📚 KS3 CCEA Physical Education: Formula and Theorem Quick Reference Handbook | KS3 CCEA 体育：公式定理速查手册
This handbook provides a concise collection of essential formulas, equations, and key biomechanical principles that underpin the KS3 CCEA Physical Education curriculum. Understanding these quantitative relationships helps you analyse human movement, training, and health-related fitness. Use it as a quick reference for homework, revision, and practical investigations.
本手册汇集了支撑KS3 CCEA体育课程的基本公式、方程和关键生物力学原理。理解这些定量关系有助于你分析人体运动、训练和与健康相关的体能。可将其作为作业、复习和实际研究的快速参考。
1. Maximum Heart Rate (MHR) | 最大心率（MHR）
Maximum heart rate (MHR) is the highest number of beats per minute your heart can achieve during all-out effort. It is widely estimated using a simple formula based on age, and it forms the foundation for setting training zones.
最大心率（MHR）是指心脏在全力运动时每分钟所能达到的最高跳动次数。通常根据年龄用一个简单公式估算，它是设定训练区间的基础。
MHR = 220 − age
0 − 12 = 208 bpm. Coaches and athletes use this value to tailor exercise intensity safely.
例如，一名12岁学生的估算最大心率是220 − 12 = 208次/分钟。教练和运动员利用该数值安全地调整运动强度。
2. Target Heart Rate Zone | 靶心率区间
To improve cardiovascular fitness effectively, you need to exercise within a target heart rate zone. A straightforward method calculates this as a percentage of your maximum heart rate. Moderate-intensity work typically uses 60-70% MHR, while vigorous activity targets 70-85% MHR.
为了有效提高心血管健康，你需要在靶心率区间内运动。一种简单的方法是将最大心率的某个百分比作为靶心率。中等强度运动通常使用60-70% MHR，而剧烈运动则瞄准70-85% MHR。
Target HR = MHR × intensity (as a decimal)
If a 13-year-old (MHR 207 bpm) wants to train at 75% onen formula incorporates resting heart rate: Target HR = ((MHR − RHR) × intensity) + RHR.
如果一名13岁学生（MHR 207 bpm）想以75%的强度训练，靶心率为207 × 0.75 = 155次/分钟。为了更精确的设定，卡沃宁公式引入了安静心率：靶心率 = ((MHR − RHR) × 强度) + RHR。
3. Body Mass Index (BMI) | 身体质量指数（BMI）
Body Mass Index is a screening tool used to categorise a person's weight relative to their height. It helps identify whether an individual is underweight, healthy weight, overweight or obese, though it does not distinguish between muscle and fat.
身体质量指数是一种筛查工具，依据身高对体重进行分类。它有助于识别一个人是过轻、健康体重、超重还是肥胖，但不能区分肌肉和脂肪。
BMI = weight (kg) ÷ (height (m))²
n KS3 contexts, this formula helps students understand the link between body composition and performance.
例如，一名学生体重45千克，身高1.50米，其BMI为45 ÷ (1.50 × 1.50) = 45 ÷ 2.25 = 20.0 kg/m²。在KS3情境中，该公式帮助学生理解身体成分与运动表现之间的联系。
4. Speed | 速度
Speed is a scalar quantity that measures how fast an object or person is moving. In sport, it is often calculated over a set distance to evaluate sprinting, swimming or cycling performance.
速度是标量，用来衡量物体或人移动的快慢。在体育运动中，通常通过设定距离来计算速度，以评估短跑、游泳或自行车运动的表现。
Speed = distance ÷ time
s sometimes express speed in metres per second (m/s) or kilometres per hour (km/h) for easier comparison.
如果一名跑步运动员用12.5秒跑完100米，其速度为100 ÷ 12.5 = 8 m/s。教练有时用米每秒（m/s）或千米每小时（km/h）表示速度，以便比较。
5. Acceleration | 加速度
Acceleration is the rate at which velocity changes. In games like football or netball, rapid acceleration helps players beat opponents to the ball. It can be positive (speeding up) or negative (deceleration).
加速度是速度变化的快慢。在足球或无挡板篮球等比赛中，快速加速有助于球员抢在对手之前触球。加速度可以是正的（加速）或负的（减速）。
a = (v − u) ÷ t
ses velocity from 0 m/s to 8 m/s in 2 seconds has an acceleration of (8 − 0) ÷ 2 = 4 m/s².
其中v是末速度，u是初速度，t是所用时间。一名短跑运动员在2秒内将速度从0 m/s提升到8 m/s，其加速度为(8 − 0) ÷ 2 = 4 m/s²。
6. Newton's Second Law of Motion | 牛顿第二运动定律
Newton's Second Law explains the relationship between force, mass and acceleration. In sport, applying greater force to an object (like a shot put or a hockey ball) produces more acceleration, assuming mass stays constant.
牛顿第二定律解释了力、质量和加速度之间的关系。在体育运动中，假设质量不变，对物体（如铅球或曲棍球）施加更大的力会产生更大的加速度。
F = m × a
s). When designing training drills, understanding this law helps students appreciate how technique affects force production.
一个质量0.16千克的曲棍球以50 m/s²的加速度被击打，施加的力为0.16 × 50 = 8牛顿。在设计训练方案时，理解该定律有助于学生领悟技术动作如何影响力的大小。
7. Work Done | 做功
In physics, work is done when a force moves an object in the direction of the force. In sports, work is accomplished every time a weight is lifted, a body is propelled upwards, or resistance is overcome.
在物理学中，当力使物体沿力的方向移动时，就做了功。在体育运动中，每举一次重物、将身体向上推进或克服阻力时，都在做功。
W = F × d
ward force of 500 N over a vertical distance of 0.8 m, the work done is 500 × 0.8 = 400 J.
其中W代表功，单位为焦耳（J）；F代表力，单位为牛顿（N）；d代表移动的距离，单位为米。如果举重运动员施加500 N的向上力，垂直移动0.8米，做的功为500 × 0.8 = 400 J。
8. Power | 功率
Power measures how quickly work is done or energy is transferred. Explosive athletes require high power output. Power can be calculated using work and time, or directly from force and velocity.
功率衡量做功或能量传递的快慢。爆发力强的运动员需要高功率输出。功率可利用功和时间，或直接通过力和速度来计算。
P = W ÷ t or P = F × v
at a velocity of 3 m/s, the power generated is 1000 × 3 = 3000 W (3 kW). This explains why strength and speed are both essential for jumping ability.
一名篮球运动员进行垂直跳时，如果腿部在起跳期间产生平均1000 N的力，且质心以3 m/s的速度向上移动，则产生的功率为1000 × 3 = 3000瓦。这解释了为什么力量和速度对弹跳能力都至关重要。
9. Principle of Moments | 力矩原理
The principle of moments states that for a lever to be in balance (rotational equilibrium), the sum of clockwise moments about a pivot must equal the sum of anticlockwise moments. This principle is fundamental to understanding body levers and sports equipment.
力矩原理指出，要使杠杆平衡（转动平衡），绕支点的顺时针力矩之和必须等于逆时针力矩之和。这一原理是理解人体杠杆和运动器材的基础。
Clockwise moment = Anticlockwise moment
F₁ × d₁ = F₂ × d₂
m, this explains how a small force from the biceps can lift a heavier load in the hand, due to different lever arms.
在跷跷板上，一个重300 N的孩子坐在距支点2米处，可以与一个重600 N的孩子坐在另一侧1米处平衡，因为300 × 2 = 600 × 1。在人体手臂中，这解释了为何肱二头肌较小的力能举起手中较重的负荷，因为力臂不同。
10. Kinetic Energy | 动能
Kinetic energy is the energy an object possesses due to its motion. In sport, a faster-moving ball or sprinter has more kinetic energy, which must be absorbed when stopped or caught.
动能是物体由于运动而具有的能量。在运动中，快速移动的球或冲刺的运动员拥有更多动能，在停下或接住时必须被吸收。
KE = ½ × m × v²
decelerate this energy when making a save, which links to the concepts of work and force.
对于一颗0.43千克的足球以20 m/s的速度运动，动能为½ × 0.43 × (20)² = 0.215 × 400 = 86 J。守门员在扑救时必须使这些能量减速，这与功和力的概念相关。
11. Gravitational Potential Energy | 重力势能
Gravitational potential energy (GPE) is the energy stored in an object because of its height above the ground. In activities like high jump, gymnastics or climbing, athletes convert muscular work into GPE.
重力势能（GPE）是物体由于位于地面以上一定高度而储存的能量。在跳高、体操或攀岩等活动中，运动员将肌肉做的功转化为重力势能。
GPE = m × g × h
his energy is converted to kinetic energy on the way down, illustrating energy conservation.
地球表面附近的重力场强度g约为10 N/kg。一名体操运动员质量40千克，跳至2.5米高度所获得的重力势能为40 × 10 × 2.5 = 1000 J。下落时这些能量转化为动能，体现了能量守恒。
12. Levers and Mechanical Advantage | 杠杆与机械效益
Levers in the human body and sports equipment allow us to multiply force or speed. Mechanical advantage (MA) compares the load (resistance) to the effort applied. It determines whether a lever system favours strength or range of movement.
人体内部和运动器材中的杠杆使我们能够增大力或速度。机械效益（MA）比较负荷（阻力）与施力的大小，它决定一个杠杆系统是省力还是增大运动幅度。
MA = Load ÷ Effort
-class lever like the ankle joint during a calf raise, the load is between the fulcrum and the effort, producing an MA greater than 1 and allowing the body to be lifted with less muscular force.
如果用撬棍需施力100 N才能抬起400 N的重物，机械效益为400 ÷ 100 = 4。在像提踵时的踝关节这样的第二类杠杆中，负荷位于支点和施力之间，产生的MA大于1，使得用较小的肌肉力量就能抬起身体。
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