📚 AS Edexcel PE Formula & Theorem Quick Reference | AS Edexcel 体育：公式定理速查手册
This quick-reference handbook compiles the essential formulas, principles, and theorems required for the AS Edexcel Physical Education specification. Covering biomechanics, exercise physiology, and training science, it provides clear, exam-ready summaries to support effective revision and application.
本速查手册汇编了 AS Edexcel 体育课程所需的核心公式、原理和定理，涵盖生物力学、运动生理学和训练科学，提供清晰、贴近考试的总结，帮助考生高效复习和灵活运用。
1. Kinematics and Dynamics Formulas | 运动学与动力学公式
Average speed is the rate of distance covered: speed = distance / time or v = s / t.
平均速率是所经距离的时间率：速度 = 距离 / 时间 或 v = s / t。
Velocity is defined as the rate of change of displacement: v = Δs / Δt, where Δs is displacement and Δt is time taken.
速度定义为位移变化率：v = Δs / Δt，其中 Δs 为位移，Δt 为时间。
Acceleration is the rate of change of velocity: a = (v – u) / t, where u is initial velocity and v is final velocity.
加速度是速度变化率：a = (v – u) / t，其中 u 为初速度，v 为末速度。
The first suvat equation relates final velocity to initial velocity, acceleration, and time: v = u + at.
第一个匀加速运动方程将末速度与初速度、加速度和时间联系起来：v = u + at。
Displacement is given by s = ut + ½at², requiring consistent units.
位移由公式 s = ut + ½at² 计算，单位须保持一致。
The independent-of-time equation links velocity and displacement: v² = u² + 2as.
不含时间的方程将速度与位移相关联：v² = u² + 2as。
2. Newton’s Laws of Motion | 牛顿运动定律
Newton’s First Law (Law of Inertia): A body remains at rest or in uniform motion unless acted upon by an external resultant force.
牛顿第一定律（惯性定律）：除非受到外力作用，物体将保持静止或匀速直线运动状态。
Newton’s Second Law describes the relationship among force, mass, and acceleration: F = m × a. Net force equals mass times acceleration.
牛顿第二定律描述力、质量和加速度的关系：F = m × a。合力等于质量乘以加速度。
Newton’s Third Law: For every action force there is an equal and opposite reaction force acting on different bodies.
牛顿第三定律：每一个作用力都有一个大小相等、方向相反的反作用力，且作用在不同物体上。
In sports, ground reaction force (GRF) is the reaction force exerted by the ground on the athlete; sprinting and jumping involve applying large forces against the ground to generate high acceleration.
在体育运动中，地面反作用力是地面对运动员施加的反作用力；短跑和跳跃需对地面施加较大力量以产生高加速度。
3. Momentum and Impulse | 动量与冲量
Linear momentum is the product of mass and velocity: p = m × v (unit: kg m s⁻¹).
线动量是质量与速度的乘积：p = m × v（单位：千克·米/秒）。
Impulse is the product of force and the time for which it acts: J = F × t (unit: N s).
冲量是力与其作用时间的乘积：J = F × t（单位：牛·秒）。
The impulse-momentum relationship states that impulse equals change in momentum: F × t = m(v – u) or J = Δp.
冲量-动量定理表明冲量等于动量的变化量：F × t = m(v – u) 或 J = Δp。
In a closed system, the law of conservation of momentum applies: total momentum before collision equals total momentum after collision, m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
在封闭系统中，动量守恒定律成立：碰撞前总动量等于碰撞后总动量，m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。
4. Levers and Moments | 杠杆与力矩
A moment (torque) is the turning effect of a force: Moment = Force × perpendicular distance from the pivot, or τ = F × d⊥.
力矩（扭矩）是力的转动效应：力矩 = 力 × 支点的垂直距离，或 τ = F × d⊥。
First-class lever: fulcrum between effort and load (e.g., elbow extension). Mechanical advantage can be >1, <1, or =1.
第一类杠杆：支点在力点和重点之间（如肘关节伸展）。机械利益可大于、小于或等于1。
Second-class lever: load between fulcrum and effort (e.g., plantar flexion during jumping); always mechanical advantage >1, suited to producing large force.
第二类杠杆：重点在支点和力点之间（如跳跃时的跖屈）；机械利益始终大于1，适合产生大力。
Third-class lever: effort between fulcrum and load (e.g., bicep curl at the elbow); mechanical advantage <1, allows large range and speed of movement.
第三类杠杆：力点在支点和重点之间（如肱二头肌弯举）；机械利益小于1，可增大运动幅度和速度。
5. Projectile Motion | 抛射体运动
The horizontal and vertical components of an initial velocity u launched at angle θ are: u_x = u cosθ and u_y = u sinθ.
以角度 θ 发射的初速度 u 的水平分量和垂直分量分别为：u_x = u cosθ 和 u_y = u sinθ。
Time of flight for a symmetrical trajectory: t_flight = 2u sinθ / g, where g = 9.8 m s⁻².
对称轨迹的飞行时间：t_flight = 2u sinθ / g，其中 g = 9.8 m/s²。
Maximum height reached: H = (u² sin²θ) / (2g).
最大高度：H = (u² sin²θ) / (2g)。
Horizontal range (R) for a projectile launched from ground level: R = (u² sin2θ) / g; optimal angle for maximum range is 45° in a vacuum.
从地平面发射的抛射体的水平射程：R = (u² sin2θ) / g；真空中最大射程的最佳角度为45°。
Factors affecting horizontal displacement in real sport include release height, release angle, speed, air resistance, and Magnus effect.
实际运动中影响水平位移的因素包括出手高度、出手角度、出手速度、空气阻力和马格努斯效应。
6. Fluid Mechanics and Spin | 流体力学与旋转
Bernoulli’s principle: In a horizontal flow of an ideal fluid, an increase in flow velocity leads to a decrease in pressure; P + ½ρv² + ρgh = constant (for incompressible flow).
伯努利原理：在理想流体的水平流动中，流速增加导致压强降低；不可压缩流动满足 P + ½ρv² + ρgh = 常数。
The Magnus effect explains the curved path of a spinning ball: a spinning object drags air, creating a pressure difference that causes the ball to deviate towards the low-pressure side.
马格努斯效应解释了旋转球的弯曲轨迹：旋转的物体带动空气，产生压差，导致球向低压侧偏移。
Lift force is an upward force generated by pressure difference across a surface, perpendicular to the oncoming flow; a discus or javelin benefits from lift during flight.
升力是由表面两侧压差产生的、垂直于来流的向上作用力；铁饼或标枪在飞行中利用升力。
Drag force opposes motion and depends on velocity, cross-sectional area, fluid density, and surface characteristics; streamlining reduces pressure drag.
阻力与运动方向相反，其大小取决于速度、横截面积、流体密度和表面特性；流线型可减小压差阻力。
7. Cardiovascular Training Formulas | 心血管训练公式
Estimated maximum heart rate (HRmax) using the traditional formula: HRmax = 220 – age, or the more accurate HRmax = 208 – (0.7 × age).
最大心率估算传统公式：HRmax = 220 – 年龄，或更精确的 HRmax = 208 – (0.7 × 年龄)。
The Karvonen formula calculates target heart rate based on heart rate reserve (HRR): Target HR = HRrest + (%intensity × (HRmax – HRrest)).
卡氏公式根据心率储备计算目标心率：目标心率 = 安静心率 + (强度百分比 × (最大心率 – 安静心率))。
Training zones are often expressed as percentages of HRmax: aerobic zone ~60-70% HRmax, anaerobic threshold ~80-90% HRmax.
训练区间常以最大心率百分比表示：有氧区间约为 HRmax 的60-70%，无氧阈约为80-90%。
Heart rate recovery (HRR) after exercise is an indicator of cardiovascular fitness; faster decline suggests better aerobic conditioning.
运动后心率恢复是衡量心血管适能的指标；心率下降越快，有氧条件越好。
8. Energy Expenditure and Metabolism | 能量消耗与代谢
A MET (metabolic equivalent) is the ratio of work metabolic rate to resting metabolic rate: 1 MET ≈ 3.5 ml O₂/kg/min.
MET（代谢当量）是工作代谢率与静息代谢率之比：1 MET 约等于 3.5 毫升氧气/千克/分钟。
Energy expenditure (kcal) can be estimated using METs: Energy (kcal) = METs × body mass (kg) × time (hours).
可利用 METs 估算能量消耗（千卡）：能量（千卡）= METs × 体重（kg）× 时间（小时）。
To convert to kJ, multiply kcal by 4.184: Energy (kJ) = kcal × 4.184.
转换为千焦时，将千卡乘以 4.184：能量（千焦）= 千卡 × 4.184。
The respiratory exchange ratio (RER) = VCO₂ / VO₂ indicates substrate utilisation: RER ~1.0 suggests pure carbohydrate oxidation, RER ~0.7 suggests pure fat oxidation.
呼吸交换率 RER = VCO₂ / VO₂ 反映底物利用：RER 约 1.0 表示纯碳水化合物氧化，约 0.7 表示纯脂肪氧化。
9. Training Load and Recovery | 训练负荷与恢复
Session RPE load is a subjective measure of internal load: Session RPE load = sRPE (1–10 scale) × session duration (min).
课次 RPE 负荷是内部负荷的主观测量：课次 RPE 负荷 = sRPE（1–10 量表）× 课时长（分钟）。
The acute:chronic workload ratio (ACWR) aids injury risk monitoring: ACWR = acute load (7-day rolling average) / chronic load (28-day rolling average).
急性：慢性工作负荷比值用于监测损伤风险：ACWR = 急性负荷（7日滑动平均） / 慢性负荷（28日滑动平均）。
Training monotony represents day-to-day training variability: monotony = mean daily load / standard deviation of daily load.
训练单调性反映日间负荷变异：单调性 = 日均负荷 / 日均负荷标准差。
Training strain combines monotony and absolute load: strain = total weekly load × monotony; high strain with low variation increases overtraining risk.
训练应变结合单调性和绝对负荷：应变 = 周总负荷 × 单调性；高应变及低变异增加过度训练风险。
10. Body Composition Assessment | 体成分评估
Body Mass Index (BMI) is a simple weight-for-height measure: BMI = body mass (kg) / height² (m²). It does not distinguish between fat and lean mass.
身体质量指数是一种简单的身高别体重指标：BMI = 体重（kg）/ 身高²（m²）。它不区分脂肪和瘦体重。
Waist-to-hip ratio (WHR) estimates fat distribution: WHR = waist circumference / hip circumference; higher values indicate greater central adiposity.
腰臀比评估脂肪分布：WHR = 腰围 / 臀围；较高值表示中心性肥胖程度更高。
Skinfold measurements estimate body density using equations such as Durnin & Womersley; body density is then converted to body fat percentage using the Siri equation: % Body Fat = (495 / body density) – 450.
皮褶厚度通过 Durnin & Womersley 等方程估算身体密度，然后利用 Siri 方程转换为体脂百分比：体脂 % = (495 / 身体密度) – 450。
Bioelectrical impedance analysis (BIA) and other methods also appear in AS specification, though they rely on prediction equations rather than direct formulas.
生物电阻抗分析法等其他方法亦见于 AS 考纲，但这些方法依赖预测方程，而非直接公式。
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