📚 IGCSE WJEC PE: Quick Reference Handbook of Formulas & Principles | IGCSE WJEC 体育：公式定理速查手册
This quick reference handbook brings together all the essential formulas, equations and key principles you need to master for IGCSE WJEC Physical Education. From heart rate zones to biomechanics, use these clear summaries to support your revision and problem solving.
这本速查手册汇集了 IGCSE WJEC 体育课程中你必须掌握的所有关键公式、方程和重要原理。从心率区间到生物力学，借助这些清晰的总结来支持你的复习与解题。
1. Maximum Heart Rate & Training Zones | 最大心率与训练区间
Estimating maximum heart rate (HRmax) is the first step to setting training intensities. The simplest formula uses your age.
估算最大心率 (HRmax) 是设定训练强度的第一步。最简单的公式使用你的年龄。
HRmax (bpm) = 220 − age (years)
Once you know HRmax, you can calculate training zones as percentages of this value. A typical aerobic training zone for improving cardiovascular fitness lies between 60% and 80% of HRmax. The anaerobic threshold zone is approximately 80–90% HRmax, while a general health zone sits at 50–60% HRmax.
一旦知道 HRmax，你就可以将此值的百分比作为训练区间进行计算。改善心血管健康的典型有氧训练区间位于 HRmax 的 60% 至 80% 之间。无氧阈区间约为 HRmax 的 80–90%，而一般健康区间则处于 HRmax 的 50–60%。
2. Karvonen Formula for Target Heart Rate | 卡沃宁目标心率公式
The Karvonen method uses your resting heart rate (HRrest) to give a more personalised training zone that reflects your fitness level.
卡沃宁法利用你的安静心率 (HRrest) 得出更个性化的训练区间，更能反映你的体能水平。
Target HR = ((HRmax − HRrest) × % intensity) + HRrest
For example, if an athlete has HRmax of 190 bpm, HRrest of 60 bpm and wants to train at 70% 0 = 151 bpm. This formula is especially useful for programming aerobic endurance sessions.
例如，一名运动员的 HRmax 为 190 bpm，HRrest 为 60 bpm，想以 70% 的强度训练，则目标心率为 ((190 − 60) × 0.7) + 60 = 151 bpm。此公式对于制定有氧耐力训练课尤为有用。
3. Body Mass Index (BMI) | 身体质量指数
BMI is a simple screening tool used to classify weight status in relation to height. It is widely referenced in health and fitness assessments.
BMI 是一项简单的筛查工具，用于根据身高对体重状况进行分类，广泛应用于健康与体适能评价。
BMI = mass (kg) ÷ (height (m))²
÷ (1.75)² ≈ 22.9 kg/m². Standard classifications are: underweight below 18.5, normal 18.5–24.9, overweight 25–29.9 and obese 30+.
例如，体重 70 kg、身高 1.75 m 的人，其 BMI 为 70 ÷ (1.75)² ≈ 22.9 kg/m²。标准分类为：偏瘦低于 18.5，正常 18.5–24.9，超重 25–29.9，肥胖 30 及以上。
4. Basal Metabolic Rate (BMR) | 基础代谢率
BMR represents the energy your body needs at complete rest to maintain vital functions. A quick estimation can be made using body mass.
BMR 代表身体在完全休息状态下维持生命机能所需的能量。可使用体重快速估算。
BMR (kcal/day) ≈ 1.0 × body mass (kg) × 24 (males)
BMR (kcal/day) ≈ 0.9 × body mass (kg) × 24 (females)
These coefficients reflect average differences in body composition. Knowing BMR helps when calculating total daily energy expenditure (TDEE) by adding physical activity multipliers.
这些系数反映身体成分的平均差异。了解 BMR 后，再加上身体活动乘数，即可计算每日总能量消耗 (TDEE)。
5. Linear Motion: Speed, Velocity & Acceleration | 线运动：速率、速度与加速度
In sport, understanding how quickly a performer moves or how rapidly their motion changes is fundamental. Average speed is a scalar, while velocity is a vector quantity.
在运动中，了解运动员移动的快慢或动作变化的快慢是基础。平均速率是标量，而速度是矢量。
speed = distance ÷ time v = d / t
acceleration = change in velocity ÷ time a = (v − u) / t
where u is initial velocity, v final velocity, t time, s displacement and a acceleration.
对于匀加速运动，还适用运动学方程：v = u + at，s = ut + ½ at²，以及 v² = u² + 2as，其中 u 为初速度，v 为末速度，t 为时间，s 为位移，a 为加速度。
6. Force & Newton's Second Law | 力与牛顿第二定律
The relationship between force, mass and acceleration is central to analysing sporting movements, from sprint starts to tackling.
力、质量与加速度之间的关系是分析从短跑起跑到擒抱等运动动作的核心。
F = m × a
vitational field strength (9.8 m/s² on Earth). When a resultant force acts on an object, it accelerates in the direction of the force; if forces are balanced, the object moves at constant velocity or remains stationary.
重量是由重力产生的力，计算公式为 W = m × g，其中 g 为重力场强（地球取 9.8 m/s²）。当一个合力作用于物体时，它将沿力的方向加速；若力相互平衡，则物体保持匀速或静止。
7. Work, Energy & Power | 功、能量与功率
These concepts explain how much effort is applied and how quickly energy is transferred in physical activities.
这些概念解释了在身体活动中施加了多少力以及能量转换的快慢。
work done (J) = force (N) × distance moved in direction of force (m)
kinetic energy (J) = ½ m v²
gravitational potential energy (J) = m g h
power (W) = work done ÷ time taken P = W / t
n also be expressed as force × velocity when the force is constant and parallel to motion.
一名举重运动员在 0.5 s 内完成 1000 J 的功，则产生 2000 W 的功率。当力恒定且与运动方向平行时，功率也可表示为力 × 速度。
8. Levers and Moments | 杠杆与力矩
The body moves through a system of bones acting as levers, with joints serving as fulcrums. Understanding lever classes helps analyse mechanical efficiency.
身体通过骨骼作为杠杆、关节作为支点的系统运动。理解杠杆类别有助于分析机械效率。
moment (Nm) = force (N) × perpendicular distance from fulcrum (m)
In a first-class lever the fulcrum lies between effort and load (e.g. neck extending). In a second-class lever the load is between fulcrum and effort (e.g. calf raise). In a third-class lever the effort is applied between the fulcrum and the load — the most common arrangement in the body (e.g. biceps curl).
在第一类杠杆中，支点在力点和阻力之间（如颈部后伸）。在第二类杠杆中，阻力在支点和力点之间（如提踵）。在第三类杠杆中，力作用在支点和阻力之间——这是人体最常见的排列（如肱二头肌弯举）。
9. Mechanical Advantage and Velocity Ratio | 机械利益与速度比
Mechanical advantage (MA) tells us how much a lever multiplies the effort force; velocity ratio (VR) compares the distances moved by effort and load.
机械利益 (MA) 告诉我们杠杆能将力放大多少；速度比 (VR) 则比较动力点与阻力点移动的距离。
MA = load (N) ÷ effort (N)
VR = distance moved by effort ÷ distance moved by load in the same time
Third-class levers have an MA less than 1, meaning they sacrifice force for speed and range of motion. In contrast, second-class levers give MA greater than 1, favouring force production.
第三类杠杆的 MA 小于 1，意味着它牺牲力量来换取速度和运动幅度。相反，第二类杠杆的 MA 大于 1，有利于产生力量。
10. Angular Motion | 角运动
Most human movements involve rotation around joints. Angular quantities describe how quickly bodies spin or rotate.
大多数人体运动都涉及绕关节的转动。角量用于描述身体旋转的快慢。
angular velocity ω = angular displacement (θ) / time (t)
linear velocity v = radius (r) × ω
angular acceleration α = (ω₂ − ω₁) / t
torque = force × perpendicular distance from axis
Moment of inertia (I) depends on mass distribution: bringing limbs close to the axis reduces I and increases angular velocity for the same angular momentum, as seen in spinning skaters or divers.
转动惯量 (I) 取决于质量分布：将肢体靠近转轴会减小 I，在相同角动量下增大角速度，如旋转的滑冰者或跳水运动员所示。
11. Projectile Motion | 抛体运动
Projectile motion describes the curved path of a body or object released into the air, governed by gravity, air resistance and release parameters.
抛体运动描述被抛入空中的身体或物体的曲线轨迹，受重力、空气阻力和出手参数支配。
range = (u² sin(2θ)) / g
maximum height = (u² sin²θ) / (2g)
Here u is the release velocity, θ the angle of release, and g the acceleration due to gravity. The optimal angle of release for maximum range on level ground is 45° in a vacuum, but air resistance and release height modify this in real sports.
此处 u 为出手速度，θ 为出手角度，g 为重力加速度。在真空中，达到最大水平位移的最佳出手角为 45°，但在真实运动中，空气阻力和出手高度会改变这一角度。
12. Training Principles: FITT and SPORT | 训练原则：FITT 与 SPORT
These two acronyms summarise the fundamental guidelines for designing safe and effective training programmes.
这两个缩写概括了设计安全有效训练计划的基本指导方针。
FITT stands for: Frequency (how often), Intensity (how hard), Time (how long), Type (mode of exercise). Adjusting any of these variables will change the training stimulus.
FITT 指：频率（多常训练）、强度（多艰苦）、时间（持续多久）、类型（运动模式）。调整任一变量都会改变训练刺激。
SPORT stands for: Specificity (training must match the activity), Progression (gradually increase workload), Overload (push beyond normal levels), Reversibility (fitness declines when training stops), Tedium (vary training to avoid boredom). Applying these principles helps optimize performance and prevent injury.
SPORT 指：专项性（训练必须匹配活动）、渐进性（逐步增加负荷）、超负荷（超出日常水平）、可逆性（一旦停止训练体能便会下降）、单调性（变换训练以避免乏味）。运用这些原则有助于优化表现并预防损伤。
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