📚 Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This comprehensive quick-reference handbook brings together the essential formulae and theoretical principles required for AQA A-level Physical Education. Spanning linear and angular mechanics, fluid dynamics, physiological calculations, statistical analysis and sport psychology, the guide presents each concept in a concise, dual-language format. Use it as a rapid revision tool to reinforce your understanding of the quantitative and theoretical foundations of the specification.
这本速查手册汇总了 AQA A-level 体育课程所需的核心公式与定理，涵盖线性与角运动力学、流体力学、生理计算、统计分析和运动心理学等多个领域。手册以中英双语、简明扼要的方式呈现每个知识点，可作为快速复习工具，帮助巩固考试大纲中的量化与理论基础。
1. Linear Motion (SUVAT) | 直线运动 (SUVAT方程)
Average speed & velocity: Average speed = total distance / time; velocity is the rate of change of displacement. When acceleration is constant, the four SUVAT equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t).
平均速率与速度：平均速率 = 总路程 / 时间；速度是位移的变化率。当加速度恒定时，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。
v = u + at
Final velocity is obtained by adding the product of acceleration and time to the initial velocity.
末速度等于初速度加上加速度与时间的乘积。
s = ut + ½at²
Displacement is the sum of the product of initial velocity and time, and half the product of acceleration and the square of time.
位移等于初速度乘以时间，再加上二分之一加速度乘以时间的平方。
v² = u² + 2as
This equation avoids time; it links the change in velocity squared to twice the product of acceleration and displacement.
此式不含时间，将速度的平方变化与两倍加速度和位移的乘积关联。
s = (u + v) t / 2
Displacement equals the average velocity multiplied by time.
位移等于平均速度乘以时间。
2. Newton’s Laws & Force | 牛顿定律与力
Newton’s First Law (inertia): A body remains at rest or in uniform motion unless acted upon by a resultant external force.
牛顿第一定律（惯性定律）：任何物体都保持静止或匀速直线运动状态，除非有合外力迫使其改变该状态。
Newton’s Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, expressed as F = ma.
牛顿第二定律：物体的加速度与所受合外力成正比，与其质量成反比，即 F = ma。
F = m a
Force (N) = mass (kg) × acceleration (m·s&supminus;²).
力（牛）= 质量（千克）× 加速度（米每二次方秒）。
Newton’s Third Law: For every action there is an equal and opposite reaction; forces act 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；作用力和反作用力作用在不同物体上。
3. Projectile Motion | 抛射运动
When a projectile is launched with initial velocity u at an angle θ to the horizontal, the horizontal component of velocity remains constant (ignoring air resistance) while the vertical component is affected by gravity, g = 9.81 m·s&supminus;².
当物体以初速度 u、与水平方向夹角 θ 抛出时，水平分速度保持不变（忽略空气阻力），而竖直分速度受重力加速度 g = 9.81 米每二次方秒影响。
Horizontal velocity: u cosθ Vertical velocity: u sinθ − g t
Horizontal displacement: x = u cosθ × t. Vertical displacement: y = u sinθ t − ½ g t².
水平位移：x = u cosθ × t；竖直位移：y = u sinθ t − ½ g t²。
Time of flight: T = 2 u sinθ / g
The total time the projectile spends in the air, derived by setting vertical displacement to zero.
总飞行时间，通过令竖直位移为零求得。
Maximum height: H = (u² sin²θ) / (2 g)
Calculated when the vertical velocity becomes zero.
当竖直速度为零时达到最大高度。
Range: R = (u² sin 2θ) / g
The maximum horizontal distance, assuming launch and landing at the same height. Optimal angle is 45° in a vacuum.
最大水平射程，假设抛出点与落地点等高。真空中的最适角度为 45°。
4. Angular Kinematics | 角运动学
Angular motion involves rotation about an axis. Key descriptors are angular displacement (θ in rad), angular velocity (ω) and angular acceleration (α). Linear and angular quantities are linked by the radius of rotation (r).
角运动涉及绕轴的转动。主要描述量有角位移（θ，弧度）、角速度（ω）和角加速度（α）。线量与角量通过转动半径（r）关联。
ω = Δθ / Δt (rad·s&supminus;¹)
Angular velocity is the rate of change of angular displacement.
角速度是角位移的时间变化率。
α = Δω / Δt (rad·s&supminus;²)
Angular acceleration is the rate of change of angular velocity.
角加速度是角速度的时间变化率。
v = r ω aT = r α aC = v²/r = r ω²
Linear velocity (v) is radius times angular velocity; tangential acceleration (aT) is radius times angular acceleration; centripetal acceleration (aC) is given by v²/r or r ω² and always points toward the centre of rotation.
线速度 v = r ω；切向加速度 aT = r α；向心加速度 aC = v²/r = r ω²，方向始终指向转动中心。
Note: the subscript T and C are used here with HTML <sub> tags for clarity, as Unicode subscripts for these letters are not available.
注意：此处的下标 T 和 C 为清晰起见使用了 HTML <sub> 标签，因为 Unicode 不提供对应的字母下标。
5. Momentum, Impulse & Coefficient of Restitution | 动量、冲量与恢复系数
Linear momentum (p) is the product of mass and velocity. Impulse is the product of net force and the time over which it acts, equalling the change in momentum. The coefficient of restitution (e) quantifies the elasticity of a collision.
线动量 (p) 是质量与速度的乘积。冲量是合外力与其作用时间的乘积，等于动量的变化。恢复系数 (e) 量化碰撞的弹性程度。
p = m v
Momentum (kg·m·s&supminus;¹) = mass × velocity.
动量（千克米每秒）= 质量 × 速度。
Impulse = F Δt = Δp = m(v − u)
The impulse-momentum relationship is the basis for analysing forces during jumping, landing and collisions.
冲量–动量关系是分析跳跃、着地和碰撞受力的基础。
e = (v2 − v1) / (u1 − u2)
Coefficient of restitution = speed of separation / speed of approach. e = 1 for perfectly elastic, e = 0 for perfectly inelastic collisions.
恢复系数 = 分离速度 / 接近速度。完全弹性碰撞 e = 1，完全非弹性碰撞 e = 0。
6. Work, Energy & Power | 功、能与功率
Work is done when a force moves its point of application in the direction of the force. Energy is the capacity to do work, appearing as kinetic, gravitational potential and other forms. Power is the rate of doing work.
当力在其作用方向上移动作用点时，力就做了功。能量是做功的能力，包括动能、重力势能等形式。功率是做功的速率。
W = F s cosθ
Work (J) = force × displacement in the direction of the force. θ is the angle between force and displacement.
功（焦耳）= 力 × 沿力方向的位移。θ 为力与位移的夹角。
KE = ½ m v²
Kinetic energy is half the product of mass and the square of velocity.
动能等于质量与速度平方乘积的一半。
PE = m g h
Gravitational potential energy = mass × gravitational field strength (9.81 N·kg&supminus;¹) × vertical height.
重力势能 = 质量 × 重力场强（9.81 牛每千克）× 竖直高度。
P = W / t = F v
Power (W) is work done per unit time; for constant velocity, power equals force × velocity.
功率（瓦）是单位时间内做的功；匀速运动时，功率等于力乘以速度。
7. Fluid Dynamics & Drag Force | 流体力学与阻力
Objects moving through a fluid (air or water) experience drag, which depends on fluid density (ρ), frontal cross-sectional area (A), velocity (v) and the drag coefficient (Cd). Bernoulli’s principle and the Magnus effect explain lift and swerve on spinning balls.
物体在流体（空气或水）中运动时会受到阻力，阻力取决于流体密度（ρ）、迎风截面积（A）、速度（v）和阻力系数（Cd）。伯努利原理和马格努斯效应可解释旋转球的升力与弧线运动。
Fd = ½ Cd ρ A v²
This drag equation shows that resistance increases with the square of velocity, making streamlining critical at high speeds.
阻力方程表明阻力与速度的平方成正比，因此在高速运动中流线型设计至关重要。
Bernoulli’s principle: Faster fluid flow over a surface results in lower pressure; the pressure differential creates lift (e.g., aerofoil, discus, javelin).
伯努利原理：流体流经表面时速度越快压强越小；压强差产生升力（如翼型、铁饼、标枪）。
Magnus effect: A spinning ball drags air around it, creating high pressure on one side and low pressure on the other, causing the ball to swerve.
马格努斯效应：旋转的球带动周围空气，一侧形成高压、另一侧形成低压，导致球的飞行轨迹弯曲。
8. Levers, Moments & Torque | 杠杆、力矩与扭矩
In biomechanics, a lever system consists of a rigid bar (bone), a pivot (joint), an effort (muscle force) and a load (resistance). Torque (moment) is the turning effect of a force.
在运动生物力学中，杠杆系统由刚性杆（骨）、支点（关节）、动力（肌力）和阻力（负荷）组成。扭矩（力矩）是力产生的转动效应。
T = F × d
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