📚 Year 7 SQA Engineering: Quick Reference Handbook of Formulas and Theorems | Year 7 SQA 工程：公式定理速查手册
Engineering at Year 7 introduces you to the fundamental principles that shape the world around us. This quick reference handbook brings together all the essential formulas, theorems and relationships you will need in SQA Engineering. Keep it close when solving problems, designing mechanisms or revising for assessments. Each formula is stated clearly with its symbols explained, so you can apply it with confidence.
Year 7 工程课将带你认识塑造世界的基本原理。这份速查手册汇集了 SQA 工程课程中所有重要的公式、定理和关系式。在解题、设计机构或准备考试时，你可以随时查阅。每个公式都配有清晰的符号说明，帮助你自信地运用它们。
1. Speed, Distance and Time | 速度、距离与时间
Speed describes how quickly an object moves. The average speed of an object can be found by dividing the total distance travelled by the time taken. Always state speed in metres per second (m/s) when distance is in metres (m) and time is in seconds (s).
速度描述物体运动的快慢。平均速度可以用总距离除以所用时间得到。当距离单位为米（m）、时间单位为秒（s）时，速度的单位是米/秒（m/s）。
v = d / t
The variable v represents speed, d stands for distance travelled and t is the time interval. You can rearrange the formula to find distance (d = v × t) or time (t = d / v).
符号 v 表示速度，d 代表移动的距离，t 为时间。公式可以变形为求距离（d = v × t）或求时间（t = d / v）。
2. Acceleration and Forces | 加速度与力
Acceleration is the rate at which an object’s velocity changes. If an object speeds up from an initial velocity u to a final velocity v over a time t, its acceleration a is given by the change in velocity divided by time.
加速度是物体速度变化的快慢。如果一个物体在时间 t 内从初速度 u 加速到末速度 v，加速度 a 等于速度变化量除以时间。
a = (v – u) / t
A resultant force causes an object to accelerate. Newton’s Second Law relates force, mass and acceleration with one of the most important equations in engineering: F = m a. Force is measured in newtons (N), mass in kilograms (kg) and acceleration in metres per second squared (m/s²).
合外力使物体产生加速度。牛顿第二定律将力、质量和加速度联系起来，是工程中最核心的公式之一：F = m a。力的单位是牛顿（N），质量用千克（kg），加速度用米每二次方秒（m/s²）。
3. Newton’s Laws of Motion | 牛顿运动定律
First Law (Inertia): An object remains at rest or in uniform motion in a straight line unless acted upon by an external force. This explains why a moving vehicle continues to coast when the engine is switched off, and why passengers are pushed forward during sudden braking.
第一定律（惯性定律）： 任何物体都保持静止或匀速直线运动状态，直到外力迫使它改变。这解释了为什么关掉发动机后车辆仍会滑行，以及急刹车时乘客会向前冲。
Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = m a).
第二定律： 物体的加速度与所受合外力成正比，与质量成反比（F = m a）。
Third Law: For every action, there is an equal and opposite reaction. When a rocket engine pushes exhaust gases downward, the gases push the rocket upward with the same size of force.
第三定律： 作用力与反作用力大小相等、方向相反。火箭发动机向下喷出燃气，燃气就给火箭一个同样大小的向上推力。
4. Moments and Levers | 力矩与杠杆
A moment is the turning effect of a force. It depends on both the size of the force and the perpendicular distance from the pivot to the line of action of the force. Moments are measured in newton metres (N m).
力矩是力产生的转动效应，与力的大小以及支点到力作用线的垂直距离有关。力矩的单位是牛顿米（N·m）。
M = F × d
In levers, a small effort can move a large load if the effort is far from the pivot. The principle of moments states that a lever is balanced when the clockwise moments equal the anticlockwise moments. Classes of lever (first, second and third) are identified by the relative positions of effort, load and fulcrum.
在杠杆中，如果施力点离支点很远，用较小的力就能移动较大的负载。力矩原理指出，当顺时针力矩等于逆时针力矩时杠杆平衡。根据施力点、负载和支点的位置不同，杠杆分为一类、二类和三类。
5. Work, Energy and Power | 功、能与功率
Work is done when a force moves an object in the direction of the force. It is calculated as the product of the force and the distance moved in the direction of the force. The unit of work is the joule (J).
当力使物体沿力的方向移动时即做了功。功等于力与沿力方向上移动距离的乘积，单位是焦耳（J）。
W = F × d
Energy exists in many forms. Gravitational potential energy gained by an object lifted through a height h is Eₚ = m g h, where g is the gravitational field strength (approximately 9.8 N/kg on Earth). Kinetic energy of a moving object is Eₖ = ½ m v².
能量有多种形式。物体被举高 h 后获得的重力势能为 Eₚ = m g h，其中 g 为重力场强度（地球表面约为 9.8 N/kg）。运动物体的动能是 Eₖ = ½ m v²。
Power is the rate at which work is done or energy is transferred. A machine that does the same amount of work in a shorter time has a greater power output. Power is measured in watts (W), where 1 W = 1 J/s.
功率是做功或转移能量的速率。能在更短时间内完成同样功的机器输出功率更大。功率的单位是瓦特（W），1 W = 1 J/s。
P = W / t or P = E / t
6. Ohm’s Law and Electrical Circuits | 欧姆定律与电路
Ohm’s Law describes the relationship between voltage (V), current (I) and resistance (R) in an electrical circuit. For a given resistor at constant temperature, the current flowing through it is directly proportional to the voltage across it.
欧姆定律描述了电路中电压（V）、电流（I）和电阻（R）之间的关系。对定温下的某个电阻器，流过它的电流与两端电压成正比。
V = I R
Voltage is measured in volts (V), current in amperes (A) and resistance in ohms (Ω). If you know any two values, you can calculate the third. A high resistance limits the current for a given voltage; lowering the resistance allows more current to flow.
电压单位是伏特（V），电流单位是安培（A），电阻单位是欧姆（Ω）。已知任意两个量即可求出第三个。在电压一定时，高电阻会限制电流，降低电阻则会使电流增大。
7. Series and Parallel Circuits | 串联与并联电路
In a series circuit, components are connected end to end so there is only one path for the current. The current is the same at all points in the loop. The total voltage supplied by the battery is shared between the components. The total resistance is found by adding all the individual resistances together.
在串联电路中，元件首尾相连，电流只有一条通路。回路中各点的电流都相等。电池提供的总电压由各元件分担。总电阻等于所有单独电阻相加。
Rₜₒₜₐₗ = R₁ + R₂ + R₃ + …
In a parallel circuit, components are connected across the same two points, providing multiple paths for the current. The voltage across each branch is the same as the source voltage. The current divides among the branches, and the total resistance is found using the reciprocal formula.
在并联电路中，元件连接在相同的两点之间，电流有多条通路。各支路两端的电压都等于电源电压。电流在支路间分流，总电阻由倒数公式求得。
1 / Rₜₒₜₐₗ = 1 / R₁ + 1 / R₂ + 1 / R₃ + …
The table below summarises the key differences between series and parallel circuits.
下方的表格总结了串联电路与并联电路的主要区别。
| Feature | Series Circuit | Parallel Circuit |
|---|---|---|
| Current | Same everywhere | Shared between branches |
| Voltage | Shared across components | Same across each branch |
| Total resistance | Sum of all resistances | Less than smallest individual resistance |
| Effect of a break | All components stop working | Only the broken branch stops |
8. Density and Pressure | 密度与压强
Density describes how much mass is packed into a given volume. Materials with tightly packed particles, like metals, have a high density; gases have a very low density. Density is measured in kilograms per cubic metre (kg/m³).
密度表示单位体积内包含的质量。金属等粒子排列紧密的材料密度较高，气体密度则很低。密度的单位是千克每立方米（kg/m³）。
ρ = m / V
Pressure is the force acting per unit area when a force is applied over a surface. Sharp objects exert large pressures because the force is concentrated over a small area. The standard unit of pressure is the pascal (Pa), where 1 Pa = 1 N/m².
压强是作用在单位面积上的力。锋利物体因为力集中在很小面积上，可以产生很大的压强。压强的国际单位是帕斯卡（Pa），1 Pa = 1 N/m²。
p = F / A
9. Material Properties: Stress and Strain | 材料性质：应力与应变
When an external force is applied to a solid object, it experiences stress. Tensile stress is the force per unit cross‑sectional area when the object is being stretched. Compressive stress occurs when it is being squashed. Stress has the same units as pressure (Pa).
当固体受到外力作用时，其内部会产生应力。拉伸应力是物体被拉伸时单位横截面积上的力，压缩应力则是被挤压时产生的。应力的单位与压强相同（Pa）。
σ = F / A
Strain measures how much a material deforms compared with its original size. Tensile strain is the extension per unit original length. Strain is a ratio, so it has no units.
应变衡量材料相对于初始尺寸的变形程度。拉伸应变是单位原长上的伸长量。应变是一个比值，没有单位。
ε = ΔL / L
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