📚 Formula & Theorem Quick Reference Handbook for Year 12 Edexcel PE | 爱德思A-Level体育公式定理速查手册
This handbook brings together the essential equations, laws, and quantitative principles required for Year 12 Edexcel Physical Education. Covering biomechanics, cardiovascular and respiratory physiology, training zones, and body composition, it is designed as a quick-reference revision tool. Each formula is explained in plain English and paired with a sport‑science context so that you can confidently apply it in exam questions and practical analysis.
本手册汇总了 Year 12 爱德思体育课程所必需的核心方程、定律与定量原理，涵盖生物力学、心血管与呼吸生理、训练区间以及身体成分等领域，旨在作为快速查阅的复习工具。每个公式均以简明英语解释并配有中文说明，同时提供运动科学情境，帮助你自信应对考试题目与实践分析。
1. Linear Motion Kinematics | 直线运动学公式
For an object moving with uniform acceleration, the four SUVAT equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). These equations are fundamental when analysing sprints, jumps, and projectiles in sport.
对于匀加速直线运动的物体，四个 SUVAT 方程将位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t) 联系起来。在分析短跑、跳跃以及抛射体运动时，这些方程是根本工具。
v = u + at
Equation 1 states that final velocity equals initial velocity plus the product of acceleration and time. It helps determine how quickly an athlete reaches top speed.
方程一：末速度等于初速度加加速度与时间的乘积，用于确定运动员达到最大速度所需的时间。
s = ut + ½at²
Equation 2 calculates displacement when initial velocity, time, and acceleration are known – useful for computing the distance covered during the drive phase of a sprint.
方程二：在已知初速度、时间和加速度时计算位移，用于计算短跑蹬伸阶段所移动的距离。
s = ½(u + v)t
Equation 3 gives displacement as the average velocity multiplied by time, often applied to estimate the horizontal jump distance of a long jumper.
方程三：位移等于平均速度乘以时间，常用来估算跳远运动员的水平跳跃距离。
v² = u² + 2as
Equation 4 links final velocity, initial velocity, acceleration, and displacement without involving time, making it ideal for analysing take‑off and landing velocities.
方程四：将末速度、初速度、加速度和位移联系在一起而不含时间变量，非常适合分析起跳与落地时的速度。
2. Newton's Laws of Motion | 牛顿运动定律
Newton's three laws govern how forces affect motion, providing the theoretical backbone for almost every sporting action. Understanding them is essential for analysing collisions, starts, and changes of direction.
牛顿三大定律描述了力如何影响运动，为几乎所有的体育动作提供了理论基础。理解这些定律对于分析碰撞、起跑和方向变化至关重要。
First Law (Inertia): A body remains at rest or in uniform motion in a straight line unless acted upon by an external resultant force. A footballer will keep sliding on wet grass until friction brings them to a stop.
第一定律（惯性）： 除非受到外合力作用，否则物体将保持静止或匀速直线运动状态。足球运动员在湿滑草地上滑行时，直到摩擦力使其停下来为止。
Second Law (Acceleration): l to the net force and inversely proportional to its mass, expressed as F = ma. A sprinter' eration out of the blocks depends on the force they can apply relative to their body mass.
第二定律（加速度）： 物体的加速度与净外力成正比，与质量成反比，公式为 F = ma。短跑运动员起跑时的加速度取决于他们相对于自身体重所能施加的力量。
Third Law (Action‑Reaction): For every action there is an equal and opposite reaction. When a swimmer pushes against the water, the water pushes back, propelling the swimmer forward.
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。游泳者向后推水时，水向前推游泳者，推动其前进。
3. Force Resolution and Vector Components | 力的分解与矢量分量
Forces often act at an angle in sport, so we resolve them into horizontal and vertical components using trigonometry. This is key to understanding angled kicks, tackles, or the forces on a skier on a slope.
在体育运动中，力经常以一定角度作用，因此我们利用三角学将其分解为水平和垂直分量。这对于理解有角度的踢球、擒抱或斜坡上滑雪者受力至关重要。
ll is kicked with 200 N at 30° to the ground, the forward component is 200 cos30° ≈ 173 N.
如果力 F 与水平方向成 θ 角，则水平分量为 F cosθ，垂直分量为 F sinθ。当足球以 200 N 与地面成 30° 踢出时，前进分量为 200 cos30° ≈ 173 N。
Free‑body diagrams are diagrams that show all forces acting on a body. Weight always acts vertically downward, normal reaction perpendicular to the surface, and friction opposes motion. Drawing these correctly helps predict whether an athlete will slip or accelerate.
隔离体图是显示作用在物体上所有力的示意图。重力始终垂直向下，法向反力垂直于接触面，摩擦力与运动方向相反。正确绘制这些图有助于判断运动员会打滑还是加速。
4. Momentum and Impulse | 动量与冲量
ity that reflects the quantity of motion an athlete possesses. Heavier and faster players carry more momentum, making them harder to stop.
动量 (p) 是质量与速度的乘积，p = mv。它是一个矢量，反映了运动员所拥有的运动量。体重更大、速度更快的运动员动量更大，更难被拦截。
se is the change in momentum produced by a force acting over a time interval: Ft = Δp = mv – elivers a large force over a very short time, generating a large impulse to break a board.
冲量是力在一段时间内作用导致的动量变化：Ft = Δp = mv – mu。空手道劈掌在极短时间内施加很大的力，产生大冲量以击碎木板。
The principle of conservation of momentum states that in a closed system with no external forces, total momentum before a collision equals total momentum after. This principle explains why two rugby players colliding and clinging together move as a single unit with a combined velocity.
动量守恒定律表明，在没有外力的封闭系统中，碰撞前的总动量等于碰撞后的总动量。这解释了为何两名橄榄球运动员碰撞后抱在一起时会以一个公共速度继续运动。
5. Work, Energy, and Power | 功、能与功率
isplacement and θ is the angle between force and displacement. Lifting a barbell vertically requires the greatest work because force and displacement are parallel.
在体育中，当力使物体移动时即做功：W = F × d × cosθ，其中 d 为位移，θ 为力与位移的夹角。垂直提起杠铃做功最大，因为力与位移方向相同。
Kinetic energy (KE = ½mv²) is the energy of motion. A sprinter' ntial energy (PE = mgh) is stored owing to height, critical for high jumpers and gymnasts.
动能（KE = ½mv²）是运动能量。短跑运动员达到最大速度时动能急剧上升。重力势能（PE = mgh）是因高度而储存的能量，对跳高运动员和体操选手至关重要。
nstant velocity. A weightlifter producing the same work in a shorter time generates more power, a key determinant of explosive performance.
功率是做功或能量转化的速率：P = W/t，或在匀速下 P = Fv。举重运动员在更短时间内做出同样的功则产生更大的功率，这是爆发力表现的关键决定因素。
6. Levers and Mechanical Advantage | 杠杆与机械优势
A lever system consists of an effort force, a load, and a fulcrum. In the human body, bones act as levers, joints as fulcrums, and muscles provide effort. The arrangement determines mechanical advantage.
杠杆系统由动力、阻力和支点组成。在人体中，骨骼充当杠杆，关节为支点，肌肉提供动力。其排列方式决定了机械优势。
rm ÷ load arm. When the effort arm is longer than the load arm, the lever amplifies force but reduces speed and range of motion (e.g., standing on tiptoe using a second‑class lever at the ankle).
机械优势 (MA) = 动力臂 ÷ 阻力臂。当动力臂大于阻力臂时，杠杆放大力量但降低速度和运动范围（如用踝关节的第二类杠杆踮脚站立）。
Most sporting levers are third‑class levers (effort between fulcrum and load), which favour speed and range of movement over force, as seen in the biceps curl. The load arm is always longer, so MA is always less than 1, but this arrangement allows the hand to move faster than the muscle shortens.
体育中的大多数杠杆为第三类杠杆（动力位于支点与阻力之间），以速度和运动范围换取力量，如肱二头肌弯举。阻力臂始终较长，因此 MA 小于 1，但这种排列使手的移动速度快于肌肉缩短速度。
7. Angular Motion | 角运动
ration (α) = Δω/t. A gymnast somersaulting in the air experiences angular motion about their centre of mass.
角运动描述绕轴的转动。角位移 (θ) 以弧度计量，角速度 (ω) = Δθ/t，角加速度 (α) = Δω/t。体操运动员在空中做团身翻腾时，绕质心进行角运动。
he axis, I = Σmr². By pulling limbs closer to the axis, a diver reduces I and spins faster – conservation of angular momentum (L = Iω) keeps product Iω constant.
转动惯量 (I) 是对角加速度的阻抗，它取决于质量及其距轴分布，I = Σmr²。跳水运动员通过将四肢贴近转轴来减小 I 并令旋转更快——角动量守恒 (L = Iω) 使 Iω 乘积保持不变。
ar distance from the axis of rotation. In a golf swing, applying force through the handle at a greater distance from the shaft's long axis creates more torque and thus greater club‑head speed.
力矩 (T) 引起角加速度：T = Fr，其中 r 为到转轴的垂直距离。在高尔夫挥杆中，在离杆身纵轴更远处通过握把施加力会产生更大转矩，从而获得更快的杆头速度。
8. Cardiovascular Dynamics | 心血管动力学
The heart's pumping ability is quantified by cardiac output (Q or CO), which is the volume of blood ejected by the left ventricle per minute. It is determined by heart rate and stroke volume.
心脏的泵血能力用心输出量 (Q 或 CO) 量化，即左心室每分钟射出的血液体积。它由心率和每搏输出量决定。
CO = HR × SV
ses during exercise due to enhanced venous return and stronger myocardial contraction. End‑diastolic volume (EDV) and end‑systolic volume (ESV) give SV = EDV – ESV.
每搏输出量 (SV) 是每次心跳泵出的血量，运动时因静脉回流增大和心肌收缩增强而增加。舒张末期容积 (EDV) 与收缩末期容积 (ESV) 的关系为 SV = EDV – ESV。
pheral resistance. During aerobic exercise, vasodilation in muscles reduces TPR, helping to maintain a safe pressure while CO rises.
血压 (BP) 可表示为 BP = CO × TPR，其中 TPR 是总外周阻力。有氧运动期间，肌肉中的血管舒张降低了 TPR，有助于在心输出量上升的同时维持安全的血压。
9. Pulmonary Ventilation and Lung Volumes | 肺通气与肺容量
Minute ventilation (VE) is the volume of air moved in and out of the lungs per minute, a crucial measure of respiratory performance during exercise.
分钟通气量 (VE) 是每分钟进出肺部的空气量，是衡量运动时呼吸机能的关键指标。
VE = TV × f
Tidal volume (TV) is the volume inhaled or exhaled per normal breath, and f is breathing frequency (breaths per minute). During intense exercise, both TV and f increase, but f rises disproportionately at very high intensities.
潮气量 (TV) 是每次正常呼吸吸入或呼出的气体量，f 为呼吸频率（次/分钟）。高强度运动中，TV 和 f 均增加，但在极高强度下 f 的上升比例更大。
ERV). Total lung capacity (TLC) = VC + residual volume (RV). Athletes often show higher VC due to trained respiratory muscles.
通过肺活量计测定的肺容量包括肺活量 (VC)，VC = TV + 补吸气量 (IRV) + 补呼气量 (ERV)。肺总容量 (TLC) = VC + 残气量 (RV)。运动员因经过呼吸肌训练常表现出更高的 VC。
10. Heart Rate and Training Zones | 心率与训练区间
) allows coaches to prescribe training intensities. The traditional formula is HRmax = 220 – age, although individual variation exists.
估算最大心率 (HRmax) 有助于教练制定训练强度。传统公式为 HRmax = 220 – 年龄，尽管个体间存在差异。
e Karvonen method calculates target heart rate (THR) using heart rate reserve (HRR = HRmax – HRrest) and desired intensity. It provides a personalised training zone.
Karvonen 法使用储备心率 (HRR = HRmax – HRrest) 和期望强度计算目标心率 (THR)，提供个性化的训练区间。
THR = (HRmax – HRrest) × Intensity% + HRrest
For aerobic base development, an intensity of 60–70% is typical, while high‑intensity interval training may use 85–95%. A 17‑year‑old with HRrest 60 bpm aiming for 70% intensity would have THR = (203 – 60) × 0.7 + 60 ≈ 160 bpm.
发展有氧基础通常采用 60–70% 的强度，而高强度间歇训练可能使用 85–95%。一位 17 岁、安静心率 60 bpm 的运动员若以 70% 强度训练，目标心率 THR = (203 – 60) × 0.7 + 60 ≈ 160 bpm。
11. Gas Exchange and Dalton's Law | 气体交换与道尔顿定律
Dalton's law states that the total pressure of a gas mixture is the sum of the partial pressures of each component gas. In the alveoli, the partial pressure of oxygen (PAO₂) drives O₂ diffusion into the blood, while PCO₂ drives elimination.
道尔顿定律指出，混合气体的总压等于各组分气体分
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