📚 Year 9 AQA Physical Education: Formula & Theorem Quick Reference Handbook | 九年级 AQA 体育：公式定理速查手册
Welcome to your handy quick-reference guide for the key formulae, equations and principles covered in the Year 9 AQA Physical Education course. This handbook brings together the essential calculations you need to master – from heart rate zones and body composition indicators to the mechanics of movement, levers and training load. Understanding the numbers behind sport gives you a powerful toolkit for analysing performance, setting targets and designing safer, more effective training programmes. Keep this revision companion close as you prepare for written assessments and practical application.
欢迎使用这本快捷的速查手册，它汇集了九年级 AQA 体育课程中最关键的公式、方程和原理。手册涵盖心率区间、身体成分指标以及运动力学、杠杆作用和训练负荷等必须掌握的核心计算内容。理解运动背后的数字，能为你提供分析运动表现、设定目标和设计更安全有效的训练计划的有力工具。在准备书面考试和实际应用时，请将这本复习伴侣放在手边。
1. Maximum Heart Rate (HRmax) | 最大心率
The simplest way to estimate maximum heart rate is the age-predicted formula. It gives a baseline value used to set aerobic and anaerobic training zones. Remember that individual variation exists, and this is most accurate for large populations.
估算最大心率最简单的方法是年龄预测公式。它提供了一个用于设定有氧和无氧训练区间的基准值。请注意个体差异是存在的，这一公式在针对大样本人群时最为准确。
HRmax = 220 – age (in years)
HRmax = 220 – 年龄（以年为单位）
For a 14-year-old student, the estimated HRmax would be 220 – 14 = 206 beats per minute (bpm). This value is then used to calculate target heart rate zones, such as 60–80% of HRmax for moderate aerobic work.
对于一名14岁的学生，估算的最大心率将是 220 – 14 = 206 次/分钟 (bpm)。此值随后用于计算目标心率区间，例如用于中等强度有氧运动的 HRmax 的 60–80%。
2. Karvonen Formula – Target Heart Rate Reserve | 卡式公式 – 目标储备心率
A more personalised method for setting training zones uses resting heart rate (RHR) together with HRmax. The Karvonen formula calculates heart rate reserve, giving a more tailored intensity range, especially useful if you have a very low or high resting pulse.
一种更个性化的设定训练区间的方法，会同时用到安静心率 (RHR) 和最大心率 (HRmax)。卡式公式计算储备心率，能提供更贴合自身的强度范围，在安静脉搏很低或很高时尤其有用。
Target HR = (HRmax – RHR) × target intensity % + RHR
目标心率 = (HRmax – RHR) × 目标强度百分比 + RHR
If a student has a resting heart rate of 65 bpm and a HRmax of 206 bpm, then 70% intensity is calculated as (206 – 65) × 0.70 + 65 = 141 × 0.70 + 65 = 98.7 + 65 = 163.7 bpm, rounded to 164 bpm.
如果一名学生的安静心率为 65 bpm，最大心率为 206 bpm，那么 70% 强度计算为 (206 – 65) × 0.70 + 65 = 141 × 0.70 + 65 = 98.7 + 65 = 163.7 bpm，四舍五入为 164 bpm。
3. Body Mass Index (BMI) | 身体质量指数
BMI is a quick screening tool used to categorise weight status. It relates mass to the square of height and helps identify potential health risks linked to underweight, overweight and obesity. However, it does not distinguish between muscle and fat, so it must be interpreted carefully, especially in muscular athletes.
BMI 是一种用于划分体重状态的快速筛查工具。它将体重与身高的平方联系起来，有助于识别与过轻、超重和肥胖相关的潜在健康风险。但它不区分肌肉与脂肪，因此必须谨慎解读，尤其是对于肌肉发达的运动员。
BMI = mass (kg) ÷ (height (m))²
BMI = 体重 (kg) ÷ (身高 (m))²
For example, a student weighing 55 kg with a height of 1.65 m has a BMI of 55 ÷ (1.65 × 1.65) = 55 ÷ 2.7225 ≈ 20.2 kg/m², which falls within the normal weight range.
例如，一名体重 55 kg、身高 1.65 m 的学生，BMI 为 55 ÷ (1.65 × 1.65) = 55 ÷ 2.7225 ≈ 20.2 kg/m²，属于正常体重范围。
4. Speed, Distance and Time | 速度、距离与时间
The relationship between speed, distance and time is fundamental to measuring performance in many sports. Speed is the rate at which someone covers a distance. Calculating speed allows you to compare performances over different distances and durations.
速度、距离和时间之间的关系是衡量许多运动项目表现的基础。速度是指人移动一段距离的速率。计算速度可以让你比较不同距离和持续时间下的表现。
Speed = Distance ÷ Time
速度 = 距离 ÷ 时间
If a runner covers 100 metres in 12.5 seconds, speed = 100 m ÷ 12.5 s = 8.0 m/s. You can also rearrange the formula: Distance = Speed × Time, and Time = Distance ÷ Speed. Always ensure units are consistent.
如果一名跑步运动员用 12.5 秒跑完 100 米，速度 = 100 m ÷ 12.5 s = 8.0 m/s。你也可以对公式进行变形：距离 = 速度 × 时间，时间 = 距离 ÷ 速度。务必确保单位一致。
5. Acceleration | 加速度
Acceleration measures how quickly velocity changes. It is a vector quantity, meaning direction matters. In sport, positive acceleration means speeding up, while negative acceleration (deceleration) means slowing down. Useful for analysing sprint starts and changes of direction.
加速度衡量速度变化的快慢。它是一个矢量，意味着方向很重要。在运动中，正的加速度代表加速，而负的加速度（减速度）代表减速。加速度对于分析短跑起跑和改变方向很有用。
Acceleration = (Final velocity – Initial velocity) ÷ Time taken
加速度 = (最终速度 – 初始速度) ÷ 所用时间
A footballer increases velocity from 2 m/s to 7 m/s in 1.5 seconds. Acceleration = (7 – 2) ÷ 1.5 = 5 ÷ 1.5 ≈ 3.33 m/s².
一名足球运动员在 1.5 秒内将速度从 2 m/s 增加到 7 m/s。加速度 = (7 – 2) ÷ 1.5 = 5 ÷ 1.5 ≈ 3.33 m/s²。
6. Force and Newton’s Second Law | 力与牛顿第二定律
Newton’s Second Law explains the relationship between the force applied to an object, its mass and the acceleration produced. In physical education, we use it to understand how athletes generate force to overcome inertia or change direction. Greater force produces greater acceleration for the same mass.
牛顿第二定律解释了对一个物体施加的力、其质量和产生的加速度之间的关系。在体育中，我们用它来理解运动员如何产生力以克服惯性或改变方向。在质量不变的情况下，更大的力会产生更大的加速度。
Force (N) = Mass (kg) × Acceleration (m/s²)
力 (N) = 质量 (kg) × 加速度 (m/s²)
If a tennis player accelerates a 0.057 kg ball at 20 m/s², the force applied is 0.057 × 20 = 1.14 N. This principle also underpins momentum and impulse calculations seen later in the course.
如果一名网球运动员使一个 0.057 kg 的球获得 20 m/s² 的加速度，施加的力为 0.057 × 20 = 1.14 N。这一原理也是课程稍后会讲到的动量和冲量计算的基础。
7. Moment of Force (Torque) and Levers | 力矩与杠杆
A moment is the turning effect of a force around a fulcrum. It is important when analysing how levers work in the human body. Levers allow us to amplify force or increase speed of movement. The size of the moment depends on the force applied and the distance from the pivot.
力矩是力绕支点产生的转动效应。在分析人体杠杆如何工作时，力矩非常重要。杠杆使我们能够增大力或提高运动速度。力矩的大小取决于所施加的力以及力到支点的距离。
Moment (Nm) = Force (N) × Distance from fulcrum (m)
力矩 (Nm) = 力 (N) × 离支点的距离 (m)
In a bicep curl, if the bicep muscle pulls with 400 N at a distance of 0.04 m from the elbow joint (fulcrum), the effort moment = 400 × 0.04 = 16 Nm. The load moment must be equal or smaller for the movement to occur.
在肱二头肌弯举中，如果肱二头肌在离肘关节（支点）0.04 m 处以 400 N 的力牵拉，则动力矩 = 400 × 0.04 = 16 Nm。要使动作发生，阻力矩必须等于或小于动力矩。
8. Mechanical Advantage of Levers | 杠杆的机械利益
Mechanical advantage (MA) tells you how effectively a lever multiplies the effort force. A mechanical advantage greater than 1 means the lever amplifies the effort, making it easier to move a heavy load but over a shorter range. An MA less than 1 means the lever favours speed and range of movement over force.
机械利益 (MA) 说明杠杆放大动力的效果如何。机械利益大于 1 意味着杠杆放大了动力，使移动重负荷变得更容易，但活动范围较小。MA 小于 1 意味着杠杆牺牲力来换取速度和运动范围。
Mechanical Advantage = Effort arm ÷ Load arm
机械利益 = 动力臂 ÷ 阻力臂
In a second-class lever like the ankle joint during plantar flexion, the effort arm (from Achilles tendon to ankle) is typically longer than the load arm (ball of foot to ankle). If effort arm = 0.09 m and load arm = 0.03 m, MA = 0.09 ÷ 0.03 = 3. This helps push the body upwards efficiently.
在像踝关节跖屈这样的第二类杠杆中，动力臂（从跟腱到踝关节）通常比阻力臂（从前脚掌到踝关节）长。如果动力臂 = 0.09 m，阻力臂 = 0.03 m，则 MA = 0.09 ÷ 0.03 = 3。这有助于高效地将身体向上推起。
9. Work Done | 做功
Work is done when a force moves an object through a distance in the direction of the force. In sport, work represents the energy transferred during muscular contractions. It is measured in joules (J) and helps quantify training volume and effort over repeated movements.
当一个力使物体沿力的方向移动一段距离时，力就做了功。在运动中，功代表肌肉收缩期间传递的能量。它以焦耳 (J) 为单位，有助于量化重复动作中的训练量和负荷。
Work (J) = Force (N) × Distance moved in direction of force (m)
功 (J) = 力 (N) × 沿力的方向移动的距离 (m)
Lifting a 10 kg weight (gravity pull ~ 100 N) through a vertical height of 0.8 m requires work of 100 N × 0.8 m = 80 J. If the weight is lowered, negative work is done, which is equally relevant in eccentric training.
将一个 10 kg 的物体（重力约为 100 N）竖直上举 0.8 m，需要做功 100 N × 0.8 m = 80 J。如果放下重物，力做了负功，这在离心训练中同样重要。
10. Power Output | 功率输出
Power is the rate at which work is done or energy is transferred. A more powerful athlete can perform the same amount of work in a shorter time, which is crucial for explosive activities like sprinting, jumping and throwing. Power links strength with speed.
功率是做功或能量传递的速率。更强大的运动员能在更短的时间内完成同样的功，这对于短跑、跳跃和投掷等爆发性活动至关重要。功率将力量与速度联系了起来。
Power (W) = Work done (J) ÷ Time (s)
功率 (W) = 所做的功 (J) ÷ 时间 (s)
If a weightlifter does 2,000 J of work lifting a barbell in 1.5 s, their power output is 2,000 ÷ 1.5 ≈ 1,333 W (or about 1.33 kW). Because Work = Force × Distance, power can also be calculated as Force × Velocity when movement speed is constant.
如果一名举重运动员在 1.5 秒内举起杠铃做了 2,000 J 的功，其功率输出为 2,000 ÷ 1.5 ≈ 1,333 W（约 1.33 kW）。因为功 = 力 × 距离，当运动速度恒定时，功率也可用 力 × 速度 计算。
11. Training Load and the FITT Principle | 训练负荷与 FITT 原则
Training load is a key concept for planning and monitoring exercise. The FITT principle (Frequency, Intensity, Time, Type) is used to manipulate load. A simple way to estimate weekly training load is to multiply training volume by perceived intensity, often expressed as session RPE times duration in minutes.
训练负荷是规划和监控运动的关键概念。FITT 原则（频率、强度、时间、类型）用于调控负荷。估算周训练负荷的一个简单方法是将训练量与主观强度相乘，通常表示为课次 RPE × 持续时间（分钟）。
Training Load = Session RPE × Duration (minutes)
训练负荷 = 课次 RPE × 持续时间（分钟）
If a student rates their 45-minute football session as 7 on the modified Borg CR10 RPE scale, the session training load = 7 × 45 = 315 arbitrary units (AU). Summing all sessions gives a weekly load, which helps prevent overtraining.
如果一名学生在改良的博格 CR10 RPE 量表上将 45 分钟的足球课评为 7，那么该课次的训练负荷 = 7 × 45 = 315 任意单位 (AU)。将所有课次相加即可得到周负荷，这有助于预防过度训练。
12. Calculation of Velocity from Displacement-Time Graphs | 从位移-时间图计算速度
In movement analysis, the gradient of a displacement–time graph gives velocity. For uniform motion, the slope is constant, giving average velocity. In more complex movements, the tangent at a point shows instantaneous velocity. This graphical skill supports the interpretation of sprint performances.
在动作分析中，位移-时间图的斜率代表速度。对于匀速运动，斜率恒定，给出的是平均速度。在更复杂的运动中，某一点的切线斜率表示瞬时速度。这种图形技能有助于解读短跑表现。
Velocity = Change in displacement ÷ Change in time (slope)
速度 = 位移变化量 ÷ 时间变化量（斜率）
If a 30-metre sprint phase is plotted, and the steepest part of the graph shows a rise of 10 m over 1.2 s, the instantaneous velocity is 10 ÷ 1.2 ≈ 8.33 m/s. Velocity-time graphs further give acceleration from the slope and displacement from the area under the graph.
如果要绘制 30 米短跑阶段图，图中最陡的部分显示 1.2 秒内位移上升了 10 米，则瞬时速度约为 10 ÷ 1.2 ≈ 8.33 m/s。速度-时间图还能从斜率求出加速度，从图下面积求出位移。
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