📚 Year 11 Eduqas PE Formula & Theorem Quick Reference Handbook | 11年级 Eduqas 体育：公式定理速查手册
Mastering the essential formulas and biomechanical principles is a key part of success in Year 11 Eduqas GCSE Physical Education. This quick reference handbook gathers every important equation, law, and theorem you need to know – from heart rate calculations to levers, moments, and Newton’s laws. Use it to revise key numerical relationships and to understand how they apply to real sporting examples. Each section presents a formula or concept in English immediately followed by its Chinese equivalent, so you can build both your subject knowledge and your bilingual terminology.
掌握核心公式和生物力学原理是11年级 Eduqas GCSE 体育成功的关键。这本速查手册汇集了你需要掌握的所有重要方程、定律和定理——从心率计算到杠杆、力矩以及牛顿定律。可以利用它来复习关键的数值关系，并理解它们如何应用于真实的运动实例。每个部分都以英文呈现公式或概念，紧接着是其对应的中文解释，有助于你同时积累学科知识和双语术语。
1. Heart Rate & Cardiac Output | 心率与心输出量
Maximum Heart Rate (MHR) = 220 − age (years) – to predict the upper limit of heart beats per minute during exhaustive exercise. For a 16‑year‑old, MHR ≈ 204 bpm.
最大心率 (MHR) = 220 − 年龄（岁） – 通过这个简单的估计值，可以预测力竭运动时每分钟心跳的上限。16岁青少年的最大心率约为204次/分。
Karvonen Formula for Target Heart Rate: ) × exercise intensity) + resting HR. Intensity is expressed as a decimal (e.g. 0.7 for 70 %). This method gives a personalised training zone that accounts for fitness level.
卡沃宁目标心率公式：靶心率 = ((最大心率 − 静息心率) × 运动强度) + 静息心率。强度用小数表示（如70%为0.7）。该方法提供了一个考虑体能水平的个性化训练区间。
Cardiac Output (Q) = Heart Rate (HR) × Stroke Volume (SV) Stroke volume is the amount of blood pumped out of the left ventricle per beat. Cardiac output represents the total volume of blood pumped by the heart per minute, increasing dramatically during exercise.
心输出量 (Q) = 心率 (HR) × 每搏输出量 (SV) 每搏输出量是指左心室每次搏动泵出的血量。心输出量代表心脏每分钟泵出的血液总量，运动时会显著增加。
2. Minute Ventilation & Tidal Volume | 分钟通气量与潮气量
Minute Ventilation (VE) = Tidal Volume (TV) × Breathing Rate (BR) Tidal volume is the amount of air inhaled or exhaled during a normal breath. Breathing rate is the number of breaths per minute. During intense sport, both TV and BR rise, causing VE to increase from around 6 L/min at rest to over 100 L/min in elite athletes.
分钟通气量 (VE) = 潮气量 (TV) × 呼吸频率 (BR) 潮气量是每次正常呼吸时吸入或呼出的空气量。呼吸频率是每分钟呼吸的次数。在剧烈运动中，潮气量和呼吸频率均上升，使得分钟通气量从安静时约6升/分增至精英运动员的100升/分以上。
3. Body Mass Index (BMI) | 身体质量指数
BMI = weight (kg) ÷ height² (m²) y be asked to calculate BMI and interpret the result: underweight (<18.5), normal (18.5–24.9), overweight (25–29.9), or obese (≥30).
BMI = 体重(kg) ÷ 身高² (m²) 虽然它不能区分肌肉和脂肪，但BMI是一种广泛使用的筛查工具。在GCSE体育中，你可能需要计算BMI并解读结果：体重过轻(<18.5)、正常(18.5–24.9)、超重(25–29.9)或肥胖(≥30)。
4. Speed, Velocity & Acceleration | 速率、速度与加速度
Speed (m/s) = distance (m) ÷ time (s) Speed is a scalar quantity; it only describes how fast an athlete moves. A 100 m sprinter who runs 10.5 s has an average speed of about 9.52 m/s.
速率 (m/s) = 距离 (m) ÷ 时间 (s) 速率是标量，只描述运动员移动的快慢。一位100米短跑运动员用时10.5秒，其平均速率约为9.52 m/s。
Velocity (m/s) = displacement (m) ÷ time (s) Velocity is a vector – it includes direction. If a footballer runs 40 m East in 5 s, her velocity is 8 m/s East.
速度 (m/s) = 位移 (m) ÷ 时间 (s) 速度是矢量，包含方向。如果一位足球运动员5秒内向正东方向跑动了40米，她的速度为8 m/s 东。
Acceleration (m/s²) = (final velocity − initial velocity) ÷ time Acceleration measures the rate of change of velocity. A long jumper who accelerates from 4 m/s to 10 m/s in 2 seconds experiences an acceleration of 3 m/s².
加速度 (m/s²) = (末速度 − 初速度) ÷ 时间 加速度衡量速度变化的快慢。一位跳远运动员在2秒内从4 m/s加速到10 m/s，其加速度为3 m/s²。
5. Newton’s Laws of Motion | 牛顿运动定律
First Law (Inertia): A body remains at rest or in uniform motion unless acted upon by an external resultant force. In sport, a stationary ball stays still until kicked; a moving ball continues rolling until friction or a player stops it.
第一定律（惯性）：任何物体都将保持静止或匀速直线运动状态，除非受到外力作用。在运动中，静止的球保持不动直到被踢；滚动的球继续运动，直到摩擦力或有球员将其停下。
Second Law (F = ma): celeration (m/s²). The harder a tennis player strikes a ball (greater force), the greater its acceleration, provided the mass stays constant.
第二定律（F = ma）：物体的加速度与所受合外力成正比，与其质量成反比。力 (N) = 质量 (kg) × 加速度 (m/s²)。网球运动员击球越用力（力越大），球的加速度就越大，前提是质量不变。
Third Law (Action‑Reaction): For every action, there is an equal and opposite reaction. When a swimmer pushes water backwards, the water pushes the swimmer forwards. This law underpins ground reaction forces and all propulsion in sport.
第三定律（作用力与反作用力）：每一个作用力都有一个大小相等、方向相反的反作用力。当游泳运动员向后推水时，水同时向前推动运动员。这一定律是地面反作用力和所有运动推进力的基础。
6. Momentum | 动量
Momentum (kg m/s) = mass (kg) × velocity (m/s) Momentum describes the quantity of motion an object possesses. A rugby forward (mass 100 kg) moving at 4 m/s has a momentum of 400 kg m/s. When two players collide, the total momentum is conserved (assuming no external forces), which is crucial in tackling and contact sports.
动量 (kg m/s) = 质量 (kg) × 速度 (m/s) 动量描述了物体运动的量。一个质量为100 kg的橄榄球前锋以4 m/s的速度移动，其动量为400 kg m/s。当两名球员碰撞时，总动量守恒（假设没有外力），这对擒抱和接触类运动至关重要。
Force and momentum: entum ÷ time. A rapid change in momentum requires a large force, which explains why follow‑ a tennis stroke extends the time and reduces the force on the hand, lowering injury risk.
力与动量的关系：力 = 动量变化量 ÷ 时间。动量的快速变化需要较大的力，这就解释了为何网球击球的随挥动作会延长作用时间、减小对手的冲击力，从而降低受伤风险。
7. Work, Power & Energy | 功、功率与能量
Work done (J) = force (N) × distance moved in the direction of the force (m) When a weightlifter lifts a 1000 N barbell through 2 m, 2000 J of work is done. Work transfers energy from the athlete to the object.
做功 (J) = 力 (N) × 沿力方向移动的距离 (m) 当举重运动员将1000 N的杠铃向上举起2米时，做了2000 J的功。做功将能量从运动员转移至物体。
Power (W) = work done (J) ÷ time (s) Power represents the rate at which work is performed. If the lift above takes 0.8 s, the power output is 2500 W. Sprinters generating high power over a short time illustrate explosive strength.
功率 (W) = 做功 (J) ÷ 时间 (s) 功率表示做功的快慢。若上述举重动作用时0.8秒，则输出功率为2500 W。短跑运动员在短时间内产生高功率，体现了爆发力。
Kinetic energy (KE) = ½ × mass × velocity² Although not always tested, this relationship shows why a small increase in speed leads to a large increase in energy, explaining the extra effort needed to accelerate at high speeds.
动能 (KE) = ½ × 质量 × 速度² 虽然不常直接考查，但这一关系表明速度的小幅提升会导致能量大幅增加，解释了高速下加速所需额外付出的努力。
8. Levers & Mechanical Advantage | 杠杆与机械优势
All lever systems have a fulcrum (pivot), effort (force applied by the muscle), and load (resistance). The arrangement determines the mechanical advantage.
所有杠杆系统都有一个支点（枢轴）、动力（肌肉施加的力）和阻力（负荷）。它们的排列方式决定了机械优势。
Mechanical Advantage (MA) = Effort Arm ÷ Resistance Arm The effort arm is the distance from the fulcrum to the point of effort; the resistance arm is the distance from the fulcrum to the load. A mechanical advantage greater than 1 means the lever multiplies the effort force, making it easier to move a heavy load (e.g. second‑class lever like the calf raise).
机械优势 (MA) = 动力臂 ÷ 阻力臂 动力臂是从支点到动力作用线的距离；阻力臂是从支点到负荷作用线的距离。机械优势大于1意味着杠杆放大了动力，使移动重物更容易（例如，二类杠杆如提踵动作）。
First‑ rt and load (e.g. neck extension). MA can be >1, <1, or =1 depending on arm lengths.
一类杠杆：支点在动力与负荷之间（如头部后仰）。机械优势视力臂长度可大于、小于或等于1。
Second‑class lever: load between fulcrum and effort (e.g. ankle plantarflexion). Always MA >1 – good for force production.
二类杠杆：负荷在支点与动力之间（如踝关节跖屈）。机械优势始终大于1，有利于产生较大力量。
Third‑class lever: effort between fulcrum and load (e.g. elbow flexion during a bicep curl). Always MA <1 – favours range and speed of movement.
三类杠杆：动力在支点与负荷之间（如肱二头肌弯举时的肘屈）。机械优势始终小于1，有利于运动幅度和速度。
9. Moments, Torque & Stability | 力矩、转矩与稳定性
Moment of a force (Nm) = force (N) × perpendicular distance from the pivot (m) When a gymnast holds an iron cross, the moment created by body weight about the shoulder joint must be balanced by an opposing muscular moment. A larger distance increases the turning effect, demanding greater muscular force.
力的力矩 (Nm) = 力 (N) × 到支点的垂直距离 (m) 当体操运动员保持十字支撑时，体重绕肩关节产生的力矩必须由肌肉产生的相反力矩来平衡。距离越大，转动效应越强，需要更大的肌力。
Torque is essentially a rotational moment. In sprinting, the torque generated at the hip joint by the glutes determines stride power. The same principle applies to opening a door or applying a twist in diving.
转矩本质上就是转动力矩。在短跑中，臀肌在髋关节处产生的转矩决定了步幅的爆发力。同样的原理也适用于开门或跳水中的翻转动作。
Stability is increased by: a low centre of mass, a wide base of support, a large mass, and ensuring the line of gravity falls within the base. These principles explain why a sumo wrestler stands with feet apart and knees bent – maximising stability by lowering the centre of mass and widening the base.
稳定性通过以下因素增强：低重心、宽支撑面、较大的质量、重力线落在支撑面内。这解释了为何相扑运动员双腿分开、屈膝站立——通过降低重心和加宽支撑面来最大化稳定性。
10. Impulse & Ground Reaction Force | 冲量与地面反作用力
Impulse (Ns) = force (N) × time (s) Impulse is equal to the change in momentum. In a long jump take‑off, the athlete applies a large force over a short contact time, producing a high impulse that changes horizontal momentum into vertical lift. Coaches often emphasise increasing the time of force application to generate a greater impulse without increasing peak force.
冲量 (Ns) = 力 (N) × 时间 (s) 冲量等于动量的变化量。在跳远起跳中，运动员在短暂的着地时间内施加巨大的力，产生高冲量，将水平动量转化为向上的提升。教练经常强调延长力的作用时间，以便在不增加峰值力的情况下产生更大的冲量。
Ground Reaction Force (GRF) is the equal and opposite force exerted by the ground when an athlete pushes against it (Newton’s third law). GRF can be measured with force plates; its vertical component helps analyse jumping performance and its horizontal component is crucial for sprint starts.
地面反作用力 (GRF) 是运动员向下推地面时地面施加的大小相等、方向相反的力（牛顿第三定律）。GRF可以通过测力台测量；其垂直分量有助于分析跳跃表现，水平分量对短跑起跑至关重要。
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