📚 Quick Reference Handbook: Formulas & Theorems for Year 11 Eduqas PE | 速查手册：Eduqas 体育公式定理
This quick reference handbook brings together all the essential formulas and theorems you need to master for the Eduqas GCSE Physical Education examination. From calculating training zones to understanding the mechanics of movement, these principles underpin both paper 1 and paper 2 topics. Use this guide to memorise the equations, learn how to apply them, and strengthen your exam answers with accurate numerical examples.
这份速查手册汇总了你需要为 Eduqas 体育（GCSE）考试掌握的所有基本公式和定理。从计算训练区间到理解运动力学，这些原理贯穿试卷一和试卷二。利用本指南记住公式、学会应用它们，并用准确的数字范例巩固你的考试答案。
1. Maximum Heart Rate (MHR) | 最大心率
The most widely used estimation of maximum heart rate is 220 minus your age. For a 15‑year‑old student, this gives an MHR of 205 beats per minute (bpm). Although individual variation exists, this formula provides a baseline figure for setting training intensities in aerobic and anaerobic sessions.
最常用的最大心率估算公式是 220 减去年龄。对 15 岁的学生来说，得出 MHR 为 205 次/分。尽管存在个体差异，该公式为设定有氧和无氧训练强度提供了基准数值。
MHR = 220 − age (years)
For example, a 16‑year‑old performer would have an estimated MHR of 204 bpm. This number is then used to calculate aerobic and anaerobic training zones, making it the foundation of any heart‑rate‑based training programme.
例如，一名 16 岁的运动员估算 MHR 为 204 次/分。这一数值随后用于计算有氧和无氧训练区间，成为一切基于心率的训练计划的基础。
2. Training Zones (Karvonen Method and Simple Percentage) | 训练区间（卡氏法和简单百分比法）
Training zones target specific physiological adaptations. The simplest method multiplies MHR directly by the desired intensity percentage. A more precise method, the Karvonen formula, uses resting heart rate (RHR) to calculate heart rate reserve (HRR). For GCSE, the direct percentage method is most common: aerobic zone is typically 60–80% of MHR, and anaerobic zone is 80–90% of MHR.
训练区间针对特定的生理适应。最简单的方法是将 MHR 直接乘以所需强度百分比。更精确的卡氏公式则利用安静心率（RHR）计算储备心率（HRR）。在 GCSE 阶段，直接百分比法最常见：有氧区间通常为 MHR 的 60%–80%，无氧区间为 MHR 的 80%–90%。
Target HR = MHR × Intensity (%)
For a performer with MHR 200 bpm, an aerobic session at 70% intensity would aim for 200 × 0.70 = 140 bpm. Working in the correct zone ensures that the body’s energy systems are trained effectively—fat metabolism in the aerobic zone and lactate tolerance in the anaerobic zone.
对于 MHR 为 200 次/分的运动员，70% 强度的有氧训练目标是 200 × 0.70 = 140 次/分。在正确的区间内训练，能确保身体的能量系统得到有效锻炼——有氧区间促进脂肪代谢，无氧区间提高乳酸耐受。
3. Speed, Distance, and Time | 速度、距离和时间
Speed describes how fast a performer moves and is a scalar quantity. It is calculated by dividing the distance covered by the time taken. This simple relationship is vital for analysing sprint performance, recording match running data, and calculating average speeds in every sport from athletics to rugby.
速度描述运动员移动的快慢，是一个标量。它通过移动距离除以所用时间计算得出。这个简单的关系对于分析冲刺表现、记录比赛跑动数据和计算从田径到橄榄球各项运动的平均速度至关重要。
Speed (m/s) = Distance (m) ÷ Time (s)
A 100 m sprinter crossing the line in 11.0 seconds has an average speed of 100 ÷ 11.0 ≈ 9.09 m/s. Understanding this formula also helps coaches interpret data from GPS trackers and set benchmarks for pace during endurance events.
一名 100 米短跑运动员以 11.0 秒冲线，其平均速度为 100 ÷ 11.0 ≈ 9.09 m/s。理解此公式还有助于教练解读 GPS 追踪器数据，并为耐力项目设定配速基准。
4. Velocity and Displacement | 速度与位移（矢量）
Velocity differs from speed because it is a vector: it accounts for direction. It is defined as displacement (the straight‑line distance in a given direction) divided by time. In many sports, direction matters—think of a return pass in hockey or a shuttle run in fitness testing.
速度（矢量）不同于速率，因为它考虑了方向。它定义为位移（给定方向上的直线距离）除以时间。在许多运动中，方向至关重要——想想曲棍球中的回传球或体能测试中的折返跑。
Velocity (m/s) = Displacement (m) ÷ Time (s)
If a netball player runs from the centre circle to a sideline and back, her total distance may be 30 m but her displacement is zero, so average velocity is zero. Recognising this distinction is essential when analysing changes in movement patterns and momentum.
如果一名篮网球运动员从中圈跑到边线再折返，总距离可能是 30 米，但位移为零，因此平均速度为零。在分析运动模式变化和动量时，认识到这一区别至关重要。
5. Acceleration | 加速度
Acceleration measures how quickly velocity changes. It is particularly relevant at the start of a race or when an athlete changes direction sharply. Positive acceleration means speeding up; negative acceleration (deceleration) means slowing down, often important in injury prevention.
加速度衡量速度变化的快慢。它在比赛起跑阶段或运动员急剧变向时尤为相关。正加速度意味着加速；负加速度（减速）意味着减速，在损伤预防中往往很重要。
Acceleration (m/s²) = Change in Velocity (m/s) ÷ Time (s)
A footballer accelerating from rest to 8 m/s in 2 seconds has an acceleration of (8 − 0) ÷ 2 = 4 m/s². Explosive athletes exhibit high acceleration values, which are critical for creating space and beating opponents over short distances.
一名足球运动员从静止加速到 8 m/s 用时 2 秒，其加速度为 (8 − 0) ÷ 2 = 4 m/s²。爆发力强的运动员展现出高加速度值，这在短距离内创造空间和击败对手时至关重要。
6. Force, Mass, and Acceleration (Newton’s Second Law) | 力、质量和加速度（牛顿第二定律）
Newton’s second law of motion states that the net force acting on an object equals its mass multiplied by its acceleration. In sport, every time a player pushes against the ground, kicks a ball, or rows a boat, this principle applies. The greater the force, the greater the acceleration for a given mass.
牛顿第二运动定律指出，作用在物体上的合外力等于其质量乘以加速度。在体育运动中，每当运动员蹬地、踢球或划船，都适用这一原理。在给定质量下，力越大，加速度越大。
F = m × a (Force in newtons, N; mass in kg; acceleration in m/s²)
A tennis player hitting a ball of mass 0.057 kg which accelerates at 200 m/s² exerts a force of 0.057 × 200 = 11.4 N. This law also explains why lighter rackets can be swung faster—reduced mass allows quicker acceleration with the same muscular force.
一名网球运动员击打质量为 0.057 kg 的球，其加速度为 200 m/s²，施加的力为 0.057 × 200 = 11.4 N。该定律也解释了为何更轻的球拍能挥得更快——在相同肌肉力量下，减轻质量可加快加速度。
7. Momentum | 动量
Momentum is the product of an object’s mass and velocity. A moving performer or object with greater momentum is harder to stop or change direction. In contact sports, tackling an opponent with high momentum requires a large impulse (force × time) to bring them to rest.
动量是物体质量和速度的乘积。动量更大的运动员或物体更难被拦停或改变方向。在对抗性运动中，擒抱动量高的对手需要较大的冲量（力 × 时间）才能使其停下。
Momentum (kg m/s) = Mass (kg) × Velocity (m/s)
A rugby player of mass 95 kg sprinting at 7 m/s has a momentum of 95 × 7 = 665 kg m/s. Coaches often refer to this when designing defensive drills—defenders need to generate an equal or greater impulse to stop a forward’s momentum.
一名体重 95 kg 的橄榄球运动员以 7 m/s 冲刺，其动量为 95 × 7 = 665 kg m/s。教练在设计防守训练时常提及此概念——防守者需要产生相等或更大的冲量才能阻止前锋的动量。
8. Impulse and the Force–Time Relationship | 冲量与力–时间关系
Impulse is the change in momentum of an object. It equals the average net force multiplied by the time over which the force acts. In sport, increasing the time of contact (e.g., ‘giving’ with the hands when catching a ball) reduces the peak force and lowers injury risk.
冲量是物体动量的变化量。它等于平均合外力乘以力作用的时间。在体育运动中，延长接触时间（例如，接球时手随球后收）可减小峰值力并降低受伤风险。
Impulse = F × t = Δ Momentum
When a hockey goalkeeper pads a fast shot, pulling the hands back at the moment of impact increases the time t, thus reducing the force F for the same impulse. This principle underpins all safe landing and catching actions.
当曲棍球守门员用护腿挡出快速射门时，在触球瞬间将手后撤可增加时间 t，从而在同样冲量下减小力 F。这一原理是安全落地和接球动作的基础。
9. Weight and Gravity | 重量与重力
Weight is the force due to gravity acting on an object’s mass. On Earth the acceleration due to gravity g is approximately 9.8 m/s². A performer’s weight changes if they were on a different planet, but their mass remains constant. In biomechanics, weight acts through the centre of mass and influences stability.
重量是由于重力作用在物体质量上的力。地球上的重力加速度 g 约为 9.8 m/s²。如果运动员在另一颗行星上，重量会改变，但质量不变。在生物力学中，重量通过重心作用，并影响稳定性。
Weight (N) = Mass (kg) × g (9.8 m/s²)
A gymnast of mass 60 kg has a weight of 60 × 9.8 = 588 N. When she performs a balance on a beam, her line of gravity must fall within her base of support to remain stable—a concept directly linked to weight distribution.
一名体重 60 kg 的体操运动员重量为 60 × 9.8 = 588 N。当她在平衡木上做平衡动作时，她的重力线必须落在支撑面内才能保持稳定——这一概念直接与重量分布有关。
10. Levers and Mechanical Advantage | 杠杆与机械效益
The body acts as a system of levers where bones are levers, joints are fulcrums, and muscles provide effort. The mechanical advantage (MA) of a lever tells you whether it favours speed and range of motion or force production. In Eduqas, you need to identify first, second and third class levers and recognise their mechanical advantage in sporting actions.
人体是一个杠杆系统，骨骼为杠杆，关节为支点，肌肉提供力。杠杆的机械效益（MA）表明它是有利于速度和运动幅度，还是有利于产生力量。在 Eduqas 课程中，你需要识别第一、第二和第三类杠杆，并认识它们在运动动作中的机械效益。
Mechanical Advantage = Effort Arm Length ÷ Resistance Arm Length
If the effort arm is longer than the resistance arm, MA > 1, favouring force (e.g., calf muscles acting at the ankle during plantar flexion, a second‑class lever). If the resistance arm is longer, MA < 1, favouring speed (e.g., biceps curling a weight, a third‑class lever). Sprinters’ long legs create a large resistance arm, requiring high muscular effort to generate rapid leg speed.
如果力臂长于阻力臂，MA > 1，有利于产生力量（例如，趾屈时小腿肌在踝关节处的作用，这是第二类杠杆）。如果阻力臂更长，MA < 1，有利于速度（例如，肱二头肌弯举重物，第三类杠杆）。短跑运动员的长腿形成较大的阻力臂，需要高度肌力来产生快速的腿部速度。
11. Centre of Mass and Stability | 重心与稳定性
The centre of mass (COM) is the point where the body’s mass is concentrated. Stability increases when the COM is low, the base of support is wide, and the line of gravity falls centrally within the base. These principles are applied in defensive stances and gymnastics.
重心是身体质量集中的点。当重心较低、支撑基座较宽、重力线落在支撑基座中央时，稳定性增加。这些原理应用于防守站姿和体操中。
Stability ∝ Base of Support width × Low COM
A rugby scrum‑half waiting to receive the ball adopts a low, wide stance to resist being pushed over. A high jumper, by contrast, uses a curved run‑up to manipulate the COM so that it actually passes underneath the bar while the body arches over it—an application of COM that astounds biomechanists.
一名等待接球的橄榄球传锋采用低重心、宽基座站姿以抵抗被撞倒。相比之下，跳高运动员利用弧形助跑来操控重心，使重心实际上从横杆下方通过，而身体则拱形越过横杆——这是让生物力学学者惊叹的重心应用。
12. Aerobic Capacity: VO₂ max | 有氧能力：最大摄氧量
VO₂ max represents the maximum volume of oxygen the body can use per minute per kilogram of body weight during intense exercise. It is the gold‑standard measure of aerobic fitness. While direct measurement requires laboratory equipment, the concept underpins training prescriptions for endurance athletes.
最大摄氧量代表在剧烈运动中身体每分钟每公斤体重所能使用的最大氧气体积。它是衡量有氧适能的金标准。虽然直接测量需要实验室设备，但这一概念支撑着耐力运动员的训练处方。
VO₂ max (ml/kg/min) = Maximum O₂ uptake (ml/min) ÷ Body Mass (kg)
An Olympic rower might have a VO₂ max of 70 ml/kg/min, meaning each kilogram of her body can consume 70 ml of oxygen every minute at maximal effort. Training principles such as interval training and continuous training are designed to push this ceiling higher, delaying the onset of fatigue.
一名奥运赛艇运动员的最大摄氧量可能达 70 ml/kg/min，意味着在全力运动时，她每公斤体重每分钟能消耗 70 毫升氧气。间歇训练和持续训练等训练原则就是为了推高这一上限，延缓疲劳出现。
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