📚 A-Level AQA Physical Education: Formula & Theorem Quick Reference Handbook | A-Level AQA 体育：公式定理速查手册
Mastering the key equations and biomechanical principles in AQA A-Level Physical Education is essential for analysing performance and answering applied questions. This handbook compiles the most important formulas across anatomy, physiology, biomechanics and training, presented with clear explanations and practical sporting examples.
掌握 AQA A-Level 体育课程中的关键方程与生物力学原理，对于分析运动表现和回答应用题至关重要。本手册汇编了解剖学、生理学、生物力学和训练领域最重要的公式，并配有清晰的解释和实用的运动案例。
1. Linear Motion & Kinematics | 直线运动与运动学
Kinematic equations describe the motion of bodies without considering the forces that cause it. In sport, these formulas quantify acceleration, velocity and displacement during sprint starts, jumps or throws.
运动学方程描述物体的运动，而不考虑引起运动的力。在体育运动中，这些公式可以量化冲刺起跑、跳跃或投掷过程中的加速度、速度和位移。
The average velocity of an object is equal to its displacement divided by the time taken. This helps compare the speed of a 100 m sprinter with that of a marathon runner.
v = s / t
物体的平均速度等于位移除以所用时间。这有助于比较百米短跑运动员和马拉松运动员的速度。
Acceleration measures the rate of change of velocity. When a rugby player accelerates from a standstill to top speed, the same principle applies to calculate the rapidness of the movement.
a = (v − u) / t
加速度衡量速度的变化率。当橄榄球运动员从静止加速到最高速度时，同样的原理可用于计算动作的迅捷程度。
For uniformly accelerated motion, such as a long jumper in flight, three suvat equations model the relationship between displacement, initial velocity, final velocity, acceleration and time.
v = u + at
s = ut + ½at²
v² = u² + 2as
对于均匀加速运动（例如跳远运动员在空中飞行），三个 SUVAT 方程描述了位移、初速度、末速度、加速度和时间之间的关系。
2. Newton’s Laws of Motion & Force | 牛顿运动定律与力
Newton’s laws underpin every movement in sport, from the force exerted on starting blocks to the impact of a tennis racket on a ball. The net force acting on an object determines its acceleration.
牛顿定律是体育运动中每一个动作的基础，从施加在起跑器上的力到网球拍对球的撞击。作用在物体上的合力决定其加速度。
Newton’s second law states that the acceleration of an object is directly proportional to the net force and inversely proportional to its mass. A shot‑putter applying greater force to the shot results in higher acceleration.
F = m × a
牛顿第二定律指出，物体的加速度与净力成正比，与其质量成反比。铅球运动员对铅球施加更大的力，就会产生更高的加速度。
Weight is the force of gravity acting on a mass. It is critical when calculating ground reaction force in walking or landing from a jump.
W = m × g
重量是重力作用于质量上的力。在计算行走或跳跃落地时的地面反作用力时，重量至关重要。
Impulse is the product of force and the time over which it acts, and equals the change in momentum. When a cricketer follows through after hitting the ball, the prolonged contact time increases impulse and thus the ball’s velocity.
Impulse = F × t = Δp
冲量是力与其作用时间的乘积，等于动量的变化量。板球运动员击球后的顺势动作延长了接触时间，从而增大冲量和球的飞出速度。
3. Momentum, Impulse & Collisions | 动量、冲量与碰撞
Momentum conservation explains collisions and rebounds in sport. The total momentum before impact equals the total momentum after impact in a closed system.
动量守恒解释了体育运动中的碰撞和反弹。在封闭系统中，碰撞前的总动量等于碰撞后的总动量。
Linear momentum is the product of mass and velocity. A linebacker with larger momentum is harder to stop, which is a key reason mass and speed are both important in contact sports.
p = m × v
线动量是质量与速度的乘积。动量较大的线卫更难被阻挡，这也是在对抗性运动中质量和速度都很重要的关键原因。
When two objects collide, such as a cue ball striking another billiard ball, the sum of their momenta remains constant. The equation below can be used to predict post‑collision velocities.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
当两个物体碰撞时（例如母球撞击另一个台球），它们的动量总和保持不变。下面的方程可用于预测碰撞后的速度。
The impulse–momentum relationship shows that a greater force applied over a longer time produces a greater change in momentum. A goalkeeper catching a fast ball extends the arms backward to absorb the impact over a longer time, reducing the force felt.
冲量‑动量关系表明，在较长时间内施加较大的力会产生更大的动量变化。守门员接住高速球时手臂后收，以延长缓冲时间，从而减小感受到的力。
4. Work, Energy & Power | 功、能与功率
Energy transfer and mechanical work are central to understanding muscular effort, efficiency and output in athletic performance. All forms of mechanical work can be expressed through the work done equation.
能量转换和机械功对于理解运动表现中的肌肉用力、效率和输出至关重要。所有形式的机械功都可以通过做功方程来表达。
Mechanical work is done when a force moves an object through a distance in the direction of the force. Lifting a barbell vertically exemplifies this formula.
W = F × d × cos θ
当一个力使物体沿力的方向移动一段距离时，就做了机械功。垂直举起杠铃体现了这一公式。
Kinetic energy represents the energy of motion, while gravitational potential energy is stored energy due to height. A pole‑vaulter converts kinetic energy into GPE and back during the vault.
KE = ½ m v²
GPE = m g h
动能代表运动的能量，而重力势能是取决于高度的储存能量。撑杆跳高运动员在跳跃过程中将动能转化为重力势能，再转化回动能。
Power is the rate of doing work. In a Wingate sprint test, higher power output indicates better anaerobic capacity. Power can also be calculated as the product of force and velocity for movements such as rowing.
P = W / t = F × v
功率是做功的速率。在温盖特冲刺测试中，较高的功率输出表明更好的无氧能力。对于划船等动作，功率也可以用力与速度的乘积来计算。
Efficiency compares useful work output to total energy input. Muscular efficiency is usually around 20–25%, with the rest lost as heat. The formula highlights energy wastage in performance.
Efficiency (%) = (useful work output ÷ total energy input) × 100
效率将有用功输出与总能量输入进行比较。肌肉效率通常约为20%–25%，其余能量以热量形式散失。该公式突出了运动表现中的能量浪费。
5. Levers & Torque | 杠杆与力矩
Levers amplify force or speed depending on their class. In the human body, bones act as levers, joints as fulcrums and muscles provide effort. The principle of moments determines equilibrium.
杠杆根据类型可以放大力量或速度。在人体中，骨骼充当杠杆，关节作为支点，肌肉提供动力。力矩原理决定平衡状态。
Torque (moment of force) is the turning effect produced by a force acting at a distance from a pivot. In a biceps curl, the biceps generates a torque that rotates the forearm.
T = F × d
力矩（力的转动效应）是由作用在离支点一定距离处的力产生的。在肱二头肌弯举中，肱二头肌产生使前臂旋转的力矩。
For a lever system to be in static equilibrium, the sum of clockwise moments must equal the sum of anticlockwise moments. This principle explains why an athlete leans backward when carrying a heavy load.
Σ clockwise moments = Σ anticlockwise moments
要使杠杆系统保持静态平衡，顺时针力矩之和必须等于逆时针力矩之和。这个原理解释了运动员在搬运重物时身体后倾的原因。
Mechanical advantage (MA) indicates how much a lever multiplies effort. Velocity ratio (VR) compares the effort arm length to the load arm length. Their ratio gives the efficiency of the lever.
MA = load ÷ effort
VR = effort arm ÷ load arm
Efficiency = (MA ÷ VR) × 100%
机械利益 (MA) 表示杠杆放大了多少用力。速度比 (VR) 比较动力臂与阻力臂的长度。两者之比给出了杠杆的效率。
6. Angular Motion | 角运动
Rotational movements dominate sports such as gymnastics, ice skating and diving. Angular kinematics describe how quickly an athlete spins and how that relates to linear speed.
旋转运动在体操、花样滑冰和跳水等运动中占主导地位。角运动学描述运动员旋转的速率及其与线速度的关系。
Angular velocity is the rate of change of angular displacement. A figure skater pulling arms in reduces moment of inertia and increases angular velocity, conserving angular momentum.
ω = θ / t
角速度是角位移的变化率。花样滑冰运动员收拢手臂可减小转动惯量并增大角速度，从而保持角动量守恒。
The tangential velocity of a point on a rotating body is proportional to the radius and the angular velocity. A discus thrower uses a longer lever arm (extended arm) to increase release speed.
v = r × ω
旋转体上某一点的切向速度与半径和角速度成正比。铁饼运动员利用较长的力臂（伸展的手臂）来提高出手速度。
Angular acceleration describes how quickly spin rate changes. During a golf swing, rapid angular acceleration contributes to greater clubhead speed at impact.
α = (ω − ω₀) / t
角加速度描述旋转速率变化的快慢。在高尔夫挥杆中，快速的角加速度有助于在击球瞬间获得更大的杆头速度。
7. Fluid Dynamics & Bernoulli’s Principle | 流体动力学与伯努利原理
Fluid forces significantly influence projectiles, balls and the human body moving through air or water. Bernoulli’s principle explains lift, drag and the Magnus effect in sports.
流体力学显著影响在空气或水中运动的抛射体、球类以及人体。伯努利原理解释了体育运动中的升力、阻力和马格努斯效应。
Bernoulli’s equation states that an increase in fluid velocity occurs simultaneously with a decrease in pressure. This effect is used to create lift on a discus or a javelin when the angle of attack is optimised.
P + ½ρv² + ρgh = constant
伯努利方程表明，流体流速增加时压强会同时降低。当优化攻角时，该效应可在铁饼或标枪上产生升力。
The Magnus force is a consequence of pressure differences caused by spin. A tennis topspin shot creates a high‑pressure zone above the ball, forcing it downward faster and making it dip into the court.
马格努斯力是由旋转引起的压强差所导致的。网球上旋球在球上方形成高压区，迫使球更快下落，从而进入场内。
Drag force opposes motion through a fluid. Minimising drag by streamlining body position or equipment is crucial in cycling, swimming and downhill skiing. The drag equation identifies the key factors.
FD = ½ CD ρ A v²
阻力是在流体中运动时阻碍运动的力。通过流线型身体姿势或装备来最小化阻力在自行车、游泳和高山滑雪中至关重要。阻力方程指出了关键因素。
8. Heart Rate & Training Zones | 心率与训练区间
Heart rate formulas allow athletes and coaches to prescribe training intensity and monitor adaptations. The Karvonen method refines standard maximum heart rate estimates by factoring in resting heart rate.
心率公式使运动员和教练能够制定训练强度并监测身体的适应性。卡沃宁公式通过引入安静心率，进一步细化了标准最大心率的估算。
The simplest method to estimate maximum heart rate is the age‑predicted equation. However, individual variation exists, so it serves as a guideline rather than an absolute measure.
HRmax = 220 − age
估算最大心率的最简单方法是年龄预测方程。然而存在个体差异，因此它只能作为指导而非绝对指标。
The Karvonen formula calculates target heart rate using heart rate reserve (HRR). It provides a personalised zone for developing aerobic or anaerobic capacity more accurately than percentage of HRmax alone.
Target HR = HRrest + (intensity × (HRmax − HRrest))
卡沃宁公式利用心率储备 (HRR) 计算目标心率。它比单纯使用最大心率百分比能更准确地为发展有氧或无氧能力提供个性化区间。
Common training zones based on HRmax provide a quick reference for endurance sessions and interval training. The table below summarises typical AQA‑recommended ranges.
| Training Zone | % HRmax | Purpose |
|---|---|---|
| Recovery | 50–60% | Active recovery, warm‑up |
| Aerobic (easy) | 60–70% | Fat burning, base endurance |
| Aerobic (moderate) | 70–80% | Cardiovascular fitness |
| Anaerobic threshold | 80–90% | Lactate tolerance, speed |
| Maximum effort | 90–100% | Power, sprint |
常见的基于最大心率的训练区间为耐力课和间歇训练提供了快速参考。上表总结了 AQA 推荐的一般范围。
9. Energy Systems & ATP Yield | 能量系统与ATP产量
The three energy systems regenerate ATP at different rates and capacities. Knowing the ATP yield allows athletes to understand the fuel costs of high‑intensity versus endurance activities.
三个能量系统以不同的速率和容量再合成 ATP。了解ATP产量有助于运动员理解高强度活动和耐力活动的能量消耗。
The ATP‑PC system provides immediate energy for very short, explosive efforts up to about 10 seconds. One molecule of phosphocreatine resynthesises one ATP.
PC + ADP → ATP + C
ATP‑PC 系统为约10秒以内的极短爆发性用力提供即时能量。一分子磷酸肌酸可再合成一分子 ATP。
Anaerobic glycolysis breaks down glucose without oxygen, producing limited ATP and lactic acid. This system fuels high‑intensity efforts lasting up to around 60–90 seconds.
Glucose → 2 ATP + 2 lactic acid
无氧糖酵解在无氧条件下分解葡萄糖，产生少量ATP和乳酸。该系统为持续约60–90秒的高强度运动提供能量。
The aerobic system yields far more ATP per glucose molecule but requires oxygen. It is the primary system for prolonged, steady‑state exercise. The summary equation shows the complete oxidation of glucose.
Glucose + 6 O₂ → 6 CO₂ + 6 H₂O + ~38 ATP
有氧系统每个葡萄糖分子产生的 ATP 多得多，但需要氧气。它是长时间稳态运动的主要系统。总反应式展示了葡萄糖的完全氧化。
Fatty acids also undergo aerobic oxidation and yield even more ATP per molecule, making them essential for ultra‑endurance events. However, the rate of ATP production is slower than from glucose.
脂肪酸也进行有氧氧化，每分子产生的 ATP 更多，因此对超耐力项目至关重要。然而，其ATP生成速率比葡萄糖慢。
10. Fitness Testing & Performance Metrics | 体能测试与表现指标
Standardised equations underpin many laboratory and field tests used in AQA coursework and examinations. They quantify aerobic power, body composition and cardiac function.
标准化方程是 AQA 课程作业和考试中许多实验室及场地测试的基础。它们可以量化有氧功率、身体成分和心脏功能。
Maximal oxygen uptake (VO₂max) is the gold standard measure of aerobic capacity. It is the product of cardiac output and the arterial‑venous oxygen difference, reflecting oxygen delivery and extraction.
VO₂max = Q × (a-v)O₂ diff
最大摄氧量 (VO₂max) 是衡量有氧能力的金标准。它是心输出量与动静脉氧差的乘积，反映氧的输送和提取。
Cardiac output is the volume of blood pumped by the heart per minute. It is calculated from stroke volume and heart rate, both of which adapt with training.
Q = SV × HR
心输出量是心脏每分钟泵出的血量。它由每搏输出量和心率计算得出，两者都会通过训练产生适应性变化。
Body mass index (BMI) provides a simple ratio of mass to height squared, useful for large‑scale screenings. However, it does not differentiate between muscle and fat mass.
BMI = mass (kg) ÷ height² (m)
身体质量指数 (BMI) 提供了体重与身高平方的简单比值，适用于大规模筛查。但该指标无法区分肌肉和脂肪重量。
Running economy measures the oxygen cost of maintaining a given submaximal speed. A lower VO₂ at the same pace indicates better efficiency, and is often used to compare endurance athletes alongside VO₂max.
Running economy = VO₂ (ml·kg⁻¹·min⁻¹) at a standard speed
跑步经济性衡量维持某一固定次最大速度所需的氧气消耗。同样配
Published by TutorHao | A-Level 体育 Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导