📚 AS WJEC Physical Education: Formula & Theorem Quick Reference Handbook | AS WJEC 体育：公式定理速查手册
This quick reference handbook brings together the essential formulas, principles and theorems required for the AS WJEC Physical Education specification. The content covers key areas of biomechanics alongside skill acquisition, providing a clear, bilingual summary to support revision and accurate application in exam-style questions. Every formula is presented with its standard units and a concise explanation of how it relates to sport and human movement.
本速查手册汇总了 AS WJEC 体育课程中必备的关键公式、原则与定理，内容涵盖生物力学和技能习得的重点，以清晰的双语提纲帮助考生在复习和答题中准确应用。每个公式都附有标准单位，并简要说明其在体育运动与人体运动中的实际意义。
1. Speed and Velocity | 速率与速度
Speed is a scalar quantity measuring how fast an object moves, calculated as the distance covered divided by the time taken. Velocity is a vector quantity, taking direction into account, and is defined as the rate of change of displacement.
速率是标量，衡量物体运动快慢，由通过的路程除以时间计算；速度是矢量，考虑运动方向，定义为位移的变化率。
v = d ÷ t
eplaces displacement. In a 100 m sprint, average speed reflects total path length per second, while average velocity over the straight race is also 10 m/s eastwards, but for a lap the net displacement may be zero, giving average velocity zero despite high speed.
v = 速度 (m/s)，d = 位移 (m)，t = 时间 (s)。速率中路程代替位移。在 100 米短跑中，平均速率反映每秒经过的路程，而沿直线跑的平速度同为 10 m/s 向东；但对于环形跑道一圈，净位移为零，平均速度为零而平均速率很大。
2. Acceleration | 加速度
Acceleration is the rate at which an object’s velocity changes. In sport, acceleration is crucial for evaluating how quickly a performer can reach top speed or change direction.
加速度是物体速度变化的速率。在运动中，加速度对于评价运动员多快能达到最大速度或多快能改变方向至关重要。
a = (v − u) ÷ t
icates deceleration. For a footballer accelerating from rest (0 m/s) to 8 m/s in 2 seconds, acceleration equals 4 m/s².
a = 加速度 (m/s²)，v = 末速度 (m/s)，u = 初速度 (m/s)，t = 时间 (s)。负值表示减速。一名足球运动员从静止（0 m/s）用 2 秒加速到 8 m/s，加速度为 4 m/s²。
3. Momentum and Impulse | 动量与冲量
Momentum is the product of a body’s mass and its velocity. Impulse is the change in momentum and equals the force applied multiplied by the time for which it acts.
动量是物体质量与速度的乘积。冲量是动量的变化量，等于施加的力乘以其作用时间。
p = m × v
Impulse = F × t = Δp = m(v − u)
(s). During a rugby tackle, a player of mass 80 kg moving at 6 m/s has momentum 480 kg m/s. A tackle applying a large force over a short time brings this momentum to zero.
p = 动量 (kg m/s)，m = 质量 (kg)，v = 速度 (m/s)，F = 力 (N)，t = 时间 (s)。橄榄球擒抱时，一名 80 kg、以 6 m/s 移动的运动员动量为 480 kg m/s。一次短时间的大力擒抱可将该动量减至零。
4. Newton’s Laws of Motion | 牛顿运动定律
Newton’s three laws underpin all linear motion in sport. They explain why objects move, how forces change motion, and why interactions are reciprocal.
牛顿三大定律是所有体育运动中线性运动的基础，解释了物体为何运动、力如何改变运动状态以及相互作用的对等性。
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）：物体在不受外力作用时，将保持静止或匀速直线运动状态。
is directly proportional to the net force applied and inversely proportional to its mass. | 第二定律（F = ma）：物体加速度与所受合外力成正比，与自身质量成反比。
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。
te forward (Third Law). The force determines the forward acceleration according to F = ma.
短跑起跑时，运动员向后蹬起跑器，起跑器施加等大反向的反作用力将运动员向前推进（第三定律），该力根据 F = ma 决定向前加速度。
5. Weight, Friction and Normal Reaction | 重力、摩擦力与法向反作用力
Weight is the force due to gravity acting on a mass. Friction opposes motion or the tendency for motion between surfaces. Normal reaction acts perpendicular to surfaces in contact.
重力（重量）是地球引力对物体质量的作用力。摩擦力阻碍接触面间的相对运动或运动趋势。法向反作用力垂直于接触面。
W = m × g
ational field strength (9.8 m/s²). Friction depends on the coefficient of friction (μ) and the normal reaction (R): Ffriction = μ × R. On a horizontal surface R = W. Studded boots increase μ, improving grip.
W = 重量 (N)，m = 质量 (kg)，g = 重力场强度 (9.8 m/s²)。摩擦力取决于摩擦系数 (μ) 和法向反作用力 (R)：摩擦力 = μ × R。水平面上 R = W。钉鞋通过增大 μ 来提升抓地力。
6. Moments and Torque | 力矩与转矩
A moment (or torque) is the turning effect of a force about a pivot or axis. In human movement, muscles generate torque around joints.
力矩（或转矩）是力绕支点或轴所产生的转动效应。人体运动中，肌肉围绕关节产生力矩。
T = F × d
ivot to the line of action of the force (m). To increase rotational effect, either increase force or moment arm. In a bicep curl, the biceps brachii force and its distance from the elbow joint create a torque to lift the forearm.
T = 力矩/转矩 (Nm)，F = 力 (N)，d = 支点到力作用线的垂直距离（力臂）(m)。增大转动效应可以加大力或加大力臂。在肱二头肌弯举中，肱二头肌施力及其与肘关节的距离产生力矩，使前臂上举。
7. Centre of Mass and Stability | 重心与稳定性
Centre of mass (CoM) is the point where all the body’s mass is considered to be concentrated. Stability depends on the position of CoM, the area of the base of support, and line of gravity.
重心（质心）是身体全部质量视为集中的点。稳定性取决于重心位置、支撑面面积以及重力线。
A body is more stable when CoM is low, base of support is wide, and the line of gravity falls centrally within the base. In a defensive stance in netball or rugby, players widen their feet and lower their hips, increasing stability.
重心低、支撑面宽且重力线落在支撑面中央时，身体更稳定。在无板篮球或橄榄球防守中，运动员会分腿降低重心，以增大稳定性。
8. Angular Kinematics | 角运动学
Angular motion describes rotation about an axis. Angular distance, angular displacement, angular velocity and angular acceleration are the core descriptors.
角运动描述物体绕轴的转动。角路程、角位移、角速度和角加速度是核心描述量。
ω = θ ÷ t
α = (ω₂ − ω₁) ÷ t
v = r × ω, where r is the radius of rotation. A diver pulling into a tight tuck reduces r, so for the same angular velocity, tangential velocity v decreases, but angular momentum effects dominate (see later law).
ω = 角速度 (rad/s)，θ = 角位移 (rad)，t = 时间 (s)，α = 角加速度 (rad/s²)。直线运动与角运动相关联：v = r × ω，其中 r 为旋转半径。跳水运动员收紧身体成团身姿势会减小 r，相同角速度下切向速度 v 减小，但角动量效应更为关键（见后续定律）。
9. Angular Kinetics: Moment of Inertia and Angular Momentum | 角动力学：转动惯量与角动量
Moment of inertia quantifies an object’s resistance to change in angular motion. It depends on mass and its distribution relative to the axis of rotation. Angular momentum is the product of moment of inertia and angular velocity.
转动惯量衡量物体对转动状态改变的抵抗程度，取决于质量及其绕转轴的分布。角动量是转动惯量与角速度的乘积。
I = Σ m r²
L = I × ω
. According to the conservation of angular momentum, when no external torque acts, L stays constant. If a figure skater pulls arms in, I decreases, so ω must increase, causing faster spins.
I = 转动惯量 (kg m²)，m = 质点质量 (kg)，r = 到转轴的距离 (m)。L = 角动量 (kg m²/s)。根据角动量守恒定律，在没有外力矩时，L 保持不变。花样滑冰运动员收拢手臂，转动惯量 I 减小，则角速度 ω 必然增大，旋转更快。
10. Hick’s Law in Skill Acquisition | 技能习得中的希克定律
Hick’s law describes the relationship between the number of stimulus-response choices and reaction time. It is widely used to explain decision-making delays in fast-paced sports.
希克定律描述了刺激 – 反应选择数量与反应时间之间的关系，广泛用于解释快节奏运动中的决策延迟。
RT = a + b log₂(n)
y probable choices. As n increases, log₂(n) grows, so RT rises. In a cricket batsman facing a bowler with only two possible deliveries, choice reaction time is lower than when facing a wide repertoire; coaches therefore develop strategies to reduce the effective number of choices, e.g. ‘play straight unless it’s on your legs’.
RT = 反应时间，a = 简单反应时间（常数），b = 每比特信息处理时间（斜率），n = 等可能选择的数量。随着 n 增加，log₂(n) 增大，RT 上升。板球击球手面对只有两种可能球路的投手时，选择反应时间较短；而面对多变线路时反应时间更长。因此教练会制定策略以减少有效选项，例如“除非来球接近腿部，否则直向挥击”。
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