📚 Year 9 CCEA PE: Formulas & Principles Quick Reference | Year 9 CCEA 体育：公式定理速查手册
Welcome to your go-to quick reference for essential formulas and principles in Year 9 CCEA Physical Education. This handbook covers the key calculations and theoretical concepts you need for health, fitness and sports performance topics. Keep it handy for revision and exam success!
欢迎使用 Year 9 CCEA 体育学科必备公式与定理速查手册。本手册涵盖了健康、体适能和运动表现相关的关键计算和理论概念。随身携带，助力复习和考试成功！
1. Maximum Heart Rate (MHR) | 最大心率公式
Your maximum heart rate (MHR) is the highest number of beats per minute (bpm) your heart can safely achieve during all-out exercise. It is most commonly estimated using a simple age-based formula, which provides a baseline for setting training zones.
最大心率 (MHR) 是你在极限运动时心脏每分钟能够安全达到的最高搏动次数。通常使用一个基于年龄的简单公式来估算，它为设定训练区间提供了基准。
MHR = 220 – age (years)
最大心率 = 220 – 年龄（岁）
For a 14-year-old student, the estimated MHR would be 220 – 14 = 206 bpm. While this formula is widely used, it gives an average estimate only; individual variation due to genetics, fitness level and testing conditions can cause actual MHR to differ by ±10 bpm. Some alternative formulas, such as 208 – (0.7 × age), are also used in sports science.
以一名14岁的学生为例，估算最大心率为 220 – 14 = 206 次/分钟。尽管该公式被广泛应用，但它仅给出平均估值；基因、体能水平和测试条件造成的个体差异可使实际 MHR 上下浮动约10次/分钟。运动科学中有时也使用 208 – (0.7 × 年龄) 等替代公式。
2. Target Heart Rate (Karvonen Formula) | 目标心率（卡沃宁公式）
To train at a specific intensity, a more personalised approach uses the Karvonen formula. It factors in your resting heart rate (RHR), which reflects your baseline fitness. By plugging in your desired intensity percentage, you can calculate a target training heart rate.
为了在特定强度下进行训练，卡沃宁公式提供了一种更加个性化的方法。它纳入了反映基础体能水平的安静心率 (RHR)，代入期望的强度百分比，即可算出目标训练心率。
Target HR = [(MHR – RHR) × %Intensity] + RHR
目标心率 = [(最大心率 – 安静心率) × 强度%] + 安静心率
Example: A 14-year-old with an RHR of 68 bpm wants to work at 75% intensity. MHR = 206 bpm. Target HR = [(206 – 68) × 0.75] + 68 = (138 × 0.75) + 68 = 103.5 + 68 = 171.5, rounded to 172 bpm. Common training zones based on %MHR include: light (50-60%), moderate (60-70%), aerobic (70-80%), anaerobic (80-90%) and maximal (90-100%).
示例：一名14岁学生，安静心率为 68次/分钟，希望以75%强度训练。最大心率206次/分钟。目标心率 = [(206 – 68) × 0.75] + 68 = (138 × 0.75) + 68 = 103.5 + 68 = 171.5，取整为172次/分钟。常见的根据%MHR划分的训练区间包括：低强度 (50-60%)、中等强度 (60-70%)、有氧 (70-80%)、无氧 (80-90%) 和极限 (90-100%)。
3. Body Mass Index (BMI) | 身体质量指数
Body Mass Index is a screening tool used to classify weight status in relation to height. It is not a direct measure of body fat, but it helps identify potential health risks linked to being underweight, overweight or obese.
身体质量指数 (BMI) 是一项根据身高评估体重状况的筛查工具。它并非直接测量体脂，但有助于识别与过轻、超重或肥胖相关的潜在健康风险。
BMI = weight (kg) ÷ height² (m²)
身体质量指数 = 体重（千克）÷ 身高²（米²）
Worked example: A student weighs 52 kg and is 1.60 m tall. BMI = 52 ÷ (1.60 × 1.60) = 52 ÷ 2.56 = 20.3 kg/m². Standard adult categories (often applied loosely to adolescents) are: underweight < 18.5, normal weight 18.5-24.9, overweight 25-29.9, obese ≥ 30. For young people, percentile charts are more accurate, but the formula remains the same.
计算举例：一名学生体重52千克，身高1.60米。BMI = 52 ÷ (1.60 × 1.60) = 52 ÷ 2.56 = 20.3 kg/m²。标准成人分类（常被粗略用于青少年）为：过轻 <18.5，正常 18.5-24.9，超重 25-29.9，肥胖 ≥ 30。对于青少年，百分位数图表更为准确，但计算公式不变。
4. Speed Calculation | 速度计算
Speed quantifies how fast a body or object moves. In PE, you will often calculate average speed over a known distance. The standard unit is metres per second (m/s), although km/h is also used for longer events.
速度用于量化身体或物体运动的快慢。在体育课上，你经常会计算通过已知距离的平均速度。标准单位为米/秒 (m/s)，但在长距离项目中也会使用千米/小时 (km/h)。
Speed = Distance ÷ Time
速度 = 距离 ÷ 时间
A 100 m sprinter who finishes in 12.5 seconds achieves an average speed of 100 ÷ 12.5 = 8 m/s. In a team game, a midfielder might cover 8,000 m in 60 minutes of playing time, giving an average speed of 8,000 ÷ (60 × 60) ≈ 2.22 m/s. Always check your units: if distance is in metres and time in seconds, speed will be in m/s.
一名100米短跑运动员以12.5秒完赛，其平均速度为 100 ÷ 12.5 = 8 m/s。在一场团队比赛中，中场球员可能在60分钟上场时间内跑动8,000米，平均速度约为 8,000 ÷ (60 × 60) ≈ 2.22 m/s。务必检查单位：若距离单位为米、时间为秒，速度单位即为 m/s。
5. Acceleration | 加速度
Acceleration tells us how quickly velocity changes. In sport, rapid acceleration is crucial for sprinters, wingers and racket-sport players. It can be positive (speeding up) or negative (deceleration).
加速度表示速度变化的快慢。在运动中，快速加速对短跑运动员、边锋和持拍类运动员至关重要。加速度可为正值（加速）或负值（减速）。
a = (v – u) ÷ t
加速度 = (末速度 – 初速度) ÷ 时间
Where a = acceleration (m/s²), v = final velocity (m/s), u = initial velocity (m/s) and t = time (s). If a footballer accelerates from rest (u = 0) to 7 m/s in 1.4 seconds, a = (7 – 0) ÷ 1.4 = 5 m/s². This value means the player’s speed increases by 5 m/s every second during that burst.
其中 a = 加速度 (m/s²)，v = 末速度 (m/s)，u = 初速度 (m/s)，t = 时间 (s)。如果一名足球运动员从静止 (u = 0) 加速到7 m/s，用时1.4秒，则加速度 a = (7 – 0) ÷ 1.4 = 5 m/s²。该数值表示运动员在这段爆发加速中每秒速度增加5 m/s。
6. Newton’s Second Law: Force = Mass × Acceleration | 牛顿第二定律：力 = 质量 × 加速度
Newton’s Second Law explains how an applied force changes the motion of an object or body. The greater the mass or the required acceleration, the more force must be produced by muscles or equipment.
牛顿第二定律解释了施加的力如何改变物体或身体的运动状态。质量或所需加速度越大，肌肉或器械必须产生的力就越大。
F = m × a
力 = 质量 × 加速度
Force is measured in newtons (N). For a 0.45 kg football to be kicked with an acceleration of 40 m/s², the required force is F = 0.45 × 40 = 18 N. In a scrum, if the combined mass of the forwards is 600 kg and they push with a total force of 2,400 N, their acceleration is a = 2,400 ÷ 600 = 4 m/s². Understanding this helps coaches analyse technical efficiency.
力的单位为牛顿 (N)。要将一个0.45千克的足球以40 m/s² 的加速度踢出，所需力为 F = 0.45 × 40 = 18 N。在橄榄球争球中，若前锋总体质量为600千克，并以2,400 N 的总力前推，则加速度 a = 2,400 ÷ 600 = 4 m/s²。理解此原理有助于教练分析技术效率。
7. Work Done | 做功
In physics and PE, work is done when a force moves an object through a distance in the direction of the force. Work is a key concept when considering energy expenditure during exercise.
在物理和体育中，当力使物体沿力的方向移动一段距离时，力就对物体做了功。功是分析运动能耗时的一个关键概念。
W = F × d
功 = 力 × 距离
Work (W) is measured in joules (J). If a weightlifter lifts a barbell of 800 N through a vertical distance of 0.8 m, the work done is W = 800 × 0.8 = 640 J. No horizontal work is done when carrying an object across a level floor because the force (upwards) and motion (horizontal) are perpendicular. This principle explains why holding a heavy weight stationary does zero mechanical work, even though your muscles tire.
功 (W) 的单位为焦耳 (J)。如果举重运动员将800 N 的杠铃垂直上举0.8米，则做功为 W = 800 × 0.8 = 640 J。在水平地面搬运物体时，由于力（向上）与运动方向（水平）垂直，没有做水平方向的功。该原理解释了为何静止托举重物不做机械功，但肌肉仍会疲劳。
8. Power | 功率
Power measures the rate at which work is done or energy is transferred. Explosive athletes, such as sprinters and jumpers, need high power output to perform well.
功率用于衡量做功或能量转换的速率。短跑和跳跃等爆发性项目的运动员需要较高的功率输出以获得佳绩。
P = W ÷ t
功率 = 功 ÷ 时间
Power is expressed in watts (W), where 1 W = 1 J/s. An alternative formula for moving objects is P = F × v (force multiplied by velocity). If a cyclist does 3,600 J of work over 20 seconds while climbing, the average power is 3,600 ÷ 20 = 180 W. The same cyclist pushing at 90 N while travelling at 8 m/s also generates 90 × 8 = 720 W at that instant, highlighting the explosive demands of sprint finishes.
功率的单位为瓦特 (W)，1 W = 1 J/s。对于运动中的物体，另一公式为 P = F × v（力乘以速度）。如果一名自行车运动员在20秒的爬坡过程中做功3,600 J，则平均功率为 3,600 ÷ 20 = 180 W。若同一运动员以90 N 的力蹬踏、同时以8 m/s 骑行，此时瞬间功率为 90 × 8 = 720 W，凸显出冲刺终点的爆发性需求。
9. Lever Systems and Moments | 杠杆系统与力矩
Levers magnify force or speed of movement. In the human body, bones act as levers, joints as fulcrums, and muscles provide the effort force. Understanding levers helps analyse technique and avoid injury.
杠杆可以放大力或运动速度。在人体中，骨骼充当杠杆，关节充当支点，肌肉提供动力。理解杠杆有助于分析技术动作并预防损伤。
Moment = Force × Perpendicular distance from pivot
力矩 = 力 × 到支点的垂直距离
For a lever to balance, the clockwise moment equals the anticlockwise moment. Mechanical advantage (MA) = effort arm ÷ load arm. First-class levers (e.g. the neck when heading a ball) have the fulcrum between effort and load. Second-class levers (e.g. standing on tiptoe) have the load between fulcrum and effort, always giving MA > 1. Third-class levers
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