W 是所做的功或转移的能量（J），t 是所用时间（s）。功率更大的发动机能在更短的时间内完成同样的功，或在相同的时间内做更多的功。在实际应用中，这一公式也联系到电功率，但此处是力学中的定义。
9. Ohm’s Law | 欧姆定律
Formula:
V = I R
A core equation in electricity: voltage (V) in volts (V) equals current (I) in amperes (A) multiplied by resistance (R) in ohms (Ω). This law applies to ohmic conductors at constant temperature. If you plot a graph of V against I for a fixed resistor, you get a straight line through the origin, where the gradient is the resistance. Use this relationship to find any one of the three quantities when the other two are known.
电学中的核心等式：电压（V）以伏特（V）为单位，等于电流（I）以安培（A）为单位乘以电阻（R）以欧姆（Ω）为单位。这一定律适用于温度恒定的欧姆导体。若画出定值电阻的 V–I 图像，会得到一条过原点的直线，其斜率为电阻值。利用该关系可以已知两个量求出第三个量。
10. Factors Affecting Resistance | 影响电阻的因素
Formula:
R = ρl / A
wire → greater resistance) and on its cross-sectional area A (thicker wire → lower resistance), as well as on the material type (resistivity ρ). You do not necessarily have to calculate with ρ, but you must be able to describe and predict how changing l or A affects R. For a given material, R ∝ l and R ∝ 1/A.
尽管完整的公式可能稍后才引入，但在 Year 9 SQA 中你应该理解导线的电阻 R 取决于其长度 l（导线越长 → 电阻越大）和横截面积 A（导线越粗 → 电阻越小），还取决于材料种类（电阻率 ρ）。你不一定需要用 ρ 进行计算，但必须能够描述和预测改变 l 或 A 会如何影响 R。对于给定的材料，R ∝ l 且 R ∝ 1/A。
11. Electrical Power | 电功率
Formula:
P = I V
This is equivalent to the rate at which electrical energy is converted into other forms (heat, light, motion). Combined with Ohm’s law, you can also derive P = I²R and P = V²/R. Make sure to use the correct units and check whether the component is in series or parallel when using these derived forms.
在电路中，功率（P）以瓦特（W）为单位，可以通过电流（I，单位 A）乘以元件两端的电压（V）来计算。这相当于电能转换为其他形式（热、光、运动）的速率。结合欧姆定律，还可以推导出 P = I²R 和 P = V²/R。使用这些导出形式时，务必使用正确单位，并注意元件是串联还是并联。
12. Wave Speed Equation | 波速公式
Formula:
v = f λ
All waves (sound, light, water waves) obey this relationship: wave speed v (m/s) equals frequency f in hertz (Hz) multiplied by wavelength λ in metres (m). Frequency is the number of complete waves passing a point per second, while wavelength is the distance between two consecutive crests or compressions. This formula is key when studying reflection, refraction, and the electromagnetic spectrum.
所有波（声波、光波、水波）都遵从这一关系：波速 v（m/s）等于频率 f（单位 赫兹 Hz）乘以波长 λ（单位 米 m）。频率是每秒通过某点的完整波数，波长则是相邻两个波峰或疏部之间的距离。在研究反射、折射和电磁波谱时，这一公式至关重要。
13. Density | 密度
Formula:
ρ = m / V
ume (m³). You may also see units of g/cm³; remember that 1 g/cm³ = 1000 kg/m³. Understanding density helps explain why some objects float while others sink, and it appears in problems about materials, mixtures, and buoyancy.
密度（ρ，希腊字母 rho）是物质单位体积的质量，通常以千克每立方米（kg/m³）为单位。m 为质量（kg），V 为体积（m³）。你也可能见到单位 g/cm³；请记住 1 g/cm³ = 1000 kg/m³。理解密度有助于解释为何有些物体会浮、有些会沉，它也出现在关于材料、混合物和浮力的问题中。
14. Pressure | 压强
Formula:
P = F / A
rce in newtons (N), and A is the area over which the force is spread in square metres (m²). A sharp knife exerts a high pressure because the force is concentrated on a small area, while snowshoes reduce pressure by increasing the area. Use this formula carefully, ensuring area is in m².
压强（P）定义为单位面积上受到的垂直作用力。其国际单位是帕斯卡（Pa），1 Pa = 1 N/m²。F 为垂直作用力（牛顿 N），A 为力作用的面积（平方米 m²）。锋利的刀因为力集中在很小的面积上而产生高压强，而雪鞋则通过增大面积来减小压强。使用该公式时请小心，确保面积单位是 m²。
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