📚 Year 12 Edexcel PE: Quick Reference Formulas & Principles | Year 12 Edexcel 体育：公式与定理速查手册
This handbook provides a concise and exam-focused collection of the key formulas, equations and scientific principles you need to master for Edexcel Year 12 Physical Education. It covers applied anatomy and physiology, biomechanics, skill acquisition and exercise physiology, offering paired English and Chinese explanations to reinforce your revision. Each section is designed to help you recall and apply the fundamental relationships that underpin human movement and performance.
本手册紧扣考点，汇集了 Edexcel Year 12 体育课程中必须掌握的核心公式、方程和科学原理，涵盖应用解剖学与生理学、生物力学、技能习得和运动生理学。每个小节都配有中英文对照讲解，帮助你巩固记忆并灵活运用支撑人体运动与表现的基本关系。
1. Linear Motion & Kinematics | 线性运动与运动学
ge of distance. It is a scalar quantity calculated as speed = distance / time (v = d / t).
速率 (v) 是距离的变化率，是标量，计算公式为速率 = 距离 / 时间（v = d / t）。
of change of displacement, a vector defined as velocity = displacement / time (v = s / t).
速度 (v) 是位移的变化率，是矢量，公式为速度 = 位移 / 时间（v = s / t）。
y: a = (final velocity − initial velocity) / time taken, or a = Δv / t. The unit is m s⁻².
加速度 (a) 衡量速度的变化率：a =（末速度 − 初速度）/ 所用时间，即 a = Δv / t。单位为米每二次方秒 (m s⁻²)。
re u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement.
在匀加速运动中可运用 SUVAT 方程，例如 v = u + at 和 s = ut + ½at²，其中 u 为初速度，v 为末速度，a 为加速度，t 为时间，s 为位移。
2. Projectile Motion | 抛体运动
n due to gravity (g = 9.81 m s⁻²). The vertical and horizontal components are independent.
抛体具有恒定的水平速度和因重力（g = 9.81 m s⁻²）而产生的恒定向下加速度，竖直与水平分量相互独立。
tical displacement = (uᵧ × t) − ½gt², where uᵧ is the initial vertical velocity component.
水平位移 = vₓ × t，vₓ 为水平初速度分量。竖直位移 = (uᵧ × t) − ½gt²，uᵧ 为竖直初速度分量。
release for maximum range in a symmetrical flight is 45° when release and landing heights are equal.
飞行时间 = 2uᵧ / g，最大高度 = uᵧ² / (2g)。当出手高度与落地高度相同时，对称飞行中获取最大远度的理想出手角度为 45°。
3. Newton's Laws of Motion | 牛顿运动定律
First Law (Inertia): A body remains at rest or in uniform motion in a straight line unless acted upon by an external force.
第一定律（惯性）：除非受到外力作用，物体将保持静止或匀速直线运动状态。
The net force acting on a body equals its mass multiplied by its acceleration: F = m × a.
第二定律（加速度）：作用于物体的合外力等于质量乘以加速度：F = m × a。
Third Law (Action-Reaction): For every action force there is an equal and opposite reaction force.
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。
4. Momentum & Impulse | 动量与冲量
the product of mass and velocity: p = m × v. It is a vector quantity measured in kg m s⁻¹.
线动量 (p) 是质量与速度的乘积：p = m × v，为矢量，单位是 kg m s⁻¹。
total momentum before a collision equals total momentum after: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
动量守恒定律指出，在无外力的封闭系统中，碰撞前总动量等于碰撞后总动量：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。
longer time of force application reduces instantaneous force, as used in catching a ball.
冲量是动量的变化量，也等于力与时间的乘积：冲量 = F × t = Δp。力的作用时间越长，瞬时力越小，如接球时缓冲动作即利用此原理。
5. Angular Motion | 角运动
f angular displacement: ω = Δθ / t (rad s⁻¹). Angular acceleration (α) = Δω / t (rad s⁻²).
角速度 (ω) 是角位移的变化率：ω = Δθ / t（单位 rad s⁻¹）。角加速度 (α) = Δω / t（单位 rad s⁻²）。
= Σmr². Summing all point masses multiplied by the square of their distance from the axis.
转动惯量 (I) 是物体抵抗旋转运动的能力，取决于质量及其相对于转轴的分布：I = Σmr²，即各质点的质量乘以它们到转轴距离的平方之和。
omentum is conserved when no external torque acts, so a decrease in moment of inertia (e.g. tuck position) increases angular velocity, and vice versa.
角动量 (L) = I × ω。无外力矩作用时角动量守恒，因此转动惯量减小（如团身姿势）会使角速度增加，反之亦然。
6. Energy, Work & Power | 能量、功与功率
al energy (GPE) = mgh, where h is height, g is gravitational field strength (9.81 N kg⁻¹).
动能 (KE) = ½mv²。重力势能 (GPE) = mgh，h 为高度，g 为重力场强度（9.81 N kg⁻¹）。
d displacement. When force is parallel to displacement, W = F × d, measured in joules (J).
功 (W) = F × d × cosθ，θ 为力与位移的夹角。当力与位移平行时，W = F × d，单位为焦耳 (J)。
v. The unit is watt (W). In sport, power is often measured in terms of explosive strength.
功率 (P) 是做功或能量转化的速率：P = W / t，也可表示为 P = F × v。单位为瓦特 (W)。在运动中，功率常以爆发力形式体现。
7. Fluid Mechanics & Bernoulli Principle | 流体力学与伯努利原理
Bernoulli' simultaneously with a decrease in pressure or potential energy: P + ½ρv² + ρgh = constant.
伯努利原理指出，流体速度增加时，其压力或势能会同时减小：P + ½ρv² + ρgh = 常数。
In sport, this explains the lift force on an aerofoil (e.g. discus, javelin) and a spinning ball. Faster airflow over a curved surface reduces pressure, creating a pressure gradient and a resultant lift or side force (Magnus effect).
在体育中，这解释了翼型（如铁饼、标枪）和旋转球的升力。曲面上的气流速度更快，压力降低，形成压力差并产生升力或侧向力（马格努斯效应）。
Drag force (Fd) opposes motion through a fluid and is given by Fd = ½CdρAv², where Cd is the drag coefficient, ρ is fluid density, A is cross‑sectional area, v is velocity. Reducing cross‑sectional area (e.g. cycling position) lowers drag.
阻力 (Fd) 阻碍物体在流体中的运动，计算式为 Fd = ½CdρAv²，其中 Cd 为阻力系数，ρ 为流体密度，A 为截面积，v 为速度。减小截面积（如自行车骑行姿势）可以降低阻力。
8. Cardiovascular & Respiratory Calculations | 心血管与呼吸计算
Maximum heart rate can be estimated using HRmax e (beats per minute). Karvonen formula for target heart rate: Target HR = resting HR + (HRmax − resting HR) × % intensity.
最大心率可用 HRmax = 220 − 年龄（次/分）来估算。目标心率的卡沃宁公式：目标心率 = 静息心率 + (最大心率 − 静息心率) × 强度百分比。
iac output (Q) = stroke volume × heart rate (Q = SV × HR), typically expressed in L min⁻¹.
每搏输出量 (SV) = 舒张末期容积 − 收缩末期容积。心输出量 (Q) = 每搏输出量 × 心率 (Q = SV × HR)，单位通常为 L min⁻¹。
f), where a−vO₂ diff is the arteriovenous oxygen difference. VO₂max is the product of maximal cardiac output and maximal a−vO₂ diff.
摄氧量 (VO₂) 由菲克方程计算：VO₂ = Q × (a−vO₂ 差)，其中 a−vO₂ 差为动静脉氧差。最大摄氧量 (VO₂max) 等于最大心输出量与最大动静脉氧差的乘积。
9. Levers & Mechanical Advantage | 杠杆与机械优势
rm. When MA > 1, the lever amplifies force; when MA < 1, it increases speed and range of motion.
杠杆由支点、施力和阻力组成。机械优势 (MA) = 施力臂 / 阻力臂。MA > 1 时省力；MA < 1 时增加运动速度与幅度。
First-class lever: fulcrum between effort and load (e.g. neck extension). MA can be varied. Second-class lever: load between fulcrum and effort, MA always > 1 (e.g. calf raise). Third-class lever: effort between fulcrum and load, MA always < 1 (e.g. biceps curl). Most body levers are third-class for speed and range.
第一类杠杆：支点在施力与阻力之间（如头颈后伸），机械优势可变。第二类杠杆：阻力在支点与施力之间，MA 恒大于 1（如提踵）。第三类杠杆：施力在支点与阻力之间，MA 恒小于 1（如肱二头肌弯举）。人体大多数杠杆属于第三类，追求速度与活动范围。
10. Skill Acquisition: Fitts' Law & Hick's Law | 技能习得：费茨定律与希克定律
Fitts' Law describes the trade‑ og₂(2A / W), where A is the amplitude (distance to target), W is target width, a and b are constants. As target width decreases or distance increases, movement time rises.
费茨定律描述了瞄准任务中速度与准确性的权衡。运动时间 (MT) = a + b × log₂(2A / W)，其中 A 为运动幅度（目标距离），W 为目标宽度，a 和 b 为常数。目标越窄或距离越远，运动时间越长。
Hick's Law states that reaction time increases logarithmically with the number of stimulus‑ hoices: RT = b × log₂(n + 1), where n is the number of choices. This explains why decision‑making slows in complex open skills when many options are available.
希克定律指出，反应时间随刺激‑反应选择数量的增加呈对数增长：RT = b × log₂(n + 1)，n 为选择数量。这解释了为什么在复杂的开放性技能中，可选方案越多，决策越慢。
11. Newton's Law of Gravitation & Weight | 万有引力定律与体重
1 N kg⁻¹. Weight differs from mass; mass is the quantity of matter and remains constant, while weight varies with gravitational field strength.
体重是作用于质量的引力：W = m × g。地球上 g = 9.81 N kg⁻¹。体重与质量不同；质量是物质的量且保持不变，而体重随引力场强度变化。
Centre of mass (CoM) is the point where weight is evenly distributed. In the anatomical position, the human CoM lies roughly at S2 level but shifts with posture and limb movement. Stability increases when the line of gravity falls within the base of support.
质心 (CoM) 是重量均匀分布的点。解剖学姿势下，人体质心大致位于第二骶椎水平，但会随姿势和肢体移动而改变。重力线落在支撑面内时稳定性增高。
12. Energy Systems & Mechanical Efficiency | 能量系统与机械效率
Mechanical efficiency (% = (mechanical work performed / energy expended) × 100. In cycling, efficiency is around 20–25%; much energy is lost as heat.
机械效率 (%) =（完成的机械功 / 消耗的能量）× 100。自行车运动的效率约为 20–25%，大量能量以热的形式散失。
VO₂ (L min⁻¹) × kcal per litre of O₂ (approximately 5 kcal). This links the oxygen cost of exercise to calorific burn.
能量消耗可用代谢当量 (MET) 或耗氧量估算。1 MET = 3.5 ml kg⁻¹ min⁻¹ 的 O₂。总能量 (kcal) = VO₂ (L min⁻¹) × 每升 O₂ 的千卡值（约 5 kcal）。这将运动的氧耗与热量消耗联系起来。
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