📚 A-Level Edexcel Physical Education Formula & Theorem Quick Reference | A-Level Edexcel 体育公式定理速查手册
Welcome to the A-Level Edexcel Physical Education Formula & Theorem Quick Reference. This handbook condenses the key equations, biomechanical principles, physiological relationships and psychological models you are expected to recall and apply in your examinations. Each entry presents a concise English explanation immediately followed by its Chinese equivalent, helping you to develop a bilingual command of the subject and to locate critical information rapidly during revision. Whether you are calculating angular momentum, interpreting the Yerkes–Dodson curve, or applying the laws of motion to a sporting example, this reference will serve as your compact, syllabus‑matched companion.
欢迎使用 A‑Level Edexcel 体育公式定理速查手册。本手册浓缩了考试大纲要求掌握的关键方程、生物力学原理、生理学关系式以及心理学模型。每一条目均以简明英文解释配以对应的中文翻译，帮助你在备考中建立双语理解，快速检索要点。无论是计算角动量、解读耶克斯–多德森曲线，还是将牛顿定律运用于运动实例，这本速查手册都将成为你贴合考纲的便携工具。
1. Newton’s Laws of Motion | 牛顿运动定律
First Law (Law of Inertia): A body remains at rest or continues to move with constant velocity in a straight line unless acted upon by a net external force. In a sporting context, a stationary ball stays still until kicked; a sliding puck gradually stops due to friction. The condition can be written as ΣF = 0.
ΣF = 0
第一定律（惯性定律）： 物体将保持静止或沿直线做匀速运动，除非受到净外力的作用。在运动中，静止的足球在被踢中前不会移动；冰球滑动时因摩擦力逐渐停下。可表示为 ΣF = 0。
Second Law (Law of Acceleration): The acceleration of an object is directly proportional to the net force applied and inversely proportional to its mass. This is the fundamental relationship governing sprint starts, throwing events and impact forces.
F = m × a or a = F / m
第二定律（加速度定律）： 物体的加速度与所受净外力成正比，与物体质量成反比。短跑起跑、投掷项目以及冲击力的计算都以此为核心。公式为 F = m × a 或 a = F / m。
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; when the foot strikes the ground during running, the ground exerts an equal and opposite ground reaction force.
第三定律（作用力与反作用力定律）： 每一个作用力都存在一个大小相等、方向相反的反作用力。游泳者向后推水时，水同时向前推动游泳者；跑步时脚蹬踩地面，地面便施加等大反向的地面反作用力。
2. Linear Kinematics | 线性运动学
Kinematic equations describe motion without reference to its causes. In A‑Level PE you are expected to use the SUVAT equations for situations involving constant acceleration, such as sprint phases, projectile motion of a shot put, or diving trajectories.
运动学方程用来描述运动本身，不涉及引起运动的原因。在 A‑Level 体育中，你需要运用 SUVAT 方程处理恒加速度的情形，例如短跑阶段、铅球抛物轨迹或跳水腾空路径。
The key scalar and vector quantities are: displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t). The four standard equations follow.
v = u + a t
v² = u² + 2 a s
s = u t + ½ a t²
s = ½(u + v) t
核心标量和矢量包括：位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t)。上述四个标准公式已列出。在应用时注意规定正方向，将这些关系用于计算跳远的腾起初速度或篮球出手高度。
3. Linear Kinetics | 线性动力学
Linear kinetics examines the forces that cause motion. Understanding momentum, impulse and force–time relationships is essential for analysing tackles, collisions and explosive starts.
线性动力学研究引起运动的力。理解动量、冲量以及力–时间关系，对于分析擒抱、碰撞和爆发式起跑至关重要。
Momentum: the product of mass and velocity. An athlete’s momentum changes when a net force is applied over time.
p = m × v
动量： 质量与速度的乘积。当净力作用一段时间后，运动员的动量发生改变。公式为 p = m × v。
Impulse: the product of net force and the time for which it acts. Impulse equals the change in momentum (impulse–momentum relationship).
Impulse = F × t = Δp
冲量： 净力与其作用时间的乘积。冲量等于动量的变化量（冲量–动量定理）。踢球时增大力的作用时间可增大球的动量变化。
Conservation of momentum: In a closed system, total momentum before a collision equals total momentum after the collision. This principle underlies analysis of tackles and off‑centre impacts.
动量守恒： 在封闭系统中，碰撞前的总动量等于碰撞后的总动量。禁区内防守碰撞、偏离重心的击球等情境下都可使用动量守恒进行分析。
4. Work, Energy & Power | 功、能量与功率
Work, mechanical energy and power quantify the capacity to perform movements and the rate at which energy is transferred. These concepts link directly to training zones and performance analysis.
功、机械能和功率衡量完成动作的能力以及能量转换的速率，这些概念直接联系到训练区间和运动表现分析。
Work done when a force moves its point of application in the direction of the force.
W = F × d × cosθ
功： 力在其作用方向上的位移所做的功。举起杠铃时，如果力与位移方向一致，θ=0°，cos0°=1，W = F × d。
Kinetic energy (KE) and gravitational potential energy (GPE) are the two mechanical energy forms most relevant in sport.
KE = ½ m v² and GPE = m g h
动能 (KE) 与 重力势能 (GPE) 是体育中最相关的两种机械能。动能取决于质量和速度平方，势能取决于质量、重力加速度 g (9.81 m s⁻²) 和高度。
Power is the rate of doing work. It reflects an athlete’s explosiveness and can be expressed in two common forms.
P = W / t or P = F × v
功率： 做功的快慢，体现运动员的爆发力。可用 P = W / t 或当力与速度同向时 P = F × v 计算。冲刺时达到的最大功率通常用来评估短跑和跳跃选手的爆发能力。
5. Levers & Mechanical Advantage | 杠杆与机械优势
Understanding lever systems helps explain how the human body generates speed or force. The three classes of lever are defined by the relative positions of the fulcrum (F), effort (E) and resistance (R).
理解杠杆系统有助于解释人体如何产生速度或力。三类杠杆根据支点 (F)、动力 (E) 和阻力 (R) 的相对位置划分。
| Lever Class 杠杆类型 | Arrangement 排列 | Sporting Example 运动例子 | Main Function 主要功能 |
|---|---|---|---|
| First class | F between E and R | Triceps extending the elbow (overhead throw) | Balance / speed or force depending on arm lengths |
| Second class | R between F and E | Calf raising the body on the ball of the foot | Force advantage – heavy loads overcome |
| Third class | E between F and R | Biceps curling; quadriceps extending the knee | Speed and range of motion – most common in the body |
Mechanical advantage (MA) tells you whether the lever multiplies force or speed. It is the ratio of the effort arm to the resistance arm.
MA = Effort arm length / Resistance arm length
机械优势 (MA)： 表示杠杆是省力还是放大速度。公式为 MA = 动力臂长度 / 阻力臂长度。MA > 1 表示省力杠杆（第二类），MA < 1 表示速度杠杆（第三类）。
6. Angular Motion | 角运动
Angular motion describes rotation about an axis, central to diving, gymnastics, figure skating and almost all striking skills. Key quantities link angular displacement, velocity, acceleration and inertia.
角运动描述绕轴的转动，是跳水、体操、花样滑冰以及几乎所有击球技能的核心。关键物理量将角位移、角速度、角加速度和转动惯量联系起来。
Angular velocity (ω) measures the rate of change of angular displacement.
ω = Δθ / Δt
角速度 (ω)： 角位移对时间的变化率。单位为 rad s⁻¹。高尔夫挥杆或投掷臂的角速度越大，末端线速度越高。
Angular acceleration (α) is the rate of change of angular velocity.
α = Δω / Δt
角加速度 (α)： 角速度的变化率。在发力阶段中增加角加速度有助于产生更大的旋转速度。
Linear–angular link: When a point rotates around an axis at a distance r, its linear velocity is proportional to angular velocity.
v = r × ω
线–角关系： 物体上某点绕轴旋转时，线速度 v = r × ω。对于给定的角速度，旋转半径越大，线速度越大 – 这点解释了为什么长臂投掷和长球拍击球能产生更大的球速。
Moment of inertia (I) quantifies resistance to angular acceleration. For a point mass, I = m r²; for human segments it depends on mass distribution. To spin faster, an ice skater pulls the arms in, reducing I and increasing ω because angular momentum is conserved.
L = I × ω (conserved when net external torque is zero)
转动惯量 (I)： 反映物体抵抗角加速度的能力。质点 I = m r²；人体环节的转动惯量取决于质量分布。在无外力矩时角动量 L = I × ω 守恒，因此花滑运动员缩紧手臂可减小 I、增大 ω 实现加速旋转。
7. Fluid Dynamics | 流体动力学
Fluid mechanics principles explain why projectiles swerve, why cyclists adopt streamlined positions, and how an aerofoil creates lift. Two concepts are particularly prominent: Bernoulli’s principle and the Magnus effect.
流体力学原理解释了物体为何弧线飞行、自行车运动员为何采用低风阻姿态以及翼型如何产生升力。其中伯努利原理和马格努斯效应尤其突出。
Bernoulli’s principle: In a horizontal flow, an increase in fluid speed occurs simultaneously with a decrease in pressure. For an aerofoil (e.g. a discus or javelin oriented at an angle of attack), faster airflow over one surface lowers pressure, creating a net lift force perpendicular to the flow.
Pressure + ½ρv² + ρgh = constant (along a streamline)
伯努利原理： 在水平流动中，流速增加伴随压力降低。对于翼型物体（如以一定攻角飞行的铁饼或标枪），一侧气流较快、压力较低，由此产生垂直于流动方向的净升力。等式为 压力 + ½ρv² + ρgh = 常数。
Magnus effect: A spinning object drags a boundary layer of air; on one side the air speed increases and pressure drops, while on the opposite side the air speed decreases and pressure rises. The resulting pressure difference creates a transverse force, curving the flight path
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