📚 AS Cambridge Physical Education: Quick Reference Handbook of Formulas and Principles | AS剑桥体育：公式定理速查手册
This handbook compiles the key formulas, principles and quick-reference constants that every AS Physical Education student needs for Anatomy & Physiology, Biomechanics and Training. Memorise these equations and use them to analyse sporting performance, answer calculation questions and support your written arguments.
本手册汇集了AS体育课程中解剖学与生理学、生物力学及运动训练部分核心公式、定理和常用数值。熟记这些方程，用于分析运动表现、解答计算题、支撑论述。
1. Cardiovascular Formulas | 心血管公式
Cardiac Output (Q) = Heart Rate (HR) × Stroke Volume (SV). Q = HR × SV. A typical resting Q is about 5 L/min.
心输出量 = 心率 × 每搏输出量。Q = HR × SV。安静时典型值约5升/分。
Maximum Heart Rate (MHR) ≈ 220 − age (years). This estimate provides an upper limit for exercise prescription.
最大心率 ≈ 220 − 年龄（岁）。该估算值为制定运动处方提供上限。
Karvonen Formula: Target HR = (MHR − Resting HR) × Desired Intensity (%) + Resting HR. It accounts for fitness level.
卡氏公式：目标心率 = (最大心率 − 安静心率) × 目标强度(%) + 安静心率。该公式考虑了体能水平。
Stroke Volume increases during exercise but plateaus at about 40–60% of VO₂ max. Endurance training shifts the plateau to higher intensities.
运动时每搏输出量上升，但在约40–60%最大摄氧量强度时达到平台。耐力训练可使平台向更高强度推移。
2. Respiratory Formulas and Values | 呼吸公式与数值
Minute Ventilation (V̇E) = Tidal Volume (TV) × Breathing Frequency (f). V̇E = TV × f. Resting V̇E ≈ 6–7.5 L/min.
每分通气量 = 潮气量 × 呼吸频率。V̇E = TV × f。安静时约6–7.5升/分。
Alveolar Ventilation = (Tidal Volume − Dead Space) × f. Dead space is typically ~150 mL in adults.
肺泡通气量 = (潮气量 − 死腔量) × 呼吸频率。成人死腔量通常约150毫升。
Respiratory Quotient (RQ) = Volume of CO₂ produced / Volume of O₂ consumed (V̇CO₂ / V̇O₂). RQ indicates fuel mix: 1.0 for carbohydrate, ~0.7 for fat.
呼吸商 = 二氧化碳生成量 / 氧耗量 (V̇CO₂ / V̇O₂)。RQ值指示燃料配比：碳水化合物1.0，脂肪约0.7。
VO₂ max = Maximum oxygen uptake; units: mL/kg/min or L/min. It reflects aerobic capacity. Tests include multi-stage fitness test or direct gas analysis.
最大摄氧量 = 最大氧摄取量；单位 mL/kg/min 或 L/min。反映有氧能力。测试包括多阶段体能测试或直接气体分析。
3. Energy Systems and Metabolism | 能量系统与代谢
ATP-PC system: Power = very high, Capacity = very low (≈ 8–10 s). No oxygen required. Used for explosive jumps, sprints.
ATP-PC系统：功率极高，容量极低（约8–10秒）。无需氧气。用于爆发性跳跃、短跑。
Anaerobic Glycolytic system: Power = high, Capacity = low (≈ 60–90 s). Produces lactate. Fuels 200–400 m sprint.
无氧糖酵解系统：功率高，容量低（约60–90秒）。产生乳酸。供能200–400米冲刺。
Aerobic system: Power = low, Capacity = very high (hours). Uses oxygen. Dominant in endurance events. Gross efficiency ≈ 20–25%.
有氧系统：功率低，容量极高（数小时）。利用氧气。在耐力项目中占主导。总效率约20–25%。
Energy expenditure (kcal) = METs × body mass (kg) × time (h). MET is metabolic equivalent (1 MET = 3.5 mL O₂/kg/min).
能量消耗（千卡）= MET值 × 体重(kg) × 时间(h)。MET为代谢当量（1 MET = 3.5 mL O₂/kg/min）。
4. Linear Kinematics | 直线运动学
Speed = Distance / Time. v = d / t. Measured in m/s. Average speed uses total displacement.
速度 = 距离 / 时间。v = d / t。单位m/s。平均速度使用总位移计算。
Acceleration = Change in velocity / Time taken. a = (v − u) / t. Units: m/s². Deceleration is negative acceleration.
加速度 = 速度变化量 / 时间。a = (v − u) / t。单位m/s²。减速为负加速度。
SUVAT Equations (constant acceleration):
匀加速运动方程（SUVAT）：
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
s = ½ (u + v) t
Where u = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time.
其中 u = 初速度, v = 末速度, a = 加速度, s = 位移, t = 时间。
5. Force, Momentum and Impulse | 力、动量与冲量
Newton’s Second Law: Force = mass × acceleration. F = m a. Units: Newtons (N).
牛顿第二定律：力 = 质量 × 加速度。F = m a。单位：牛顿 (N)。
Momentum = mass × velocity. p = m v. Units: kg·m/s. Momentum is conserved in collisions if no external force acts.
动量 = 质量 × 速度。p = m v。单位：kg·m/s。无外力时碰撞前后动量守恒。
Impulse = Force × time. Impulse = Δp = m v − m u. Increasing contact time reduces peak force (e.g., landing mats).
冲量 = 力 × 时间。冲量 = 动量变化 = m v − m u。延长作用时间可减小峰值力（如落地垫）。
Friction force = coefficient of friction × normal reaction force. f = μ N. Static friction > sliding friction.
摩擦力 = 摩擦系数 × 正压力。f = μ N。静摩擦力 > 滑动摩擦力。
6. Work, Power and Energy | 功、功率与能量
Work Done = Force × Distance moved in direction of force. W = F d. Units: Joules (J). If force is angled, W = F d cos θ.
功 = 力 × 沿力方向移动的距离。W = F d。单位：焦耳(J)。若力有角度，W = F d cos θ。
Power = Work done / Time = (Force × distance) / time. P = W / t = F v. Units: Watts (W).
功率 = 功 / 时间 = (力 × 距离)/时间。P = W / t = F v。单位：瓦特(W)。
Kinetic Energy = ½ m v². Gravitational Potential Energy = m g h. Total mechanical energy remains constant (ignoring air resistance).
动能 = ½ m v²。重力势能 = m g h。总机械能守恒（忽略空气阻力时）。
Athlete’s power output can be measured via Wingate test (peak power, mean power) or vertical jump test (Lewis formula: power = √(4.9) × weight × √(jump height)).
运动员功率输出可通过温盖特测试（峰值功率、平均功率）或纵跳测试（刘易斯公式：功率 = √4.9 × 体重 × √纵跳高度）测量。
7. Levers and Torque | 杠杆与力矩
Torque (Moment) = Force × Perpendicular distance from pivot. τ = F d. Units: Nm. Equilibrium requires Σ anticlockwise moments = Σ clockwise moments.
力矩 = 力 × 力臂（垂直距离）。τ = F d。单位：牛顿·米。平衡要求逆时针力矩之和 = 顺时针力矩之和。
First-class lever: pivot between effort and load (e.g., neck extension). Mechanical advantage may be >1, =1 or <1.
第一类杠杆：支点在力与负荷之间（如颈后伸）。机械效益可大于、等于或小于1。
Second-class lever: load between pivot and effort (e.g., ankle plantar-flexion). Always mechanical advantage >1 (force amplifier).
第二类杠杆：负荷在支点和力之间（如踝关节跖屈）。机械效益始终>1，属于省力杠杆。
Third-class lever: effort between pivot and load (e.g., biceps curl). Mechanical advantage <1, favours speed and range of motion.
第三类杠杆：力在支点和负荷之间（如肱二头肌弯举）。机械效益<1，但有利于速度和运动幅度。
Mechanical Advantage = Effort arm / Load arm. In the body, most levers are third-class for speed.
机械效益 = 力臂 / 阻力臂。人体多数杠杆为第三类，以速度为主。
8. Projectile Motion | 抛体运动
Horizontal component: constant velocity, vₓ = u cos θ. Range = vₓ × total flight time.
水平分量：匀速，vₓ = u cos θ。射程 = vₓ × 总飞行时间。
Vertical component: affected by gravity. v_y = u sin θ − g t. Height reached: h = (u sin θ)² / (2 g).
垂直分量：受重力影响。v_y = u sin θ − g t。最大高度：h = (u sin θ)²/(2g)。
Optimum release angle for maximum range is 45° in a vacuum. In sport, actual optimum often 30–36° for shot put due to release height and air resistance.
真空中最大射程的最佳出手角度为45°。实际运动中，铅球出手角度因出手高度和空气阻力通常为30–36°。
Factors affecting projectile range: release velocity (most important), release height, release angle, air resistance, Magnus effect (spin).
影响抛体射程的因素：出手速度（最重要）、出手高度、出手角度、空气阻力、马格努斯效应（旋转）。
9. Fluid Mechanics and Aerodynamics | 流体力学与空气动力学
Bernoulli’s Principle: faster-moving fluid exerts lower pressure. An airfoil shape creates lift; a spinning ball follows a curved path (Magnus effect).
伯努利原理：流体流速越快，压强越低。翼形产生升力；旋转球体沿曲线轨迹运动（马格努斯效应）。
Drag Force: F_d = ½ C_d ρ A v², where C_d is drag coefficient, ρ is fluid density, A is cross-sectional area, v is velocity. Streamlining reduces drag by lowering C_d and A.
阻力：F_d = ½ C_d ρ A v²，C_d 为阻力系数，ρ 为流体密度，A 为迎风面积，v 为速度。流线型通过降低 C_d 和 A 减少阻力。
Surface drag (friction) occurs between fluid and body surface; form drag relates to shape and pressure differential; wave drag is caused by air–water interface in swimming.
表面阻力（摩擦）产生于流体与表面之间；形状阻力取决于外形与压差；波浪阻力由游泳时气水界面引起。
Lift force perpendicular to flow direction can be generated by angle of attack or asymmetric shape (discus, javelin, sail).
垂直于来流方向的升力可由攻角或非对称形状产生（铁饼、标枪、帆）。
10. Training Principles and Fitness Testing | 训练原则与体能测试
FITT Principle: Frequency, Intensity, Time, Type. Used to design aerobic, anaerobic, resistance and flexibility programmes.
FITT原则：频率、强度、时间、类型。用于设计有氧、无氧、抗阻和柔韧性训练计划。
Training zones based on % MHR: Aerobic zone ~60–80% MHR; Anaerobic threshold ~80–90% MHR. More precise prescription uses heart rate reserve (Karvonen).
以%最大心率划分的训练区：有氧区约60–80% MHR；无氧阈约80–90% MHR。更精准的处方使用心率储备（卡氏公式）。
Rating of Perceived Exertion (RPE): Borg scale 6–20, where 6 = rest and 20 = maximal effort. Multiply by ~10 to estimate HR.
主观疲劳感觉量表 (RPE)：博格量表6–20级，6为安静，20为最大用力。分数约乘10可估算心率。
Body Mass Index (BMI) = Weight (kg) / Height² (m). Categories: <18.5 underweight, 18.5–24.9 normal, 25–29.9 overweight, ≥30 obese. Not a direct measure of body fat.
身体质量指数 = 体重(kg) / 身高²(m)。分级：<18.5偏瘦，18.5–24.9正常，25–29.9超重，≥30肥胖。不直接反映体脂量。
Fitness tests must be valid (measures what it claims) and reliable (consistent results). Common tests include: Cooper 12-min run, handgrip dynamometer, vertical jump, 30 m sprint, Illinois agility test.
体能测试须有效（测量其所声称的内容）且信度良好（结果一致）。常用测试：库珀12分钟跑、握力计、纵跳、30米冲刺、伊利诺伊灵敏性测试。
11. Angular Kinematics | 角运动学
Angular velocity (ω) = Angular displacement (θ) / time (t). ω = Δθ / Δt. Units: rad/s. Clockwise often taken as negative.
角速度 = 角位移 / 时间。ω = Δθ / Δt。单位：rad/s。顺时针通常记为负。
Angular acceleration (α) = Change in angular velocity / time. α = Δω / Δt. Units: rad/s².
角加速度 = 角速度变化量 / 时间。α = Δω / Δt。单位：rad/s²。
Linear–angular relationship: v = r ω, where v is tangential velocity, r is radius of rotation. a_t = r α. Centripetal acceleration a_c = v² / r = r ω².
线量与角量的关系：v = r ω，v 为切向速度，r 为旋转半径。切向加速度 a_t = r α。向心加速度 a_c = v²/r = r ω²。
Angular momentum = moment of inertia × angular velocity. L = I ω. In the air, a gymnast reduces I to increase ω (conservation of angular momentum).
角动量 = 转动惯量 × 角速度。L = I ω。空中时，体操运动员通过减小I来提高ω（角动量守恒）。
Published by TutorHao | Physical Education 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Cancel reply