Year 13 CCEA PE: Quick Reference Formula & Theorem Handbook | Year 13 CCEA 体育：公式定理速查手册

📚 Year 13 CCEA PE: Quick Reference Formula & Theorem Handbook | Year 13 CCEA 体育：公式定理速查手册

This guide brings together the essential formulas and scientific principles required for Year 13 CCEA Physical Education. From linear motion to fluid mechanics, from energy systems to psychological laws, these concepts form the analytical backbone of the course. Use this handbook to revise efficiently and apply the right equation in exam situations.

这本指南汇总了 Year 13 CCEA 体育学科必备的核心公式与科学原理。无论是线性运动、流体力学，还是能量系统与心理学定律，这些概念构成了课程的分析基础。利用这本手册高效复习，并在考试情境中准确运用正确的公式。

1. Kinematics – Linear Motion | 运动学 – 直线运动

The relationship between displacement, velocity and time is fundamental to analysing human movement. Average speed is the rate of change of distance, while velocity specifies direction. Acceleration describes how quickly velocity changes, whether in a sprint start or a decelerating tackle.

位移、速度和时间的关系是分析人体运动的基础。平均速率是距离的变化率，而速度包含方向。加速度描述速度变化的快慢，无论是短跑起跑还是减速擒抱动作中都同样适用。

v = d / t

a = (v − u) / t

Where v is final velocity, u is initial velocity, d is displacement and t is time. These scalar and vector quantities help interpret split times or video analysis of gait. In many CCEA exam questions, students must rearrange these relationships to find time or distance from given sprint data.

其中 v 表示末速度，u 表示初速度，d 表示位移，t 表示时间。这些标量和矢量可以用于解读分段计时或步态视频分析。在 CCEA 的许多考题中，考生需要变形这些关系式，根据给出的短跑数据求出时间或距离。

2. Newton’s Laws and Momentum | 牛顿定律与动量

Newton’s three laws of motion underpin nearly every biomechanical explanation in sport. The first law of inertia explains why a football remains at rest until kicked. The second law links force, mass and acceleration, while the third law accounts for the equal and opposite reaction when a swimmer pushes against the water.

牛顿三大运动定律奠定了几乎所有运动生物力学解释的基础。第一定律（惯性定律）可以解释为什么足球保持静止直到被踢开。第二定律将力、质量和加速度联系起来，第三定律则解释了游泳者向后推水时产生的大小相等、方向相反的反作用力。

F = m × a

Momentum, the product of mass and velocity, is conserved in collisions. This principle is used to evaluate tackle effectiveness or the follow‑through phase in a tennis stroke. Impulse, equal to the change in momentum, is often expressed as force multiplied by time.

动量是质量与速度的乘积，在碰撞中守恒。这一原理可用于评估抢断效果或网球击球中的随挥阶段。冲量等于动量的变化，通常表达为力与时间的乘积。

p = m × v

Impulse = F × Δt = Δp

Students should be able to apply these equations to explain how increasing the time of impact reduces the force experienced, as seen in landing techniques and protective padding.

考生应能运用这些公式解释如何通过增加冲击时间来减小作用力，例如在落地技术和保护垫的应用中所见。

3. Work, Power and Energy | 功、功率和能量

Work is done when a force moves its point of application in the direction of the force. In sport, mechanical work translates into kinetic or potential energy. Power, the rate at which work is performed, is a key determinant of explosive performance such as jumping or sprinting.

当力使其作用点在力的方向上移动时就做了功。在运动中，机械功转化为动能或势能。功率是做功的速率，是衡量纵跳或短跑等爆发性表现的关键因素。

W = F × d

P = W / t or P = F × v

Kinetic energy (½mv²) and gravitational potential energy (mgh) illustrate energy transfer, for instance during a pole vault. Understanding these transformations helps evaluate efficiency in movement and the role of the stretch‑shortening cycle.

动能（½mv²）和重力势能（mgh）能展示能量传递，例如在撑竿跳高过程中。理解这些转化有助于评估运动效率和牵拉‑缩短循环的作用。

Eₖ = ½ m v²

Eₚ = m g h

4. Levers and Torque in Biomechanics | 生物力学中的杠杆与力矩

The human body operates through a system of levers. A lever amplifies force or range of motion depending on the arrangement of fulcrum, effort and load. Torque, or moment of force, determines the turning effect around a joint.

人体通过杠杆系统运作。杠杆根据支点、动力和阻力的排列方式放大力量或增大运动范围。力矩（力的转动力矩）决定着关节周围的转动效果。

Torque = F × d

Where d is the perpendicular distance from the axis of rotation. First, second and third‑class levers are all present in the body; for example, the ankle during plantar flexion acts as a second‑class lever to produce propulsive force.

其中 d 是到转动轴的垂直距离。人体中存在第一、第二和第三类杠杆；例如，踝关节在跖屈时作为第二类杠杆产生推进力。

Summing torques helps explain stability and the ability to resist rotation, while applying the principle of moments is essential for analysing static balances in gymnastics.

合力矩可以解释稳定性和抵抗转动的能力，而力矩原理的应用对于分析体操中的静态平衡姿势至关重要。

5. Angular Motion and Moment of Inertia | 角运动与转动惯量

Angular kinematics describes rotary motion of a limb or the whole body. Angular velocity and angular acceleration mirror their linear counterparts, and the relationships are crucial for sports involving rotation, from diving to figure skating.

角运动学描述肢体或整个身体的旋转运动。角速度和角加速度与对应的线性量类似，对于涉及旋转的运动——从跳水到花样滑冰——这些关系至关重要。

ω = θ / t  α = (ω₂ − ω₁) / t

Moment of inertia (I) depends on mass and its distribution relative to the axis. The angular equivalent of Newton’s second law relates torque, moment of inertia and angular acceleration.

转动惯量 (I) 取决于质量及其相对于轴的分布。牛顿第二定律的角运动等价形式将力矩、转动惯量和角加速度联系起来。

Torque = I × α

Angular momentum (L = I × ω) is conserved when no external torque acts. This principle explains why a diver spins faster when tucking, a classic exam application of the conservation law.

当无外力矩作用时，角动量 (L = I × ω) 守恒。这一原理解释了为何跳水运动员在抱膝时旋转加快，这是角动量守恒定律的经典考题应用。

6. Fluid Mechanics – Bernoulli and Magnus | 流体力学 – 伯努利原理与马格努斯效应

Fluid forces significantly influence sporting objects in flight. Bernoulli’s principle states that an increase in fluid velocity occurs simultaneously with a decrease in pressure. This creates lift on an aerofoil or a discus, and is used to explain the curved path of a spinning ball.

流体力显著影响飞行中的运动物体。伯努利原理指出，流体速度增加的同时压力会降低。这在翼型或铁饼上产生升力，并被用来解释旋转球体的弯曲轨迹。

The Magnus effect is the resultant force on a spinning cylinder or sphere moving through a fluid. A topspin volleyball experiences a downward force, shortening its flight, while backspin can extend it. These effects are vital in tennis, football and golf.

马格努斯效应是旋转圆柱体或球体在流体中运动时受到的合力。上旋排球会受到一个向下的力，缩短其飞行距离，而下旋则可以延长飞行距离。这些效应在网球、足球和高尔夫中至关重要。

Pressure + ½ρv² + ρgh = constant

The above Bernoulli equation links pressure, fluid density (ρ) and velocity. Candidates may be asked to sketch airflow around a spinning ball and indicate regions of high and low pressure.

上式为伯努利方程，将压力、流体密度 (ρ) 和速度联系在一起。考生可能被要求示意画出绕旋转球体的气流，并标出高压和低压区域。

7. Cardiovascular Formulae | 心血管系统公式

The heart functions as a pump, and its output is a direct indicator of aerobic fitness. Cardiac output (Q) is the product of heart rate (HR) and stroke volume (SV). Changes during exercise are a staple topic in CCEA examinations.

心脏起着泵的作用，其输出量是有氧体适能的直接指标。心输出量 (Q) 是心率 (HR) 与每搏输出量 (SV) 的乘积。运动过程中的心输出量变化是 CCEA 考试中的常见考点。

Q = HR × SV

Mean arterial pressure (MAP) reflects the average blood pressure in arteries. It can be estimated from systolic and diastolic values, and understanding it helps explain blood flow redistribution during physical activity.

平均动脉压 (MAP) 反映动脉血压的平均值。它可以通过收缩压和舒张压估算，理解这一概念有助于解释身体活动期间的血流重新分配。

MAP = DBP + ⅓(SBP − DBP)

Additionally, the Fick equation for oxygen consumption (VO₂ = Q × a-v̅O₂ difference) shows how oxygen delivery and extraction jointly determine aerobic capacity. It illustrates the integration of cardiovascular and respiratory systems.

此外，计算摄氧量的菲克方程（VO₂ = Q × 动静脉氧差）表明氧输送和氧提取共同决定了有氧能力，展示了心血管和呼吸系统的一体化运作。

8. Respiratory Equations | 呼吸系统公式

Pulmonary ventilation (VE) is the volume of air moved in and out of the lungs per minute. It is calculated from tidal volume (TV) and breathing frequency (f), both of which rise dramatically during intense exercise.

每分通气量 (VE) 是指每分钟进出肺的气体量。它由潮气量 (TV) 和呼吸频率 (f) 计算得出，两者在进行剧烈运动时均会显著上升。

VE = TV × f

Alveolar ventilation accounts for dead space (VD) and represents the fresh air reaching the alveoli. This is more accurate for gauging effective gas exchange. CCEA candidates may be asked to compare values at rest and during exercise.

肺泡通气量考虑了死腔量 (VD)，代表到达肺泡的新鲜空气量，这是衡量有效气体交换的更精确指标。CCEA 考生可能被要求比较静息和运动时的相关数值。

VA = (TV − VD) × f

Lung volumes such as vital capacity (VC), residual volume (RV) and total lung capacity (TLC) are measured using spirometry. Knowledge of typical values and changes due to training helps evaluate respiratory adaptations.

肺活量 (VC)、残气量 (RV) 和肺总量 (TLC) 等肺容积指标通过肺活量计测定。了解其典型值及训练引起的变化，有助于评估呼吸系统的适应。

9. Energy Systems and Metabolic Calculations | 能量系统与代谢计算

The three energy systems – ATP‑PC, glycolytic and aerobic – resynthesise ATP at different rates and capacities. Understanding their interplay allows a coach to design appropriate training. The ATP yield from a molecule of glucose differs markedly between aerobic and anaerobic pathways.

三大能量系统——ATP‑PC 系统、糖酵解系统和有氧系统——以不同的速率和容量再合成 ATP。理解它们之间的相互作用，有助于教练设计合适的训练方案。一分子葡萄糖在有氧和无氧途径中的 ATP 产率差异显著。

Aerobic: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ~38 ATP

Anaerobic glycolysis: C₆H₁₂O₆ → 2 lactic acid + 2 ATP

Respiratory exchange ratio (RER) is the ratio of carbon dioxide produced to oxygen consumed (V̅CO₂ / V̅O₂). It indicates the predominant fuel being used. An RER of 0.7 implies mainly fat oxidation, while 1.0 indicates pure carbohydrate combustion.

呼吸交换率 (RER) 是产生的二氧化碳量与消耗的氧气量之比 (V̅CO₂ / V̅O₂)，能够指示机体主要利用的燃料类型。RER 为 0.7 时意味着主要氧化脂肪，而 1.0 则表示纯粹燃烧碳水化合物。

10. Body Composition Indices | 身体成分指数

Body mass index (BMI) offers a simple measure of body composition, although it does not distinguish between fat and muscle mass. It remains a useful population‑level screening tool for health risks linked to obesity.

身体质量指数 (BMI) 提供了一种简便的身体成分测量方法，尽管它不能区分脂肪和肌肉质量。它仍是评估肥胖相关健康风险的一种有用的群体筛查工具。

BMI = body mass (kg) / (height (m))²

Waist‑to‑hip ratio (WHR) is another predictor of cardiovascular disease risk. A high value indicates central adiposity, which is particularly relevant for athletes in weight‑category sports where body composition manipulation is common.

腰臀比 (WHR) 是心血管疾病风险的另一个预测指标。数值较高说明腹部脂肪堆积，这对于需要控制体重的运动项目的运动员尤其具有参考意义，因为此类运动中常涉及身体成分的调控。

Skinfold measurements, when converted using appropriate equations, estimate body fat percentage more accurately than BMI. The Durnin and Womersley or Jackson‑Pollock equations are frequently cited in the CCEA specification.

皮褶厚度测量值通过适当的公式换算后，能比 BMI 更准确地估算体脂百分比。Durnin 和 Womersley 公式或 Jackson‑Pollock 公式在 CCEA 考纲中经常被提及。

11. Skill Acquisition – Hick’s Law | 技能习得 – 希克定律

Hick’s law describes the relationship between the number of choices available and the time required to make a decision. It states that reaction time increases logarithmically as the number of stimulus–response alternatives grows.

希克定律描述了可选选项的数量与做出决策所需时间之间的关系。该定律指出，随着刺激‑反应备选项数量的增加，反应时间呈对数增长。

In a sport context, a midfielder scanning many passing options will have a longer reaction time than a defender with only one obvious clearance route. Coaches can simplify tactical decisions to speed up responses under pressure.

在运动情境中，一名中场球员扫视多个传球选项时的反应时间，会比仅有一个明显解围路线的后卫更长。教练可以通过简化战术决策来加快压力下的反应速度。

The mathematical form is often expressed as RT = a + b log₂(n), where n is the number of choices. This formula appears in information‑processing models alongside signal detection and attention theories.

其数学形式通常表示为 RT = a + b log₂(n)，其中 n 为选项数量。该公式与信号检测和注意力理论一样，出现在信息加工模型中。

12. Psychological Principles – Yerkes‑Dodson & Drive Theory | 心理学原理 – 耶克斯‑多德森定律与驱力理论

The Yerkes‑Dodson law proposes an inverted‑U relationship between arousal and performance. Optimal performance occurs at a moderate level of arousal, and this optimal point shifts for different tasks and individuals.

耶克斯‑多德森定律提出，唤醒水平与运动表现之间呈倒 U 形关系。中等唤醒水平时会产生最佳表现，而这一最佳点会因任务类型和个体差异而改变。

Fine motor skills, like putting in golf, require lower arousal for peak performance, whereas gross motor tasks, such as a rugby tackle, benefit from higher arousal. CCEA candidates must be able to apply this law to real sporting examples.

高尔夫推杆等精细运动技能需要较低的唤醒水平才能获得最佳表现，而橄榄球抢断等粗大运动任务则在较高唤醒水平下表现更好。CCEA 考生须能将这一定律应用于实际运动案例。

Drive theory, by contrast, states that performance is a direct product of habit strength and drive (P = H × D). Although less valid for complex skills, it still explains how a well‑learned skill can be performed more reliably under high arousal.

相比之下，驱力理论认为运动表现是习惯强度与驱力直接相乘的结果（P = H × D）。尽管该理论对复杂技能的解释力较弱，但它仍能说明为何高度熟练的技能在高唤醒状态下能够更稳定地表现出水平。

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