📚 Year 9 OCR PE: Formula & Theorem Quick Reference Handbook | 九年级OCR体育：公式定理速查手册
This quick reference handbook brings together the essential formulas, key theorems, and core calculations you will encounter in Year 9 OCR Physical Education. Each entry is explained step by step to help you understand not just how to plug in numbers, but also the scientific principles behind them. Use this guide to revise performance analysis, training programme design, and movement mechanics.
这本速查手册汇集了你在九年级OCR体育课程中会用到的基本公式、关键定理和核心计算方法。每个条目都逐步解释，不仅让你知道如何代入数字，还能理解背后的科学原理。你可以利用这本指南来复习运动表现分析、训练计划设计和运动力学知识。
1. Maximum Heart Rate (MaxHR) Estimation | 最大心率估算
The simplest way to estimate an individual's maximum heart rate is the traditional formula: 220 minus age. This value is widely used to set training intensity zones, although it is an estimate and can vary depending on genetics and fitness level. For a Year 9 student aged 14, the estimated MaxHR would be 206 bpm.
估算个人最大心率最简单的方法是传统公式：220 减去年龄。该数值被广泛用于设定训练强度区间，尽管它只是一个估算值，可能因遗传和体能水平而异。对于一名 14 岁的九年级学生来说，预估的最大心率为 206 次/分。
MaxHR = 220 − Age
e), which can give a more accurate prediction for younger athletes. However, OCR materials often refer to the 220 − age model, so it is the one you should memorise. Understanding your MaxHR is the first step in monitoring exercise intensity safely and effectively.
近期的研究提出了一个略微调整的公式：208 − (0.7 × 年龄)，这可能为年轻运动员提供更准确的预测。不过，OCR 教材通常引用的还是 220 − 年龄 这个模型，所以你应该记住它。了解自己的最大心率是安全有效监控运动强度的第一步。
2. Target Heart Rate Zones | 目标心率区间
Once you know your estimated MaxHR, you can calculate the aerobic and anaerobic training zones. The aerobic zone, which develops cardiovascular endurance, typically works between 60% and 80% of MaxHR. The anaerobic zone, used for high-intensity bursts, operates from 80% to 90% of MaxHR. These percentages help you tailor a training session to the correct energy system.
一旦得知预估的最大心率，你就可以计算有氧训练区和无氧训练区了。有氧训练区用于发展心血管耐力，通常为最大心率的 60% 至 80%。无氧训练区用于高强度爆发性运动，范围是最大心率的 80% 至 90%。这些百分比能帮助你针对正确的供能系统制定训练课。
Aerobic lower limit = MaxHR × 0.60
Aerobic upper limit = MaxHR × 0.80
Anaerobic target ≈ MaxHR × 0.85
te reserve (HRR). HRR = MaxHR − RHR. Then the target heart rate = (HRR × desired intensity % aining zones adjust automatically. In Year 9, you may be asked to compare both approaches.
若要进行更加个性化的计算，卡沃宁公式引入了安静心率（RHR）和心率储备（HRR）。HRR = 最大心率 − 安静心率。然后目标心率 = (HRR × 期望强度%) + 安静心率。这种方法会考虑体能随时间的变化；当你安静心率下降时，训练区间会自动调整。在九年级，你可能会被要求比较这两种方法。
3. Training Load and Rate of Perceived Exertion (RPE) | 训练负荷与主观疲劳度
Training load is a simple but powerful formula used to monitor the stress placed on an athlete during a session. It combines session duration with the rate of perceived exertion (RPE). RPE is typically measured on the 6–20 Borg Scale, where 6 means no exertion and 20 represents maximal exertion. The product gives an arbitrary unit that helps coaches balance training and recovery.
训练负荷是一个简单但很有用的公式，用来监控运动员在一次训练中所承受的压力。它将训练时长与主观疲劳度（RPE）结合起来。RPE 通常采用 6–20 的博格量表进行测量，6 代表毫不费力，20 代表最大程度的用力。两者的乘积得出一个任意单位，帮助教练平衡训练和恢复。
Training Load = Session Duration (minutes) × RPE
For example, a 45-minute circuit session rated at 15 RPE yields a training load of 675 units. By tracking this value across a microcycle, you can identify when an athlete might be overtraining. Remember that RPE is subjective, so it works best when the athlete is familiar with the scale and answers honestly.
例如，一节 45 分钟的循环训练课，RPE 为 15，那么训练负荷就是 675 个单位。通过在一个小周期内追踪该数值，你就能判断运动员何时可能出现了过度训练。请记住，RPE 是主观的，因此当运动员熟悉量表并诚实作答时效果才最好。
4. Body Mass Index (BMI) | 身体质量指数
BMI is a quick screening tool that estimates whether an individual has a healthy body weight for their height. It is calculated by dividing body mass in kilograms by the square of height in metres. While BMI does not distinguish between muscle, fat, and bone, it remains a useful starting point in the study of body composition and health screening.
BMI 是一种快速筛查工具，用于估计一个人的体重相对于身高是否健康。它的计算方法是：用体重（千克）除以身高（米）的平方。尽管 BMI 无法区分肌肉、脂肪和骨骼，但在身体成分研究和健康筛查中它仍然是一个有用的起点。
BMI = Body Mass (kg) ÷ (Height (m))²
The World Health Organization classifies a BMI below 18.5 as underweight, 18.5–24.9 as normal weight, 25–29.9 as overweight, and 30 or above as obese. In OCR PE, you may be asked to calculate BMI from given data and then critique its limitations, particularly for athletes with high muscle mass such as rugby players.
世界卫生组织将 BMI 低于 18.5 归为体重过轻，18.5–24.9 为正常体重，25–29.9 为超重，30 及以上为肥胖。在 OCR 体育中，你可能会被要求根据给定数据计算 BMI，然后批判其局限性，特别是对于像橄榄球运动员这样肌肉量高的运动员。
5. Speed and Velocity | 速率与速度
In biomechanics, speed and velocity are often used to analyse performance. Speed is a scalar quantity that measures how fast an athlete moves, while velocity is a vector quantity that also specifies direction. The basic formula relates distance, time, and speed, and it is essential for analysing sprinting, swimming, or cycling events.
在生物力学中，速率和速度常被用于分析运动表现。速率是一个标量，衡量运动员移动的快慢；而速度是一个矢量，还要指明运动的方向。基本公式将距离、时间和速率联系起来，对于分析短跑、游泳或自行车等项目至关重要。
Speed = Distance ÷ Time
as when an athlete runs 60 m north then 40 m south, you must calculate displacement for velocity. OCR expect you to select and apply the correct equation depending on whether the question asks for speed or velocity.
如果一名 100 米短跑选手以 12.5 秒完赛，其平均速率就是 100 ÷ 12.5 = 8 米/秒。当方向很重要时，例如运动员先向北跑 60 米，再向南跑 40 米，你就必须用位移来计算速度。OCR 期望你能根据问题是问速率还是速度来选用并应用正确的方程。
6. Acceleration | 加速度
Acceleration describes the rate at which an athlete changes velocity. It is a vector quantity measured in metres per second squared (m/s²). Positive acceleration means speeding up, while negative acceleration—often called deceleration—indicates slowing down. Quick acceleration is vital in sports like basketball, football, and tennis.
加速度描述运动员改变速度的快慢。它是一个矢量，单位为米每二次方秒（m/s²）。正加速度意味着在加速，而负加速度——通常称为减速——则表示在减慢速度。在篮球、足球和网球等运动中，快速加速至关重要。
Acceleration = Change in Velocity ÷ Time
a = (v − u) ÷ t
Where v is final velocity, u is initial velocity, and t igh acceleration requires large force production, linking directly to Newton’s second law.
其中 v 代表末速度，u 代表初速度，t 表示所用时间。如果一名无挡板篮球运动员在 2 秒内将速度从 0 米/秒提升到 5 米/秒，她的加速度就是 (5 − 0) ÷ 2 = 2.5 米/秒²。高加速度需要产生大的力量，这与牛顿第二定律直接相关。
7. Newton's Second Law: Force, Mass, and Acceleration | 牛顿第二定律：力、质量与加速度
Newton's second law of motion explains the relationship between the force applied to an object, its mass, and the resulting acceleration. The law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This theorem is fundamental to almost every movement in sport.
牛顿第二运动定律解释了施加在物体上的力、物体质量以及产生的加速度之间的关系。该定律指出，物体的加速度与作用在其上的净力成正比，与其质量成反比。这一定理是体育运动中几乎所有动作的基础。
Force = Mass × Acceleration
F = m a
The unit of force is the Newton (N). To accelerate a 70 kg rugby player at 3 m/s², a force of 210 N is required. Conversely, a lighter athlete can achieve greater acceleration with the same force. This formula also helps explain why strength training increases explosive power: greater muscular force generates higher acceleration.
力的单位是牛顿（N）。要让一名 70 千克的橄榄球运动员以 3 米/秒² 的速度加速，就需要 210 牛的力。反之，较轻的运动员用同样的力可以获得更大的加速度。这个公式还有助于解释为什么力量训练能提升爆发力：更大的肌肉力会产生更高的加速度。
8. Moments and Levers | 力矩与杠杆
A moment is the turning effect of a force around a pivot or fulcrum. In the human body, joints act as fulcrums, muscles provide the effort, and bones serve as levers to create movement. The size of a moment depends on the force applied and the perpendicular distance from the force to the fulcrum.
力矩是力绕支点或转动轴产生的转动效应。在人体中，关节充当支点，肌肉提供动力，骨骼则作为杠杆产生运动。力矩的大小取决于所施加的力以及力到支点的垂直距离。
Moment = Force × Perpendicular Distance from Fulcrum
First-class levers have the fulcrum between effort and load, like the neck extending. Second-class levers have the load between the fulcrum and the effort, seen when standing on tiptoes. Third-class levers, most common in the body, place the effort between the fulcrum and the load, as in a bicep curl. Understanding moments helps you analyse mechanical advantage and efficiency in sporting actions.
第一类杠杆的支点位于动力和阻力之间，比如颈部伸展。第二类杠杆的阻力在支点和动力之间，踮脚站立时就能看到。第三类杠杆在人体中最常见，动力位于支点和阻力之间，如肱二头肌弯举。理解力矩有助于你分析体育动作中的机械效益和效率。
9. Power | 功率
Power combines force and velocity to indicate how quickly work is done. In sport, power is a critical component of explosive actions such as jumping, throwing, and sprinting. The standard definition is the rate of doing work, but when dealing with movement, power can be calculated as the product of force and velocity.
功率将力和速度结合起来，表明做功的快慢。在体育运动中，功率是跳跃、投掷和短跑等爆发性动作的关键组成部分。标准定义是做功的速率，但在处理运动问题时，功率可以计算为力与速度的乘积。
Power = Work ÷ Time
or
Power = Force × Velocity
tively, if a cyclist applies a constant force of 50 N at a velocity of 8 m/s, the mechanical power generated is 50 × 8 = 400 W. Training to improve power often involves plyometrics and Olympic lifts.
功以焦耳（J）计量，功率以瓦特（W）计量。如果一位举重运动员在 2 秒内做了 800 焦耳的功，其输出功率就是 400 瓦。或者，如果一名自行车手以 8 米/秒的速度持续施加 50 牛的力，所产生的机械功率就是 50 × 8 = 400 瓦。提升功率的训练通常包括增强式训练和奥林匹克举重。
10. Weight and Mass | 重量与质量
Mass and weight are terms that are often confused in everyday language, but in physics—and in OCR PE—they have distinct meanings. Mass is the amount of matter in a body and remains constant regardless of location. Weight is the force due to gravity acting on that mass. The Earth's gravitational field strength is 9.8 N/kg, and this value appears frequently in exam questions.
质量和重量在日常语言中经常被混淆，但在物理学以及 OCR 体育中，它们有着明确的区别。质量是物体所含物质的多少，无论身在何处都保持不变。重量则是作用在该质量上的重力。地球的重力场强度为 9.8 牛/千克，这个数值经常出现在考题中。
Weight = Mass × Gravitational Field Strength
W = m g
× 9.8 = 637 N on Earth. This explains why resistance exercises feel different on the moon— calculating weight is useful when analysing ground reaction forces and load distribution.
一名质量为 65 千克的运动员，在地球上的重量为 65 × 9.8 = 637 牛。这就解释了为什么在月球上进行抗阻训练感觉会不同——质量不变，但重量变了。从运动科学的角度来看，计算重量在分析地面反作用力和载荷分布时非常有用。
Published by TutorHao | 体育 Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图