Year 7 WJEC Engineering Formula & Theorem Quick Reference Handbook | Year 7 WJEC 工程公式定理速查手册

2026-07-16 21:30 · 本文部分内容由AI辅助创作

📚 Year 7 WJEC Engineering Formula & Theorem Quick Reference Handbook | Year 7 WJEC 工程公式定理速查手册

This quick reference handbook brings together the essential formulas and theorems you will meet in the Year 7 WJEC Engineering curriculum. Each section presents the concept first in clear English, followed by an accurate Chinese translation, so you can build confidence in both languages. Use it as a pocket guide when tackling design challenges, calculating forces, electricity or mechanical systems – all the must‑know equations are here in one place.

本速查手册汇总了你在 Year 7 WJEC 工程课程中会遇到的核心公式与定理。每一节先用清晰的英文讲解，再配以准确的中文翻译，帮助你在两种语言中建立自信。无论是处理设计挑战、计算力、电学还是机械系统，都可以把它当作口袋指南——所有必知必会的方程都收录于此。

1. Length, Area and Volume | 长度、面积与体积

ength × width × height. Always use the same unit for all dimensions and square or cube the unit for area and volume.

在设计任何零件之前，都需要描述其尺寸。长度以米（m）为单位。对于长方形，面积 = 长 × 宽，体积 = 长 × 宽 × 高。始终对所有尺寸使用相同单位，面积的单位为平方单位，体积为立方单位。

Rectangle Area: A = l × w

长方形面积：A = l × w

Cuboid Volume: V = l × w × h

长方体体积：V = l × w × h

l = length / 长，w = width / 宽，h = height / 高
Units: area in m², volume in m³ / 单位：面积 m²，体积 m³

2. Mass, Density and Weight | 质量、密度与重量

Mass tells us how much matter an object contains (kg). Density (ρ) links mass and volume – a dense material packs more mass into the same space. Weight is the force of gravity on a mass; on Earth 1 kg weighs about 9.8 newtons (N).

质量表示物体包含物质的多少（kg）。密度（ρ）将质量与体积联系起来——密度大的材料在相同空间内包含更多质量。重量是重力对质量的作用力；在地球上 1 kg 的重量约为 9.8 牛顿（N）。

Density: ρ = m / V

密度：ρ = m / V

Weight: W = m × g

重量：W = m × g

m = mass (kg) / 质量，V = volume (m³) / 体积，ρ = density (kg/m³) / 密度
g ≈ 9.8 m/s² on Earth / 地球表面 g ≈ 9.8 m/s²

3. Force, Mass and Acceleration | 力、质量与加速度

Newton’s Second Law explains how an unbalanced force changes an object’s motion. The larger the force, the greater the acceleration; the larger the mass, the smaller the acceleration for the same force. In engineering, this principle helps us choose motors, brakes and structural supports.

牛顿第二定律解释不平衡力如何改变物体的运动。力越大，加速度越大；质量越大，相同力产生的加速度越小。在工程中，这一原理帮助我们选择电机、制动器和结构支撑。

Resultant Force: F = m × a

合力：F = m × a

F = force (N) / 力（牛顿），m = mass (kg) / 质量，a = acceleration (m/s²) / 加速度
1 N = 1 kg·m/s² / 1 N = 1 千克·米/秒²

4. Pressure | 压强

Pressure measures how concentrated a force is. A sharp blade exerts high pressure because the force acts on a tiny area. In hydraulic systems, pressure is transmitted equally throughout the fluid, allowing a small input force to create a large output force.

压强衡量力的集中程度。锋利的刀刃能产生高压强，因为力作用在很小的面积上。在液压系统中，压强在整个液体中均匀传递，使得较小的输入力可以产生很大的输出力。

Pressure: P = F / A

压强：P = F / A

P = pressure (Pa or N/m²) / 压强（帕斯卡或牛/米²），F = force (N) / 力，A = area (m²) / 面积
1 Pa = 1 N/m² / 1 帕 = 1 牛/米²

5. Work Done and Energy Transfer | 做功与能量转移

Work is done when a force moves an object. Energy is transferred from one store to another – for example, a motor does work to lift a load, transferring electrical energy into gravitational potential energy. Knowing the work done helps engineers size power supplies and motors.

当力使物体移动时，就做了功。能量从一个储存转移到另一个储存——例如，电机做功提升负载，将电能转化为重力势能。了解做功多少有助于工程师确定电源和电机的规格。

Work Done: W = F × d

做功：W = F × d

W = work done (J) / 功（焦耳），F = force (N) / 力，d = distance moved in direction of force (m) / 沿力方向移动的距离
1 J = 1 N·m / 1 焦 = 1 牛·米

6. Mechanical Advantage | 机械效益

Simple machines such as levers, pulleys and gears allow a small effort to overcome a large load. Mechanical advantage (MA) compares the load force to the effort force. An MA greater than 1 means the machine multiplies the effort force.

杠杆、滑轮和齿轮等简单机械可以用较小的作用力克服较大的负载。机械效益（MA）将负载力与作用力进行比较。MA 大于 1 表示机械将作用力放大了。

Mechanical Advantage: MA = Load / Effort

机械效益：MA = 负载力 / 作用力

Load = output force (N) / 负载力，Effort = input force (N) / 作用力
No unit; a ratio / 无单位，是一个比值

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7. Gear Ratio | 齿轮比

Gears change speed, torque and direction. The gear ratio tells you how many turns the driven gear makes for one turn of the driver gear. A large ratio reduces output speed but increases torque – essential for climbing gears on a bicycle or a robot arm.

齿轮可以改变速度、扭矩和方向。齿轮比表示从动轮相对于主动轮每转一圈所转的圈数。较大的齿轮比会降低输出速度但增大扭矩——这对自行车爬坡档位或机械臂至关重要。

Gear Ratio = Number of teeth on driven gear / Number of teeth on driver gear

齿轮比 = 从动齿轮齿数 / 主动齿轮齿数

If gear ratio > 1, speed decreases and torque increases / 齿轮比 > 1 时，速度降低、扭矩增大
Output speed = Input speed / Gear Ratio / 输出转速 = 输入转速 / 齿轮比

8. Ohm's Law | 欧姆定律

Ohm’s Law is the most important rule in basic circuit design. It links voltage (V), current (I) and resistance (R). For a given resistance, doubling the voltage doubles the current. Engineers use this law to select resistors and protect components from overcurrent.

欧姆定律是基础电路设计中最重要的规律。它将电压（V）、电流（I）和电阻（R）联系起来。对于给定的电阻，电压翻倍则电流翻倍。工程师利用这一定律选取电阻并保护元件免受过电流损坏。

V = I × R

V = voltage (V) / 电压（伏特），I = current (A) / 电流（安培），R = resistance (Ω) / 电阻（欧姆）
1 V = 1 A × 1 Ω

9. Electrical Power | 电功率

Power is the rate of energy transfer. In electrical systems, power depends on voltage and current. A higher power rating means more energy is transferred per second – think of a bright lamp versus a dim one. These equations help you choose the right fuse and cable thickness.

功率是能量转移的速率。在电气系统中，功率取决于电压和电流。额定功率越高，每秒传递的能量越多——可以想象一盏亮灯与一盏暗灯的差别。这些方程帮助你选择合适的保险丝和导线粗细。

Power: P = V × I

功率：P = V × I

Also: P = I² × R and P = V² / R

另有：P = I² × R 及 P = V² / R

P = power (W) / 功率（瓦特），1 W = 1 J/s / 1 瓦 = 1 焦/秒

10. Hooke's Law | 胡克定律

Many engineering materials behave like springs when stretched or compressed. Hooke’s Law states that the extension is proportional to the applied force, as long as the elastic limit is not exceeded. This principle is used when designing suspension systems and load‑sensing devices.

许多工程材料在拉伸或压缩时都像弹簧一样。胡克定律指出，只要不超过弹性极限，伸长量与施加的力成正比。设计悬挂系统和载荷传感装置时都会用到这一原理。

F = k × x

F = applied force (N) / 施加的力，k = spring constant (N/m) / 弹簧常数（牛/米），x = extension (m) / 伸长量
Higher k means stiffer spring / k 值越大，弹簧越硬

11. Moments (Turning Forces) | 力矩（转动力）

A moment is the turning effect of a force. The size of the moment depends on the force and its distance from the pivot. For a balanced lever, the clockwise moment equals the anticlockwise moment – the principle behind spanners, seesaws and beam balances.

力矩是力的转动效应。力矩的大小取决于力以及力与支点的距离。对于平衡的杠杆，顺时针力矩等于逆时针力矩——扳手、跷跷板和梁式天平背后的原理都是如此。

Moment: M = F × d

力矩：M = F × d

M = moment (N·m) / 力矩（牛·米），F = force (N)，d = perpendicular distance from pivot (m) / 到支点的垂直距离
Equilibrium: Σ clockwise moments = Σ anticlockwise moments / 平衡时：顺时针力矩总和 = 逆时针力矩总和

12. Speed and Velocity | 速率与速度

Understanding motion is essential for timers, conveyors and automated systems. Speed tells you how fast something is moving; velocity also includes direction. The average speed formula is used to calculate travel time or to synchronise machines.

理解运动对计时器、传送带和自动化系统至关重要。速率表示物体运动的快慢；速度还包含方向。平均速率公式可用于计算行进时间或使机器同步。

Average Speed: v = s / t

平均速率：v = s / t