📚 Year 8 WJEC PE: Formula & Theorem Quick Reference Handbook | WJEC八年级体育：公式定理速查手册
This quick reference handbook provides all the essential formulas and theorems you need for Year 8 WJEC Physical Education. Understanding these equations will help you analyse performance, monitor fitness, and apply scientific principles to sports and exercise. Read on to master the key calculations and concepts.
本速查手册为您提供WJEC八年级体育所需的所有基本公式和定理。理解这些方程式将帮助您分析运动表现、监测体能，并将科学原理应用于体育与锻炼。继续阅读，掌握关键计算和概念。
1. Maximum Heart Rate Formula | 最大心率公式
Your maximum heart rate (HRmax) is the highest number of beats per minute (bpm) your heart can achieve during all-out effort. A simple age-based estimate is widely used to set exercise intensity zones.
最大心率（HRmax）是心脏在极限运动中每分钟所能达到的最高搏动次数。一个基于年龄的简单估算被广泛用于设定运动强度区间。
HRmax = 220 − age
For a 13-year-old student, HRmax ≈ 220 − 13 = 207 bpm. This formula is an estimate; individual fitness levels and genetics can cause variations of ±10 bpm. It is best used alongside perceived exertion.
对于一名13岁学生，HRmax ≈ 220 − 13 = 207次/分钟。该公式仅为估算值；个体体能水平和遗传因素可能导致±10次/分钟的偏差。最好与主观用力感觉结合使用。
2. Karvonen Formula for Target Heart Rate Zones | 卡沃宁靶心率公式
The Karvonen formula calculates target heart rate more accurately by including resting heart rate (HRrest). It helps you train at a precise intensity, such as 60–80% of heart rate reserve.
卡沃宁公式通过纳入静息心率（HRrest）更精确地计算目标心率。它能帮助你在精确的强度下训练，例如心率和储备的60–80%。
Target HR = ((HRmax − HRrest) × %intensity) + HRrest
Example: a 13-year-old with HRrest = 70 bpm wants to work at 70% intensity. HRmax = 207 bpm, so target HR = ((207 − 70) × 0.70) + 70 = 165.9 bpm. A simpler alternative uses %HRmax directly, but Karvonen is preferred for personalised training.
示例：一名13岁学生静息心率为70次/分钟，希望以70%强度训练。HRmax = 207，因此目标心率 = ((207 − 70) × 0.70) + 70 = 165.9次/分钟。另一种简化方法是直接采用%HRmax，但卡沃宁公式更适合个性化训练。
3. Body Mass Index (BMI) Calculation | 身体质量指数（BMI）计算
BMI is a screening tool used to categorise weight status. It uses mass and height to estimate whether a person is underweight, healthy weight, overweight or obese.
BMI是一种用于划分体重状态的筛查工具。它利用体重和身高来估算一个人是否体重过轻、健康体重、超重或肥胖。
BMI = weight (kg) ÷ height2 (m2)
For a student weighing 50 kg and 1.60 m tall: BMI = 50 ÷ (1.60)2 = 50 ÷ 2.56 ≈ 19.5 kg/m2. This falls within the healthy range (18.5–24.9). BMI does not distinguish between muscle and fat, so athletic individuals may be misclassified.
一位体重50千克、身高1.60米的学生：BMI = 50 ÷ (1.60)2 = 50 ÷ 2.56 ≈ 19.5 kg/m2。该数值处于健康范围（18.5–24.9）。BMI无法区分肌肉和脂肪，因此运动员可能被错误归类。
4. Speed, Distance, Time Relationship | 速度、距离、时间关系
Speed is fundamental in many sports. The relationship between distance travelled, time taken and speed is given by a simple formula. Rearranging allows you to find any missing quantity.
速度在许多运动中是基础。行进距离、所用时间和速度之间的关系可以用一个简单公式表示。通过移项可以求出任意未知量。
Speed = distance ÷ time
If a sprinter covers 100 m in 14.0 seconds, speed = 100 ÷ 14.0 ≈ 7.14 m/s. In team games, you might calculate sprint speed over 30 m to monitor fitness. Remember to use consistent units, e.g. metres and seconds.
如果一名短跑运动员用14.0秒跑完100米，速度 = 100 ÷ 14.0 ≈ 7.14米/秒。在团队比赛中，你可以通过30米冲刺速度来监测体能。记得使用一致的单位，例如米和秒。
5. Newton’s Laws of Motion in Sport | 体育中的牛顿运动定律
Newton’s three laws explain how forces affect motion. Understanding them helps athletes improve starts, changes of direction and collision control.
牛顿三定律解释了力如何影响运动。理解这些定律有助于运动员改善起跑、变向和碰撞控制。
First Law (Inertia): An object remains at rest or moves with constant velocity unless a resultant external force acts on it. A football on the pitch stays still until kicked.
第一定律（惯性）：物体保持静止或匀速直线运动状态，除非受到合外力的作用。足球在球场保持静止，直到被踢动。
Second Law (Acceleration): The acceleration of an object is directly proportional to the net force and inversely proportional to its mass.
第二定律（加速度）：物体的加速度与合外力成正比，与其质量成反比。
F = m × a
Example: a 0.45 kg basketball is pushed with a force of 9 N. Acceleration a = F ÷ m = 9 ÷ 0.45 = 20 m/s2. A lighter ball accelerates more for the same force.
示例：一个0.45千克的篮球被9牛的力推动。加速度a = F ÷ m = 9 ÷ 0.45 = 20 m/s2。同等力量下，更轻的球加速更快。
Third Law (Action-Reaction): Whenever one body exerts a force on another, the second body exerts an equal and opposite force on the first. When a swimmer pushes water backwards, the water pushes the swimmer forwards.
第三定律（作用力与反作用力）：当一物体对另一物体施加力的作用时，另一物体同时施加一个大小相等、方向相反的力。游泳者向后推水时，水向前推动游泳者。
6. Power Output | 功率输出
Power measures the rate of doing work or transferring energy. In sport, higher power often means better performance in explosive activities like jumping, throwing and sprinting.
功率衡量做功或能量传递的速率。在运动中，更高的功率通常意味着在跳跃、投掷和短跑等爆发性活动中表现更佳。
Power = work done ÷ time taken
Power = force × velocity
If a weightlifter lifts 800 J of work in 1.6 s, power = 800 ÷ 1.6 = 500 W. Using the force-velocity form, if a cyclist exerts 50 N of force at a velocity of 8 m/s, power = 50 × 8 = 400 W. Both equations are useful depending on the data available.
如果举重运动员在1.6秒内完成800焦耳的功，功率 = 800 ÷ 1.6 = 500瓦。如果使用力-速度形式，自行车运动员以50牛的力、8米/秒的速度骑行，功率 = 50 × 8 = 400瓦。两个方程根据可用数据各有用途。
7. Levers and Moments | 杠杆与力矩
Levers consist of a rigid bar that rotates around a fulcrum. The turning effect of a force is called the moment. Understanding levers helps optimise techniques in throwing, jumping and lifting.
杠杆由一根围绕支点转动的刚性杆组成。力的转动效应称为力矩。理解杠杆有助于优化投掷、跳跃和举重技术。
Moment = force × perpendicular distance from fulcrum
In the body, muscles, bones and joints act as levers. There are three classes of lever, defined by the relative positions of fulcrum, effort and load. First-class levers (e.g. neck nodding) have the fulcrum in the middle; second-class levers (e.g. standing on tiptoes) have the load in the middle; third-class levers (e.g. bicep curl) have the effort in the middle. Third-class levers are most common in the body and favour range of motion over force.
在人体中，肌肉、骨骼和关节充当杠杆。根据支点、动力和负载的相对位置，杠杆分为三类：第一类杠杆（如点头动作）支点在中间；第二类杠杆（如踮脚站立）负载在中间；第三类杠杆（如肱二头肌弯举）动力在中间。第三类杠杆在人体中最常见，以牺牲力量为代价增大活动范围。
8. Cardiac Output Equation | 心输出量方程
Cardiac output (Q) is the volume of blood pumped by the heart per minute. It indicates how efficiently the cardiovascular system delivers oxygen during exercise.
心输出量（Q）是心脏每分钟泵出的血液量。它反映心血管系统在运动中输送氧气的效率。
Q = stroke volume (SV) × heart rate (HR)
At rest, a typical stroke volume is around 70 mL/beat and HR is 70 bpm, giving Q ≈ 70 × 70 = 4900 mL/min (4.9 L/min). During intense exercise, SV may increase to 120 mL/beat and HR to 190 bpm, so Q = 120 × 190 = 22800 mL/min (22.8 L/min). Regular training increases stroke volume, making the heart more efficient.
安静时，典型的每搏输出量约为70毫升/次，心率为70次/分钟，Q ≈ 70 × 70 = 4900毫升/分钟（4.9升/分钟）。剧烈运动时，SV可能增至120毫升/次，心率增至190次/分钟，因此Q = 120 × 190 = 22800毫升/分钟（22.8升/分钟）。经常训练可增大每搏输出量，使心脏更高效。
9. Momentum and Impulse | 动量与冲量
Momentum measures the ‘quantity of motion’ and depends on mass and velocity. Impulse describes the change in momentum caused by a force applied over time, crucial for analysing impacts and catching skills.
动量衡量’运动的量’，取决于质量和速度。冲量描述力在一段时间内作用所引起的动量变化，对于分析撞击和接球技术至关重要。
Momentum (p) = mass (m) × velocity (v)
Impulse = force × time = change in momentum (Δp)
A 0.5 kg football moving at 20 m/s has momentum p = 0.5 × 20 = 10 kg·m/s. When a goalkeeper catches the ball, bringing it to rest in 0.2 s, the force experienced is impulse ÷ time = 10 ÷ 0.2 = 50 N. Increasing the stopping time (e.g. by withdrawing hands) reduces the force and prevents injury.
一个0.5千克的足球以20米/秒飞行，动量p = 0.5 × 20 = 10千克·米/秒。当守门员接住球，使其在0.2秒内静止，所受力为冲量÷时间 = 10 ÷ 0.2 = 50牛。延长停止时间（如随球引手）可减少受力并防止受伤。
10. Training Load Calculation | 训练负荷计算
Training load combines the volume and intensity of a session to monitor how hard an athlete has worked. It helps balance stress and recovery to optimise performance and avoid overtraining.
训练负荷结合了当次训练的运动量和强度，以监测运动员的训练强度。它有助于平衡压力与恢复，优化表现并避免过度训练。
Training load = session RPE × duration (minutes)
RPE (Rate of Perceived Exertion) uses a scale, often 1–10 or 6–20. Example: a dance session of 45 minutes at RPE 7 gives a training load of 7 × 45 = 315 arbitrary units. Some coaches use heart rate zone time or distance covered. Regardless of method, recording training load helps track progress and plan deload weeks.
RPE（主观用力感觉等级）通常使用1–10或6–20的量表。示例：一次45分钟的舞蹈课，RPE为7，训练负荷 = 7 × 45 = 315任意单位。一些教练采用心率区间时长或跑步距离。无论方法如何，记录训练负荷有助于追踪进步并规划减量周。
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