Year 11 CCEA Physical Education: Formula & Theorem Quick Reference Handbook | Year 11 CCEA 体育：公式定理速查手册

📚 Year 11 CCEA Physical Education: Formula & Theorem Quick Reference Handbook | Year 11 CCEA 体育：公式定理速查手册

This quick reference handbook brings together all essential formulas, laws, and training principles for Year 11 CCEA Physical Education. Use it to check key equations for biomechanics, exercise physiology, and movement analysis at a glance.

本速查手册汇集了 Year 11 CCEA 体育课程中所有核心公式、定律和训练原则。你可以用它一站式查阅生物力学、运动生理学和动作分析的关键方程。

1. Speed, Velocity and Acceleration | 速率、速度与加速度

Speed is the rate of change of distance. It is a scalar quantity measured in metres per second (m/s).

速率是距离变化的快慢。它是标量，单位为米每秒 (m/s)。

Speed = Distance ÷ Time

Velocity is the rate of change of displacement, making it a vector quantity with both magnitude and direction.

速度是位移变化的快慢，属于矢量，既有大小也有方向。

Velocity = Displacement ÷ Time

Acceleration describes how quickly velocity changes. A positive value means speeding up; a negative value (deceleration) means slowing down.

加速度描述速度变化的快慢。正值表示加速，负值（减速度）表示减速。

Acceleration = (Final Velocity – Initial Velocity) ÷ Time

Practical example: a 100 m sprinter covers the distance in 10.0 s. Average speed = 100 m / 10.0 s = 10.0 m/s. If her velocity changes from 0 m/s to 10 m/s in 2.0 s, acceleration = (10 m/s – 0 m/s) / 2.0 s = 5.0 m/s².

实际例子：一名百米短跑运动员用时 10.0 s，平均速率 = 100 m / 10.0 s = 10.0 m/s。如果她在 2.0 s 内速度从 0 m/s 提升到 10 m/s，加速度 = (10 m/s – 0 m/s) / 2.0 s = 5.0 m/s²。

2. Force, Mass, Weight and Momentum | 力、质量、重量与动量

Force causes an object to accelerate. It is measured in newtons (N) and follows Newton’s second law.

力使物体产生加速度，单位为牛顿 (N)，遵循牛顿第二定律。

Force = Mass × Acceleration (F = m × a)

Weight is the force due to gravity acting on a mass. On Earth, the gravitational field strength (g) is 9.8 m/s², often rounded to 10 m/s² in exams.

重量是重力作用于质量所产生的力。地球的重力场强度 (g) 约为 9.8 m/s²，考试中常取 10 m/s²。

Weight = Mass × Gravitational Field Strength (W = m × g)

Momentum is ‘mass in motion’ and is especially useful when analysing collisions and tackles in sport.

动量是“运动中的质量”，在分析体育运动中的碰撞和擒抱时特别有用。

Momentum = Mass × Velocity (p = m × v)

For example, a 70 kg rugby player sprinting at 8 m/s has momentum = 70 kg × 8 m/s = 560 kg m/s. The same player hitting a stationary opponent transfers a large impulse.

例如，一名 70 kg 的橄榄球运动员以 8 m/s 冲刺，动量 = 70 kg × 8 m/s = 560 kg m/s。该运动员撞击静止的对手时会传递很大的冲量。

3. Newton’s Laws of Motion | 牛顿运动定律

Newton’s First Law (Inertia): An object remains at rest or in uniform motion unless acted upon by an external force. In sport, a football stays still until kicked; a sliding puck continues on ice until friction or a stick stops it.

牛顿第一定律（惯性定律）：物体保持静止或匀速直线运动，除非受到外力作用。在运动中，足球被踢之前静止；冰球在冰面滑行直到摩擦或球杆使其停下。

Newton’s Second Law: Acceleration is directly proportional to force and inversely proportional to mass (F = m × a). This explains why a lighter tennis ball accelerates more than a shot put when the same force is applied.

牛顿第二定律：加速度与力成正比，与质量成反比 (F = m × a)。这解释了为什么施加相同的力时，轻的网球比铅球加速更快。

Newton’s Third Law: For every action there is an equal and opposite reaction. When a swimmer pushes water backwards, the water pushes the swimmer forwards.

牛顿第三定律：每个作用力都会产生一个大小相等、方向相反的反作用力。游泳者向后推水，水则向前推游泳者。

4. Moments and Levers | 力矩与杠杆

A moment is the turning effect of a force around a fulcrum. It depends on the size of the force and its perpendicular distance from the pivot.

力矩是力绕支点产生的转动效应，取决于力的大小及其到支点的垂直距离。

Moment = Force × Perpendicular Distance from Fulcrum

In the human body, joints act as fulcrums for levers. First-class levers have the fulcrum between effort and load (e.g., neck raising the head). Second-class levers have the load between fulcrum and effort (e.g., standing on tiptoes – ball of foot is fulcrum, load is body weight). Third-class levers have the effort between fulcrum and load (e.g., biceps curl – elbow is fulcrum, effort from biceps, load in the hand).

在人体中，关节充当杠杆的支点。第一类杠杆的支点在施力与负荷之间（如颈部抬头动作）。第二类杠杆的负荷在支点和施力之间（如踮脚尖——前脚掌为支点，体重为负荷）。第三类杠杆的施力在支点与负荷之间（如肱二头肌弯举——肘为支点，肱二头肌施力，手上为负荷）。

Most body levers are third-class, favouring speed and range of movement over force.

人体大多数杠杆属于第三类，这种结构更利于速度和动作幅度而非省力。

5. Mechanical Advantage of Levers | 杠杆机械效益

Mechanical advantage (MA) tells you how much a lever multiplies the effort applied. It is the ratio of the effort arm length to the resistance arm length.

机械效益 (MA) 表示杠杆将施力放大的倍数，它是施力臂长度与阻力臂长度的比值。

Mechanical Advantage = Effort Arm ÷ Resistance Arm

An MA greater than 1 means the lever multiplies effort (good for strength), as often found in second-class levers. An MA less than 1 means a large effort is needed but the load moves further and faster, typical of third-class levers.

MA 大于 1 表示杠杆可以省力（有利于产生力量），常见于第二类杠杆。MA 小于 1 则需要较大的施力，但负荷移动得更远、更快，典型于第三类杠杆。

Example: In a wheelbarrow (second-class lever), the effort arm from handles to wheel is 1.2 m, resistance arm from COG of load to wheel is 0.4 m. MA = 1.2 m ÷ 0.4 m = 3.0, meaning the effort force required is one‑third of the load.

例子：在手推车（第二类杠杆）中，施力臂（把手到轮轴）为 1.2 m，阻力臂（负荷重心到轮轴）为 0.4 m。MA = 1.2 m ÷ 0.4 m = 3.0，意味着所需施力仅为负荷的三分之一。

6. Cardiovascular Measures: Heart Rate, Stroke Volume and Cardiac Output | 心血管指标：心率、每搏输出量与心输出量

Cardiac output is the volume of blood pumped by the heart per minute. It is a key indicator of aerobic fitness and can increase dramatically during exercise.

心输出量是心脏每分钟泵出的血液量，是有氧适能的关键指标，运动时可大幅增加。

Cardiac Output = Stroke Volume × Heart Rate (Q = SV × HR)

Stroke volume is the amount of blood ejected per beat (ml/beat); resting values are around 70 ml for an average adult and can rise to 120–150 ml during intense exercise. Heart rate (HR) is measured in beats per minute (bpm).

每搏输出量是每次心跳泵出的血液量（毫升/次）；普通成年人安静时约 70 ml，剧烈运动时可升至 120–150 ml。心率 (HR) 以每分钟心跳次数 (bpm) 测量。

Example: At rest, HR = 70 bpm, SV = 70 ml → Q = 70 × 70 = 4 900 ml/min ≈ 4.9 L/min. During maximal exercise, HR = 190 bpm, SV = 130 ml → Q = 190 × 130 = 24 700 ml/min ≈ 24.7 L/min, showing the heart’s enormous capacity to meet oxygen demands.

例子：安静时 HR = 70 bpm, SV = 70 ml → Q = 70 × 70 = 4 900 ml/min ≈ 4.9 L/min。最大运动时 HR = 190 bpm, SV = 130 ml → Q = 190 × 130 = 24 700 ml/min ≈ 24.7 L/min，可见心脏满足氧气需求的巨大能力。

7. Training Heart Rate Zones (Karvonen Formula) | 训练心率区间（卡氏公式）

To optimise training, athletes use target heart rate zones based on heart rate reserve (HRR). The Karvonen formula calculates exercise intensity with greater precision than using maximum heart rate alone.

为优化训练，运动员根据心率储备 (HRR) 使用目标心率区间。卡氏公式计算运动强度比仅用最大心率更加精准。

Maximum Heart Rate (MHR) ≈ 220 – Age

Heart Rate Reserve (HRR) = MHR – Resting Heart Rate (RHR)

Target Heart Rate = (HRR × %Intensity) + RHR

For a 16‑year‑old with RHR = 60 bpm, MHR ≈ 220 – 16 = 204 bpm. HRR = 204 – 60 = 144 bpm. For aerobic training at 65% intensity: Target HR = (144 × 0.65) + 60 = 153.6 ≈ 154 bpm. For high‑intensity intervals at 85%: (144 × 0.85) + 60 = 182.4 ≈ 182 bpm.

对于一位 16 岁、安静心率 60 bpm 的学生：MHR ≈ 220 – 16 = 204 bpm，HRR = 204 – 60 = 144 bpm。若进行 65% 强度的有氧训练：目标心率 = (144 × 0.65) + 60 = 153.6 ≈ 154 bpm。若进行 85% 的高强度间歇训练：(144 × 0.85) + 60 = 182.4 ≈ 182 bpm。

Common training zones include: 50–60% HRR for recovery, 60–70% for aerobic base, 70–80% for threshold training, and 80–90% for high‑intensity intervals.

常见训练区间：50–60% HRR 用于恢复，60–70% 用于有氧基础，70–80% 用于阈值训练，80–90% 用于高强度间歇。

8. Body Mass Index (BMI) and Simple Fitness Indices | 身体质量指数与简易体适能指数

BMI gives a rough classification of body weight status and is widely used in health screening.

BMI 提供体重状况的粗略分类，广泛用于健康筛查。

BMI = Weight (kg) ÷ Height² (m)

Example: A person weighing 65 kg with a height of 1.70 m has BMI = 65 ÷ (1.70 × 1.70) = 65 ÷ 2.89 ≈ 22.5 kg/m², which falls into the ‘healthy weight’ range (18.5–24.9).

例子：一个体重 65 kg、身高 1.70 m 的人，BMI = 65 ÷ (1.70 × 1.70) = 65 ÷ 2.89 ≈ 22.5 kg/m²，属于“健康体重”范围 (18.5–24.9)。

Other rapid fitness indices often used in PE include the Cooper 12‑minute run for estimating VO₂ max, and the Harvard Step Test for cardiovascular endurance, where a Fitness Index is calculated:

体育课常使用的其他简易体适能指数包括用于估算最大摄氧量的库珀 12 分钟跑，以及用于评估心血管耐力的哈佛台阶测试，其体适能指数公式为：

Fitness Index = (Duration of exercise in seconds × 100) ÷ (2 × sum of three pulse counts)

(Note: The formula may vary slightly in different exam boards; CCEA provides the required version in data booklets.)

（注：不同考评局公式可能略有不同；CCEA 会在数据手册中提供所需版本。）

9. Work, Power and Energy in Sport | 运动中的功、功率与能量

Work is done when a force moves an object. In the gym, every time you lift a weight you perform mechanical work.

力使物体移动时便做了功。在健身房，每次举起重物你都在做机械功。

Work = Force × Distance moved in the direction of the force (W = F × d)

Power is the rate at which work is done. A more powerful athlete completes the same amount of work in less time.

功率是做功的快慢。爆发力更强的运动员能在更短时间内完成相同的功。

Power = Work ÷ Time (P = W / t)

In sport, energy is measured in joules (J). For example, lifting a 20 kg weight (200 N force if g = 10 m/s²) through 0.5 m does work W = 200 N × 0.5 m = 100 J. If this lift takes 0.5 s, power output = 100 J / 0.5 s = 200 W.

体育运动中能量以焦耳 (J) 计量。例如，举起 20 kg 重物（若 g = 10 m/s² 则受力 200 N）0.5 m，做功 W = 200 N × 0.5 m = 100 J。若该上举耗时 0.5 s，输出功率 = 100 J / 0.5 s = 200 W。

10. Principles of Training (FITT and SPORRT) | 训练原则（FITT 与 SPORRT）

The FITT principle helps design effective training programmes by manipulating Frequency, Intensity, Time and Type. These variables are adjusted progressively to ensure overload and adaptation.

FITT 原则通过调控频率、强度、时间和类型帮助设计有效的训练计划。渐进调整这些变量以确保超负荷与适应。

Frequency – how often training occurs per week.
Intensity – how hard the exercise is (e.g., %HR max, rate of perceived exertion).
Time – duration of each session or interval.
Type – the mode of exercise (e.g., continuous, interval, circuit).

频率 (Frequency) – 每周训练的次数。
强度 (Intensity) – 运动的困难程度（如最大心率百分比、自感用力等级）。
时间 (Time) – 每次训练或间歇的持续时间。
类型 (Type) – 运动方式（如持续训练、间歇训练、循环训练）。

The extended SPORRT framework adds Specificity, Progression, Overload, Reversibility, Rest and Tedium. Applying overload can be summarised: ‘To improve, a system must be stressed beyond its accustomed level.’ This is the core theorem of physiological adaptation.

扩展的 SPORRT 框架加入了专门性、渐进性、超负荷、可逆性、恢复和单调性。超负荷原则可概括为：“要获得进步，系统必须承受超过习惯水平的压力。”这是生理适应的核心定理。

Record a simple overload progression: a runner increases weekly mileage by no more than 10% to reduce injury risk while challenging the aerobic system.

记录一个简单的超负荷进阶：跑步者每周增加不超过 10% 的跑量，以降低受伤风险同时刺激有氧系统。

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Year 11 CCEA Physical Education: Formula & Theorem Quick Reference Handbook | Year 11 CCEA 体育：公式定理速查手册