📚 Year 9 Cambridge PE: Formula and Theorem Quick Reference | 剑桥九年级体育：公式定理速查手册
Welcome to your go-to revision sheet for the essential formulas, equations, and biomechanical principles you need in Year 9 Cambridge Physical Education. Whether you are planning a personal training programme, analysing sporting movement, or understanding how your body responds to exercise, these ideas sit at the heart of the syllabus. Keep this quick reference handy and use it to deepen your practical work and written responses.
欢迎使用这份为剑桥九年级体育课程准备的核心公式、方程与生物力学原理速查手册。不论你是在设计个人训练计划、分析运动动作，还是理解身体对运动的反应，这些概念都处在课程大纲的核心位置。请随时查阅这本速查手册，并用它来深化你的实践操作和书面作答。
1. Maximum Heart Rate (MHR) | 最大心率
The simplest way to estimate your maximum heart rate is the age-based formula. It gives a general guide to how fast your heart can beat during all-out exercise.
估算最大心率最简单的方法是使用基于年龄的公式。它可以大致反映你在全力运动时心脏能跳多快。
MHR = 220 − Age
For example, a 14‑year‑old student would have an estimated MHR of 206 beats per minute (bpm). This value is used to set training zones.
例如，一名14岁学生的最大心率约为206次/分钟。该数值用于设定训练区间。
2. Target Heart Rate Zone – Karvonen Formula | 靶心率区间 – 卡沃宁公式
To train safely and effectively, athletes use target heart rate zones. The Karvonen formula takes resting heart rate (RHR) into account, making the zone personal.
为了安全而有效地训练，运动员会使用靶心率区间。卡沃宁公式将安静心率考虑在内，使训练区间更个性化。
Target HR = RHR + (Intensity % × (MHR − RHR))
Moderate intensity (50–70%) and vigorous intensity (70–85%) zones are calculated from this. A typical Year 9 task is to calculate 60% and 80% intensity using Karvonen.
中等强度（50%–70%）和高强度（70%–85%）区间由此计算得出。九年级的一个典型任务是利用卡沃宁公式计算60%和80%强度下的靶心率。
3. Body Mass Index (BMI) | 身体质量指数
BMI is a quick screening tool that relates mass to height. It does not measure body fat directly but helps identify weight categories that may impact sports performance and health.
身体质量指数是将体重与身高相关联的快速筛查工具。它不直接测量体脂，但有助于识别可能影响运动表现和健康的体重类别。
BMI = Mass (kg) ÷ Height (m)²
In Cambridge PE, you might interpret BMI values: underweight (<18.5), normal (18.5–24.9), overweight (25–29.9), and obese (≥30). Remember muscle mass can make athletes heavier without being overfat.
在剑桥体育中，你可能需要解读BMI数值：过轻（<18.5）、正常（18.5–24.9）、超重（25–29.9）和肥胖（≥30）。请记住，肌肉量大可能使运动员体重偏重，但并不意味着脂肪过多。
4. Energy Expenditure – MET and Calorie Burn | 能量消耗 – 代谢当量与卡路里消耗
Physical activity energy expenditure is often estimated using the Metabolic Equivalent of Task (MET). One MET is the energy used while sitting quietly.
体力活动的能量消耗通常使用代谢当量来估算。1 MET代表安静坐着时的能耗。
Calories burned per minute = MET × Body mass (kg) × 0.0175
For a 50 kg student playing football (7 METs), the estimated burn per minute is 7 × 50 × 0.0175 ≈ 6.1 kcal. Understanding MET helps design balanced activity programmes.
对于一名踢足球（7 MET）的50公斤学生，每分钟大致消耗7 × 50 × 0.0175 ≈ 6.1千卡。理解代谢当量有助于设计均衡的活动计划。
5. Speed, Distance and Time | 速度、距离和时间
The relationship between speed, distance, and time is fundamental in analysing athletic performance and game situations. Use the triangle method to rearrange as needed.
速度、距离和时间之间的关系是分析运动成绩和比赛情境的基础。你可以利用三角法进行需要的公式变形。
Speed = Distance ÷ Time
Units require care: metres per second (m/s) for sprinting, kilometres per hour (km/h) for endurance events. Convert units by remembering 1 m/s = 3.6 km/h.
单位需要留心：短跑用米/秒，耐力项目用千米/时。单位换算请记住1 m/s = 3.6 km/h。
6. Moment of Force (Torque) | 力矩
Moments explain why certain body positions are easier to hold and how levers produce rotation. A moment is the turning effect of a force about a joint axis.
力矩可以解释为什么某些身体姿势更容易保持，以及杠杆如何产生旋转。力矩是力围绕关节轴产生的转动效果。
Moment = Force × Perpendicular distance from pivot
When a gymnast holds an iron cross, the shoulder joint is the pivot and the distance from shoulder to hand magnifies the moment. Stronger muscles are required to balance a larger moment.
当体操运动员做十字支撑时，肩关节是支点，从肩膀到手的距离放大了力矩。需要更强的肌肉来平衡较大的力矩。
7. Work Done | 做功
In physical education, work is done when a force moves an object. This biomechanical principle links strength and distance, and appears when analysing weightlifting, throws, or jumps.
在体育中，当力使物体移动时，我们就做了功。这个生物力学原理将力量与距离联系起来，在分析举重、投掷或跳跃时会出现。
Work = Force × Distance moved in direction of force
Lifting a 20 kg barbell (force ≈ 200 N) through 0.8 m requires 160 J of work. If the force is applied at an angle, only the parallel component does work.
将一根20公斤的杠铃（力约200牛）上举0.8米需要做功160焦。如果施力有角度，只有平行分量才做功。
8. Power Output | 功率输出
Power measures how quickly work is performed. Explosive sports such as sprinting, jumping, and striking require high power output over very short time frames.
功率衡量做功的快慢。爆发力项目如短跑、跳跃和击球，需要在极短的时间内输出高功率。
Power = Work ÷ Time or Power = Force × Velocity
A vertical jump that delivers 800 J of work in 0.5 seconds produces 1600 W of power. Increasing the velocity of the movement directly raises power.
一个纵跳如果在0.5秒内做800焦的功，就产生了1600瓦的功率。提高运动速度能直接增加功率输出。
9. Law of Levers | 杠杆定律
Muscles and bones work as lever systems. The law of levers states that a small effort can move a large load if the effort arm is longer than the load arm. This principle is key to understanding mechanical advantage in the body.
肌肉与骨骼以杠杆系统运作。杠杆定律指出，如果动力臂长于阻力臂，一个较小的动力就能移动较大的负荷。这一原理对于理解人体内部机械优势至关重要。
Effort × Effort arm = Load × Load arm
A bicep curl is a third‑class lever: the effort (bicep) sits between the fulcrum (elbow) and load (hand). The effort arm is very short, so the muscle must produce a large force to lift a relatively small load – excellent for speed and range of motion.
二头肌弯举是一个第三类杠杆：动力（肱二头肌）位于支点（肘）和负荷（手）之间。动力臂非常短，因此肌肉必须产生很大的力才能举起较小的负荷——这类杠杆极利于速度和动作幅度。
10. Stability and Centre of Gravity | 稳定性与重心
Stability is a key concept in gymnastics, wrestling, and team sports. An object or body is more stable when its centre of gravity is low and its base of support is wide. The line of gravity must fall within the base to prevent toppling.
稳定性是体操、摔跤和团队运动中的关键概念。当物体的重心较低且支撑面较宽时，它就更稳定。重力线必须落在支撑面内，才能防止倾倒。
| Factor | Effect on Stability | Sporting Example |
|---|---|---|
| Lower centre of gravity | Increases stability | Wrestler in a crouched stance |
| Wider base of support | Increases stability | Sumo wrestler’s wide stance |
| Line of gravity near edge of base | Decreases stability | Sprinter in set position before explosive start |
| Greater mass | Increases stability | Rugby scrum forward |
For a Year 9 analysis task, explain how a basketball defender lowers their centre of gravity and widens their stance to resist being pushed off balance. Use drawings and the line of gravity to support your answer.
在九年级的分析任务中，请解释篮球防守者是如何降低重心、加宽站姿以抵抗被推倒的。用图示和重力线来支撑你的答案。
11. FITT Principle – Training Prescription | FITT原则 – 训练处方
While not a numerical formula in the traditional sense, the FITT principle is a scientific framework you must be able to apply to any training programme. It stands for Frequency, Intensity, Time, and Type.
虽然FITT原则不是传统意义上的数学公式，但它是一种科学的训练框架，你必须能够在任何训练计划中加以应用。它代表频率、强度、时间和类型。
- Frequency – how often you train per week.
- Intensity – how hard you work (e.g. % MHR, RPE scale).
- Time – duration of each session.
- Type – the mode of exercise (running, cycling, resistance).
- 频率 – 每周训练多少次。
- 强度 – 训练的辛苦程度（如最大心率百分比、自感用力度量表）。
- 时间 – 每次训练的时长。
- 类型 – 运动方式（跑步、骑行、抗阻训练）。
Each variable can be manipulated to achieve overload and progression. For Cambridge coursework, design a 6‑week cardiovascular programme using FITT and explain how you would progress the intensity using heart rate formulas from sections 1–2.
每一个变量都可以进行调整以实现超负荷和渐进性。在剑桥课程作业中，你需要运用FITT原则设计一个6周的心血管训练计划，并说明如何利用前述公式来逐步提升训练强度。
12. Overload, Progression and Recovery | 超负荷、渐进与恢复
Training adaptations only occur when the body is stressed beyond its current capacity (overload), the load is increased over time (progression), and adequate rest is allowed (recovery). These principles are often summarised as the ‘SPORT’ or ‘SPOR’ acronyms, with ‘R’ standing for Reversibility. Overload can be quantified: increase resistance by 2–5% weekly, or add 10% to running distance.
只有当身体被施加超出当前能力的压力（超负荷）、负荷随时间逐步增加（渐进）并留有充足休息（恢复）时，训练适应才会发生。这些原则常被概括为“SPORT”或“SPOR”缩写，其中“R”代表可逆性。超负荷可以量化：每周增加2%–5%的阻力，或将跑步距离增加10%。
Use the formulas from this handbook to monitor overload – recalculate target heart rates as fitness improves, track power output, and ensure that increases in load follow sound biomechanical principles.
请运用本手册中的公式来监控超负荷——随着体能改善重新计算靶心率，追踪功率输出，并确保负荷的增加遵循合理的生物力学原理。
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