Pre-U Edexcel Physical Education: Formula & Theorem Quick Reference Handbook | Pre-U Edexcel 体育：公式定理速查手册

📚 Pre-U Edexcel Physical Education: Formula & Theorem Quick Reference Handbook | Pre-U Edexcel 体育：公式定理速查手册

This concise handbook gathers the essential quantitative relationships, key formulas and fundamental theorems you need for Pre-U Edexcel Physical Education. It spans biomechanics, exercise physiology and basic statistical measures, providing a rapid reference for structured revision and exam preparation.

本精简手册汇集了 Pre-U Edexcel 体育学科所需的基本定量关系、关键公式和基础定理，涵盖生物力学、运动生理学和基础统计测量，为系统性复习和备考提供速查便利。

1. Linear Kinematics | 直线运动学

v = Δs / Δt

Speed (scalar) and velocity (vector) are calculated as the rate of change of displacement. Δs represents displacement in metres, Δt the time interval in seconds. The instantaneous velocity can be determined from the gradient of a displacement–time graph.

速率（标量）和速度（矢量）按位移变化率计算。Δs 表示位移（米），Δt 为时间间隔（秒）。瞬时速度可通过位移–时间图的斜率确定。

a = Δv / Δt

Acceleration is the rate of change of velocity. A constant acceleration produces the familiar SUVAT equations, which are vital in analysing sprints, jumps and throws.

加速度是速度的变化率。恒定加速度可导出经典的 SUVAT 方程，对分析短跑、跳跃和投掷至关重要。

v = u + at

Where u = initial velocity, v = final velocity, a = constant acceleration, t = time.

其中 u = 初速度，v = 末速度，a = 恒定加速度，t = 时间。

s = ut + ½ a t²

Displacement s can be computed when acceleration and initial velocity are known. The ½ and square are expressed with Unicode: ½ and ².

已知加速度和初速度时可计算位移 s。½ 和平方均使用 Unicode 符号呈现。

v² = u² + 2 a s

This time-independent equation is particularly useful when the time interval is unknown or irrelevant, such as in take-off velocity calculations for long jump.

该与时间无关的方程在时间间隔未知或不相关时非常有用，例如跳远起跳速度的计算中。

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2. Linear Kinetics – Force, Momentum & Impulse | 直线动力学：力、动量与冲量

F = m × a

Newton’s Second Law states that the net force acting on a body is directly proportional to the rate of change of momentum, simplified for constant mass to F = m × a. This explains how athletes accelerate by applying greater ground reaction forces.

牛顿第二定律表明，作用在物体上的净力与其动量变化率成正比，当质量恒定时简化为 F = m × a。这解释了运动员如何通过施加更大的地面反作用力来加速。

p = m × v

Momentum p is a vector quantity describing an object’s quantity of motion. In collisions and tackles, momentum is conserved in the absence of external net forces.

动量 p 是描述物体运动量的矢量。在碰撞和擒抱中，若无外净力，动量守恒。

Impulse = F × t = Δp

Impulse equals change in momentum. In sport, extending the time of force application (e.g., following through in a golf swing or a kick) increases impulse, thereby increasing the velocity given to the ball.

冲量等于动量的变化。在运动中，延长施力时间（如高尔夫挥杆或踢球的跟随动作）会增大冲量，从而提高传递给球的速度。

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3. Work, Energy & Power | 功、能与功率

W = F × d × cosθ

Mechanical work is done when a force moves its point of application through a displacement in the direction of the force. The angle θ between force and displacement determines the effective component.

当力沿其作用方向移动作用点时，即做机械功。力与位移之间的夹角 θ 决定了有效分量。

KE = ½ m v²

Kinetic energy depends on mass and the square of velocity. A sprinter’s kinetic energy rises sharply as speed increases, highlighting the importance of acceleration mechanics.

动能取决于质量和速度的平方。短跑运动员的动能随速度提升急剧增加，凸显了加速力学的重要性。

GPE = m g h

Gravitational potential energy is stored due to an object’s height above a reference level. In high jump or pole vault, the athlete converts kinetic energy into GPE to clear the bar.

重力势能因物体高于参考面而储存。在跳高或撑竿跳中，运动员将动能转化为重力势能以越过横杆。

P = W / t = F × v

Power is the rate of doing work. The expression F × v shows that at a given velocity, a more powerful athlete can apply a larger propulsive force, critical in cycling and rowing.

功率是做功的速率。表达式 F × v 表明，在给定速度下，更有力的运动员能施加更大的推进力，这在自行车和赛艇中至关重要。

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4. Angular Motion | 角运动

ω = Δθ / Δt

Angular velocity ω (rad/s) describes the rate of rotation. Gymnasts and divers manipulate angular velocity by altering body shape.

角速度 ω（弧度/秒）描述旋转快慢。体操与跳水运动员通过改变身体形态来调控角速度。

α = Δω / Δt

Angular acceleration α arises when a torque is applied. A figure skater spinning experiences angular acceleration when pulling the arms in or pushing out.

施加力矩时会产生角加速度 α。花样滑冰运动员收臂或展臂时，旋转会经历角加速度。

v_t = ω r

Tangential linear velocity at a point on a rotating body is proportional to the radius r from the axis. This explains why the tip of a golf club head travels faster than the hands.

旋转体上某点的切向线速度与到转轴的半径 r 成正比。这解释了高尔夫杆头尖端为何比手运动得更快。

L = I ω

Angular momentum L is conserved when net external torque is zero. Moment of inertia I = Σ m r² depends on mass distribution around the rotational axis. Tucking during a somersault reduces I, causing ω to increase.

当外合力矩为零时，角动量 L 守恒。转动惯量 I = Σ m r² 取决于质量绕转轴的分布。翻腾时团身减小 I，导致 ω 增大。

τ = I α

Newton’s Second Law for rotation: torque τ equals moment of inertia times angular acceleration. Effective torque generation is central to technique in throwing and striking sports.

旋转的牛顿第二定律：力矩 τ 等于转动惯量乘以角加速度。有效产生力矩是投掷与击打类运动技术的核心。

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5. Fluid Mechanics – Drag, Lift & Magnus Effect | 流体力学：阻力、升力与马格努斯效应

F_D = ½ ρ v² C_D A

Drag force opposes motion through a fluid. Air density ρ, velocity squared v², drag coefficient C_D and frontal area A determine its magnitude. Athletes reduce drag by streamlining posture and wearing smooth suits.

阻力阻碍物体在流体中的运动。空气密度 ρ、速度的平方 v²、阻力系数 C_D 和迎风面积 A 决定其大小。运动员通过流线型姿势和光滑服装减少阻力。

F_L = ½ ρ v² C_L A

Lift force acts perpendicular to the relative flow direction. In discuss or javelin, an appropriate angle of attack generates lift, prolonging flight.

升力垂直于相对气流方向。在铁饼或标枪中，适当的攻角产生升力，延长飞行时间。

Magnus effect: A spinning ball experiences a pressure differential due to the entrained airflow, creating a lateral force that curves its path. Topspin decreases landing angle in tennis; backspin flattens trajectory in golf.

马格努斯效应： 旋转的球因带动气流产生压力差，形成侧向力使其路径弯曲。网球中的上旋可减小落点角度；高尔夫中的后旋则使轨迹更平。

Bernoulli’s principle: An increase in fluid velocity leads to a decrease in pressure. This principle contributes to the lift produced by a discus or ski jumper’s body shape, and helps explain the curved flight of a spinning football.

伯努利原理： 流速增加导致压强降低。此原理有助于解释铁饼或跳台滑雪运动员身体产生的升力，以及旋转足球的弧线飞行。

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6. Levers, Torque & Stability | 杠杆、力矩与稳定性

τ = F × d_⟂

Torque (moment of force) is the product of force and the perpendicular distance from the axis to the line of action. Most human movement relies on third‑class levers (effort between axis and resistance) for speed and range of motion.

力矩是力与转轴到力作用线的垂直距离的乘积。大多数人体运动依赖第三类杠杆（力点在轴与阻力点之间），以获取速度和活动范围。

Mechanical advantage = effort arm / resistance arm. Although third‑class levers have mechanical advantage less than 1, they allow large angular movement at the distal end, crucial for throwing and kicking.

机械效益 = 力臂 / 阻力臂。 虽然第三类杠杆的机械效益小于 1，但它们能使远端产生大幅角运动，这对投掷和踢击至关重要。

Stability principles: A body is more stable when the centre of mass is low, the base of support is wide, and the line of gravity falls centrally within the base. Stability ∝ (base width)/(height of centre of mass).

稳定性原理： 当重心较低、支撑面较宽且重力线落在支撑面中心区域内时，物体更稳定。稳定性正比于（支撑面宽度）/（重心高度）。

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7. Cardiovascular Fitness & Training Zones | 心血管适能与训练区间

HR_max = 220 – age

The traditional estimate of maximum heart rate guides aerobic training intensities. A more accurate version: HR_max = 207 – (0.7 × age).

传统最大心率估算值用于指导有氧训练强度。更精确的版本为：HR_max = 207 – (0.7 × age)。

Karvonen formula: Target HR = RHR + (intensity % × (HR_max – RHR))

Where RHR is resting heart rate. This heart‑rate reserve method sets aerobic training zones (e.g., 60–80% for moderate intensity) and ensures individualised prescription.

其中 RHR 为安静心率。此心率储备法设定有氧训练区间（如中等强度为60–80%），确保个性化运动处方。

MET (Metabolic Equivalent): 1 MET = 3.5 ml O₂/kg/min ≈ resting energy expenditure. Activities are often expressed in METs to estimate energy cost.

代谢当量： 1 MET = 3.5 毫升氧/千克/分钟 ≈ 静息能量消耗。活动常用 MET 值估算能量消耗。

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8. Body Composition & Energy Expenditure | 身体成分与能量消耗

BMI = mass (kg) / (height (m))²

Body Mass Index offers a simple population‑level indicator of weight status, though it does not differentiate between muscle and fat mass.

身体质量指数提供了一个简单的群体层面体重状态指标，但无法区分肌肉与脂肪质量。

Energy (kcal) = MET × body mass (kg) × time (hours)

This formula estimates caloric expenditure from physical activity. For a 70 kg person walking at 3 METs for 1 hour, the energy cost is approximately 210 kcal.

此公式估算体力活动的热量消耗。一个70 公斤的人以 3 METs 步行 1 小时，约消耗 210 千卡。

Lean body mass and percent body fat are assessed via skinfold equations (e.g., Durnin‑Womersley or Jackson‑Pollock), but the fundamental concept is that body density and fat‑free mass can be used to estimate % fat.

瘦体重与体脂百分比通过皮褶厚度方程（如 Durnin‑Womersley 或 Jackson‑Pollock）评定，但其基本概念是利用身体密度和去脂质量估算体脂百分比。

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9. Statistical Measurement & Error in Sport Science | 体育科学中的统计测量与误差

Percentage error = (|actual value – predicted value| / actual value) × 100%

This expresses the accuracy of a measurement or prediction. In motion analysis, knowing the typical percentage error of a timing gate system helps interpret performance data.

该公式体现测量或预测的准确度。在运动分析中，了解计时门系统的典型百分比误差有助于解读表现数据。

Standard deviation and coefficient of variation (CV = (SD/mean) × 100%) are used to describe inter‑performer variability or test‑retest reliability. A lower CV indicates greater consistency.

标准差与变异系数 (CV = (SD/均值) × 100%) 用于描述受试者间变异或重测信度。CV 越小表明一致性越高。

Correlation (r) quantifies the relationship between two variables, e.g., between leg power and sprint time. The Pearson r ranges from -1 to +1, where values closer to ±1 indicate stronger association.

相关 (r) 量化两变量间关系，例如腿力与短跑时间。皮尔逊 r 介于 -1 到 +1，越接近 ±1 关联度越强。

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10. Key Biomechanical Principles – Newton’s Laws | 关键生物力学原理：牛顿定律

Newton’s First Law (Inertia): A body remains at rest or in uniform motion unless acted upon by a net external force. This explains why a cyclist must continue pedalling to overcome drag; otherwise, the bike decelerates.

牛顿第一定律（惯性）： 任何物体都保持静止或匀速直线运动状态，直到有外净力迫使其改变。这解释了为何骑行者必须持续踩踏以克服阻力，否则自行车会减速。

Newton’s Second Law (Acceleration): F = m × a, and the acceleration is in the same direction as the net force. Sprinters maximise forward acceleration by directing ground reaction force horizontally.

牛顿第二定律（加速度）： F = m × a，加速度方向与净力相同。短跑运动员通过将地面反作用力指向水平方向，最大化向前加速度。

Newton’s Third Law (Action–Reaction): For every action force there is an equal and opposite reaction force. When a swimmer pushes water backwards, the water pushes the swimmer forwards.

牛顿第三定律（作用与反作用）： 每一个作用力都有一个大小相等、方向相反的反作用力。当游泳者向后推水时，水则向前推动游泳者。

Principle of conservation of momentum: In the absence of external forces, total momentum before an interaction equals total momentum after. This governs collisions in contact sports and can be used to analyse effective mass in striking.

动量守恒原理： 无外力时，相互作用前后的总动量相等。这支配着对抗性运动中的碰撞，并可用于分析击打中的有效质量。

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