📚 Year 12 AQA Physical Education: Formula & Theorem Quick Reference Guide | AQA 体育 Year 12：公式定理速查手册
This concise yet comprehensive guide brings together all the essential formulas, equations, and foundational principles you need for the Year 12 AQA Physical Education specification. From linear kinematics to cardiovascular dynamics, each topic is presented with clear formulas and paired English–Chinese explanations to support bilingual learners and reinforce your understanding for both theoretical exams and practical applications.
本简明且全面的手册汇集了 AQA Year 12 体育课程所需的所有核心公式、方程与基本原理。从线性运动学到心血管动力学，每个主题均以清晰的公式和英中对照解释呈现，帮助双语学习者巩固理论考试与实践应用中的理解。
1. Linear Kinematics | 线性运动学
v = d / t defines average speed (v) as total distance (d) divided by total time (t). This is a scalar quantity and does not account for direction.
v = d / t 将平均速率 v 定义为总距离 d 除以总时间 t。这是标量，不包含方向信息。
a = (v − u) / t gives average acceleration (a) as the change in velocity (v − u) divided by time (t). Acceleration is a vector, so direction matters.
a = (v − u) / t 将平均加速度 a 表示为速度变化量 (v − u) 除以时间 t。加速度是矢量，方向至关重要。
v = u + a t is the first suvat equation, linking final velocity (v) to initial velocity (u), acceleration (a) and time (t) when acceleration is constant.
v = u + a t 是第一个 suvat 方程，在加速度恒定时将末速度 v 与初速度 u、加速度 a 和时间 t 关联起来。
s = u t + ½ a t² calculates displacement (s) using initial velocity, time and constant acceleration. The ½ accounts for the linear increase in velocity.
s = u t + ½ a t² 用初速度、时间和恒定加速度计算位移 s。½ 体现了速度的线性增长。
v² = u² + 2 a s is a time-independent suvat equation, useful when time is not given. It relates final velocity to initial velocity, acceleration and displacement.
v² = u² + 2 a s 是不含时间的 suvat 方程，用于不给定时间时，将末速度与初速度、加速度和位移联系起来。
2. Newton’s Laws & Force | 牛顿定律与力
Newton’s First Law: an object remains at rest or in uniform motion unless acted upon by a net external force. This is the law of inertia.
牛顿第一定律：除非受到净外力作用，物体将保持静止或匀速直线运动状态。这是惯性定律。
F = m a (Newton’s Second Law): the net force (F) acting on an object equals its mass (m) multiplied by its acceleration (a). Both force and acceleration are vectors in the same direction.
F = m a（牛顿第二定律）：作用在物体上的净外力 F 等于物体质量 m 与其加速度 a 的乘积。力与加速度同向，均为矢量。
W = m g is the weight formula, where weight (W) is the force of gravity on a mass (m), and g is gravitational field strength (9.81 m s⁻² on Earth).
W = m g 是重量公式，其中重量 W 是作用在质量 m 上的重力，g 为重力场强度（地球上取 9.81 m s⁻²）。
Newton’s Third Law: for every action force there is an equal and opposite reaction force. These forces act on different bodies and never cancel each other on the same body.
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。这两个力作用在不同物体上，从不会在同一个物体上抵消。
3. Momentum & Impulse | 动量与冲量
p = m v defines linear momentum (p) as the product of mass (m) and velocity (v). Momentum is a vector quantity and is conserved in closed systems.
p = m v 将线动量 p 定义为质量 m 与速度 v 的乘积。动量是矢量，在封闭系统中守恒。
Impulse = F t = Δp: impulse is the product of force (F) and time (t) during which it acts, and it equals the change in momentum (Δp). This is the impulse–momentum theorem.
冲量 = F t = Δp：冲量是作用力 F 与其作用时间 t 的乘积，等于动量的变化量 Δp。这就是冲量-动量定理。
In collisions, total momentum before impact equals total momentum after impact, provided no external forces act: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
在碰撞中，若无外力作用，碰撞前的总动量等于碰撞后的总动量：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。
4. Friction & Free-body Diagrams | 摩擦力与受力图
F = μ R gives the maximum static or kinetic friction force (F) as the product of the coefficient of friction (μ) and the normal reaction force (R). Friction always opposes motion or attempted motion.
F = μ R 表示最大静摩擦力或动摩擦力 F 等于摩擦系数 μ 与法向反作用力 R 的乘积。摩擦力总是阻碍运动或运动趋势。
Free-body diagrams isolate a body and show all forces acting on it: weight (down), normal reaction (perpendicular to surface), applied forces, friction and air resistance. Correct vector arrows are essential for resolving forces.
受力图将物体隔离出来，显示作用在其上的所有力：重力（向下）、法向反作用力（垂直于接触面）、施加的力、摩擦力和空气阻力。正确的矢量箭头对力的分解至关重要。
When forces are balanced, net force = 0 and the body remains at rest or in constant velocity (Newton’s First Law).
当力平衡时，净力为零，物体保持静止或匀速运动（牛顿第一定律）。
5. Projectile Motion | 抛体运动
A projectile’s horizontal velocity (u cos θ) remains constant because air resistance is neglected and gravity acts only vertically. The vertical motion is uniformly accelerated under g = 9.81 m s⁻².
抛体的水平速度 u cos θ 保持恒定，因为忽略空气阻力且重力只作用于竖直方向。竖直方向运动在 g = 9.81 m s⁻² 下均匀加速。
vᵧ = u sin θ − g t gives the vertical component of velocity at any time t. At the peak, vᵧ = 0.
vᵧ = u sin θ − g t 给出任意时刻 t 的竖直分速度。在最高点，vᵧ = 0。
Time of flight: t = (2 u sin θ) / g. Range: sₓ = u cos θ × t. Maximum height: h = (u² sin² θ) / (2 g).
飞行时间：t = (2 u sin θ) / g。射程：sₓ = u cos θ × t。最大高度：h = (u² sin² θ) / (2 g)。
The optimal release angle for maximum range on horizontal ground is 45° when release and landing heights are equal.
当出手高度与落地高度相同时，水平面上最大射程的最佳出手角度为 45°。
6. Centre of Mass & Stability | 重心与稳定性
The centre of mass (COM) is the point where the entire mass of an object appears to be concentrated. In a uniform gravitational field it coincides with the centre of gravity.
重心是物体全部质量看似集中的点。在均匀重力场中，重心与质心重合。
Stability increases when the COM is low, the line of gravity falls within the base of support, and the base of support is wide. These principles apply directly to athletic stances and recovery positions.
重心低、重力作用线落在支撑面内且支撑面较宽时，稳定性增强。这些原理直接运用于运动姿势与恢复体位。
An object topples when the line of gravity moves outside the base of support, creating an unbalanced moment that rotates the body.
当重力作用线移出支撑面时，物体会倾倒，产生不平衡力矩使身体转动。
7. Levers & Torque | 杠杆与力矩
T = F d defines torque (moment of force) as the product of force (F) and the perpendicular distance (d) from the pivot to the line of action. Unit: newton metre (N m).
T = F d 将力矩（扭矩）定义为力 F 与支点到力作用线的垂直距离 d 的乘积。单位：牛顿米 (N m)。
A lever system consists of an effort arm, a load arm and a fulcrum. The three classes are differentiated by the relative positions: 1st class (Fulcrum in middle, e.g. neck), 2nd class (Load in middle, e.g. ankle plantar flexion), 3rd class (Effort in middle, e.g. bicep curl).
杠杆系统由力臂、阻力臂和支点组成。三类杠杆根据相对位置区分：第一类（支点居中，如颈）、第二类（阻力居中，如踝跖屈）、第三类（动力居中，如肱二头肌弯举）。
Mechanical advantage = effort arm / resistance arm. A value >1 means the lever amplifies force; a value <1 amplifies speed and range of motion, common in many sporting actions.
机械效益 = 力臂 / 阻力臂。数值 >1 表示杠杆放大力量；<1 则放大速度和活动范围，这在许多运动动作中很常见。
8. Angular Motion | 角运动
ω = θ / t calculates angular velocity (ω) as the angle rotated (θ, in radians) divided by time (t). Unit: rad s⁻¹.
ω = θ / t 计算角速度 ω 为转动角度 θ（弧度）除以时间 t。单位：弧度/秒。
v = r ω links linear velocity (v) of a point on a rotating body to angular velocity (ω) and radius (r). The direction of v is tangential to the circle.
v = r ω 将旋转体上一点的线速度 v 与角速度 ω 和半径 r 联系起来。v 的方向沿圆的切线。
α = (ω₂ − ω₁) / t defines angular acceleration (α) as change in angular velocity per unit time. Analogous suvat-type equations can be written for angular motion: ω₂ = ω₁ + α t, θ = ω₁ t + ½ α t², ω₂² = ω₁² + 2 α θ.
α = (ω₂ − ω₁) / t 定义角加速度 α 为单位时间内角速度的变化。可类比写出角运动的 suvat 方程：ω₂ = ω₁ + α t，θ = ω₁ t + ½ α t²，ω₂² = ω₁² + 2 α θ。
9. Work, Energy & Power | 功、能量与功率
W = F s (work done) is the product of force (F) and displacement (s) in the direction of the force, when force is constant. Unit: joule (J).
W = F s（功）是力 F 与沿力方向上位移 s 的乘积（力恒定时）。单位：焦耳 (J)。
KE = ½ m v² is translational kinetic energy: the energy an object possesses due to its motion.
KE = ½ m v² 是平移动能：物体因运动而拥有的能量。
GPE = m g h is gravitational potential energy relative to a chosen reference level, where h is vertical height.
GPE = m g h 是相对于选定参考面的重力势能，h 为竖直高度。
P = W / t (power) is the rate of doing work or energy transfer. Also expressed as P = F v for an object moving at constant velocity v against a resisting force F.
P = W / t（功率）是做功或能量转移的速率。对于以恒定速度 v 克服阻力 F 运动的物体，也可表示为 P = F v。
Efficiency (%) = (useful work output / total energy input) × 100. In the body, metabolic efficiency limits the conversion of chemical energy into mechanical work.
效率 (%) = (有用功输出 / 总能量输入) × 100。在人体中，代谢效率限制了化学能向机械功的转换。
10. Cardiovascular System | 心血管系统
Q = SV × HR is the cardiac output equation: cardiac output (Q, L min⁻¹) = stroke volume (SV, mL per beat) × heart rate (HR, beats per min). All values must be in consistent units.
Q = SV × HR 是心输出量方程：心输出量 Q (L min⁻¹) = 每搏输出量 SV (mL/次) × 心率 HR (次/分)。所有数值单位须一致。
Stroke volume = EDV − ESV (end-diastolic volume minus end-systolic volume).
每搏输出量 = EDV − ESV（舒张末期容积减去收缩末期容积）。
HRmax = 220 − age provides an estimate of maximal heart rate. Intensity can be prescribed as a percentage of HRmax.
HRmax = 220 − age 预估最大心率。可用 HRmax 的百分比来设定运动强度。
Karvonen formula: Target HR = ((HRmax − HRrest) × intensity) + HRrest. This reserve heart rate method accounts for resting heart rate and better individualises training zones.
卡氏公式：目标心率 = ((HRmax − HRrest) × 强度) + HRrest。此储备心率法考虑了安静心率，能更好地个性化训练区间。
O₂ pulse = VO₂ / HR indicates the amount of oxygen consumed per heartbeat. It reflects the combined efficiency of the heart and the oxygen extraction by muscles.
O₂ pulse = VO₂ / HR 表示每次心跳所消耗的氧气量，反映心脏和肌肉氧摄取的综合效率。
11. Respiratory System & VO₂ | 呼吸系统与摄氧量
The Fick equation: VO₂ = Q × a-vO₂ diff. Oxygen uptake (VO₂) depends on cardiac output (Q) and the arterio-venous oxygen difference (a-vO₂ diff), which measures how much oxygen is extracted by tissues.
菲克方程：VO₂ = Q × a-vO₂ diff。摄氧量 VO₂ 取决于心输出量 Q 和动静脉氧差 a-vO₂ diff，后者衡量组织摄取的氧气量。
RQ = VCO₂ / VO₂ (respiratory quotient) reflects the ratio of carbon dioxide produced to oxygen consumed. An RQ of 0.7 indicates mainly fat utilisation; 1.0 indicates carbohydrate oxidation.
RQ = VCO₂ / VO₂（呼吸商）反映产生的二氧化碳与消耗的氧气之比。RQ=0.7 表示主要利用脂肪；RQ=1.0 表示碳水化合物氧化。
Minute ventilation: VE = TV × f, where TV is tidal volume (L per breath) and f is breathing frequency (breaths per minute). VE adjusts to meet exercise demands.
每分通气量：VE = TV × f，其中 TV 为潮气量（升/次），f 为呼吸频率（次/分）。VE 会调节以满足运动需求。
12. Fitness Testing & Body Composition | 体测与身体成分
BMI = weight (kg) / height² (m²) classifies individuals as underweight, normal, overweight or obese. It does not distinguish between muscle and fat mass.
BMI = 体重 (kg) / 身高² (m²) 用于分类偏瘦、正常、超重或肥胖。它不能区分肌肉与脂肪质量。
Percentage improvement: % improvement = ((new score − old score) / old score) × 100. This quantifies training progress or performance change.
进步百分比：% improvement = ((新成绩 − 旧成绩) / 旧成绩) × 100。可量化
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