📚 Year 10 CIE PE Formula & Theorem Quick Reference Guide | Year 10 CIE 体育 公式定理速查手册
This quick reference guide pulls together the most important formulas and physical theorems you need for the Year 10 CIE Physical Education course. From heart rate calculations to biomechanics and energy expenditure, every equation is presented with a clear explanation of the terms and how it is used in sport and exercise science.
本速查手册汇总了 Year 10 CIE 体育课程中最重要的公式和物理定理。从心率计算到生物力学和能量消耗，每个公式都配有清晰的术语解释，并说明其在运动和锻炼科学中的使用方式。
1. Cardiovascular Formulas | 心血管系统公式
Heart rate measurements form the basis of training intensity prescription. The age-predicted maximum heart rate provides a simple starting point, while the Karvonen method integrates resting heart rate for more personalised targets.
心率测量是制定训练强度的基础。年龄预测最大心率提供了一个简单的起点，而卡氏公式结合静息心率后可得出更具个性化的目标心率。
Maximum heart rate (HRmax) can be estimated by subtracting the athlete's age from 220. This is a population average and individual variation exists.
HRmax = 220 − age (years)
最大心率（HRmax）可通过 220 减去运动员的年龄来估算。这是人群平均值，个体之间存在差异。
Heart rate reserve (HRR) is the difference between maximum and resting heart rate (HRrest). It indicates the available heart rate range that can be used during exercise.
HRR = HRmax − HRrest
心率储备（HRR）是最大心率与静息心率（HRrest）之差，代表运动中可用的心率范围。
Target heart rate (THR) using the Karvonen formula incorporates resting heart rate to prescribe exercise intensity more accurately. The intensity is expressed as a decimal (e.g. 0.60 for 60%).
THR = HRR × intensity + HRrest
采用卡氏公式计算目标心率（THR）能整合静息心率，从而更精准地设定运动强度。强度用小数表示（如 0.60 代表 60%）。
2. Body Composition & Health Indicators | 身体成分与健康指标
Body Mass Index (BMI) and Waist-to-Hip Ratio (WHR) are simple field measures that help assess weight-related health risks and fat distribution patterns.
身体质量指数（BMI）和腰臀比（WHR）是简单的现场测量指标，有助于评估与体重相关的健康风险及脂肪分布模式。
Body Mass Index is calculated from weight (kg) divided by the square of height (m). It categorises individuals as underweight, normal, overweight or obese.
BMI = weight (kg) / height² (m²)
身体质量指数的计算方式为体重（kg）除以身高（m）的平方，可据此将个体分为偏瘦、正常、超重或肥胖。
Waist-to-Hip Ratio is the waist circumference divided by the hip circumference. It provides an indicator of central adiposity and associated cardiovascular risk.
WHR = waist circumference (cm) / hip circumference (cm)
腰臀比即腰围除以臀围，可作为中心性肥胖及相关心血管风险的指标。
3. Linear Motion Formulas | 直线运动公式
Describing how an athlete moves in a straight line requires clear definitions of speed, velocity and acceleration. These equations underpin video analysis and performance evaluation.
描述运动员沿直线运动时需要明确定义速率、速度和加速度。这些方程是视频分析和运动表现评估的基础。
Average speed is the total distance covered divided by the time taken. It is a scalar quantity with no direction.
v = s / t
平均速率等于总距离除以所用时间。它是一个标量，没有方向。
Acceleration is the rate of change of velocity. When initial velocity (u) and final velocity (v) are known, acceleration can be found over the time interval (t).
a = (v − u) / t
加速度是速度的变化率。已知初速度 (u) 和末速度 (v) 以及时间 (t)，即可求出加速度。
An alternative equation links initial velocity, final velocity, acceleration and displacement (s) without requiring a time measurement.
v² = u² + 2as
该方程将初速度、末速度、加速度和位移 (s) 联系起来，无需测量时间。
4. Newton's Laws & Force | 牛顿定律与力
Newton's Laws explain how forces cause changes in motion. The most frequently used relationship in sport biomechanics is the second law, linking net force, mass and acceleration.
牛顿定律阐明了力如何引起运动的改变。运动生物力学中最常用的关系是第二定律，它将合力、质量和加速度联系起来。
Newton's second law: the acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass.
F = ma
牛顿第二定律：物体的加速度与所受合力成正比，与其质量成反比。
Weight is the force exerted on a mass by gravity. On Earth the gravitational field strength (g) is approximately 9.8 m/s².
W = mg
重力是地球引力对质量施加的力，重力场强度 (g) 约等于 9.8 m/s²。
5. Momentum & Impulse | 动量与冲量
Momentum describes the quantity of motion an object possesses. Changing momentum relies on the application of an impulse, which connects force and time in contact sports.
动量描述物体所具有的运动量。改变动量需要施加冲量，这在接触性运动中把力和时间联系起来。
Momentum (p) is the product of mass and velocity. A heavier or faster athlete will have greater momentum, making them harder to stop or change direction.
p = mv
动量 (p) 是质量与速度的乘积。体重更大或速度更快的运动员动量更大，更不容易被阻挡或改变方向。
Impulse equals the change in momentum. When a force (F) acts over a time interval (Δt), it changes the object's velocity from u to v.
FΔt = m(v − u)
冲量等于动量的变化量。当一个力 (F) 作用一段时间 (Δt) 时，会使物体的速度从 u 变为 v。
6. Work, Energy & Power | 功、能与功率
Energy transfer and work are central to understanding athletic performance, from sprinting to weightlifting. Mechanical energy exists as kinetic and potential forms, while power indicates how quickly work is done.
能量转移和功对于理解从冲刺到举重的运动表现至关重要。机械能分为动能和势能两种形式，而功率则体现做功的快慢。
Kinetic energy (KE) is the energy of motion. Even small increases in velocity lead to large increases in KE because velocity is squared.
KE = ½ mv²;
动能 (KE) 是运动的能量。由于速度被平方，即使速度小幅增加也会导致动能大幅增加。
Gravitational potential energy (PE) depends on mass, height and gravity. It represents stored energy that can be converted when an athlete descends.
PE = mgh
重力势能 (PE) 取决于质量、高度和重力，代表运动员下降时可转化为其他能量的储存能量。
Work is done when a force moves an object through a displacement in the direction of the force. Power is the rate of doing work. In sports, power is also the product of force and velocity when force is applied in the direction of motion.
W = Fd | P = W / t | P = Fv
力使物体沿力的方向发生位移时即做功。功率是做功的速率。在运动中，当力沿运动方向施加时，功率也等于力与速度的乘积。
7. Levers & Moments | 杠杆与力矩
The skeleton acts as a system of levers. Analysing moments helps to understand how muscle forces produce movement around a joint and how athletes can maximise mechanical advantage.
骨骼系统相当于一套杠杆。分析力矩有助于理解肌力如何围绕关节产生运动，以及运动员如何最大化力学优势。
A moment is the turning effect of a force. It depends on the size of the force and the perpendicular distance (d) from the pivot to the line of action of that force.
M = F × d
力矩是力的转动效应，取决于力的大小以及支点到力作用线的垂直距离 (d)。
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