📚 AQA GCSE PE Formula & Theorem Quick Reference Guide | AQA 体育公式定理速查手册
This article collects all the essential formulas and theorems you need for the Year 10 AQA GCSE Physical Education course. Use it as a quick revision tool to secure your understanding of biomechanics, physiology, and movement analysis.
本文汇总了Year 10 AQA体育课程中所有关键公式与定理，可作为速查手册，帮助你巩固运动生物力学、生理学和动作分析的核心知识。
1. Speed | 速率
Speed measures how fast an object is moving regardless of direction. It is a scalar quantity.
速率描述物体运动的快慢，不考虑方向，是一个标量。
Speed (m/s) = Distance (m) ÷ Time (s)
In the exam you may be asked to calculate average speed from a distance-time graph: the gradient of the line equals speed.
考试中可能会要求你通过距离-时间图计算平均速率：直线的斜率代表速率。
2. Velocity | 速度
Velocity is speed in a given direction. It is a vector quantity, so both magnitude and direction matter.
速度是带有方向的速率，是一个矢量，必须同时说明大小和方向。
Velocity (m/s) = Displacement (m) ÷ Time (s)
Displacement is the shortest straight-line distance from start to finish. For a 400 m runner completing one lap, displacement is zero, so average velocity is zero.
位移指的是从起点到终点的最短直线距离。400米跑一圈后位移为零，因此平均速度为零。
3. Acceleration | 加速度
Acceleration describes the rate of change of velocity. Deceleration is negative acceleration.
加速度描述速度变化的快慢，减速则是负加速度。
Acceleration (m/s²) = (Final velocity - Initial velocity) (m/s) ÷ Time (s)
In sporting examples, a sprinter bursts from 0 m/s to 10 m/s in 2 seconds, giving an acceleration of 5 m/s².
在运动实例中，短跑运动员从0米/秒加速到10米/秒用时2秒，加速度为5米/秒²。
4. Force, Mass and Acceleration | 力、质量与加速度
Newton's Second Law of Motion links force, mass and acceleration. Larger forces produce greater acceleration for the same mass.
牛顿第二运动定律将力、质量和加速度联系起来。质量不变时，力越大加速度越大。
Force (N) = Mass (kg) × Acceleration (m/s²)
For example, kicking a 0.43 kg football to accelerate it at 300 m/s² requires 129 N of force. This formula is key to understanding how technique and strength affect performance.
例如，将0.43千克的足球以300米/秒²的加速度踢出，需要129牛的力。该公式对于理解技术和力量如何影响运动表现至关重要。
5. Momentum | 动量
Momentum is the quantity of motion an object has. It depends on mass and velocity and is a vector.
动量是物体运动的量度，取决于质量和速度，且为矢量。
Momentum (kg m/s) = Mass (kg) × Velocity (m/s)
In a tackle, a 90 kg rugby player moving at 5 m/s has a momentum of 450 kg m/s. A heavier or faster player is harder to stop.
在擒抱中，90千克的橄榄球运动员以5米/秒移动，其动量为450千克·米/秒。体重更大或速度更快的球员更难被拦下。
6. Mechanical Work and Power | 机械功与功率
Work is done when a force moves an object through a distance. Power is the rate at which work is performed.
当力使物体移动一段距离时便做功。功率是做功的速率。
Work (J) = Force (N) × Distance (m)
Power (W) = Work (J) ÷ Time (s)
r moving 1000 N through 2 m does 2000 J of work; completing the lift in 2 s yields 1000 W.
功率也可表示为力 × 速度。举重运动员将1000牛的重物举起2米做功2000焦；若2秒完成，则功率为1000瓦。
7. Gravitational Potential Energy | 重力势能
Gravitational potential energy (GPE) is stored energy due to an object's height above the ground.
重力势能是因物体离地高度而储存的能量。
GPE (J) = Mass (kg) × Gravitational field strength (N/kg) × Height (m)
8 N/kg (often rounded to 10). A 50 kg gymnast raised 3 m gains GPE = 50 × 10 × 3 = 1500 J.
地球上重力场强度g = 9.8牛/千克（常取10）。一个50千克的体操运动员升高3米，获得的重力势能为1500焦。
8. Kinetic Energy | 动能
Kinetic energy (KE) is the energy an object possesses due to its motion. It links directly to speed and mass.
动能是物体因运动而具有的能量，与速度和质量密切相关。
KE (J) = ½ × Mass (kg) × (Velocity (m/s))²
× (55)² ≈ 86.2 J. Because velocity is squared, small speed increases cause large KE rises.
一个0.057千克的网球以55米/秒发球，其动能约为86.2焦。由于速度被平方，速度的微小增加会导致动能大幅上升。
9. Heart Rate and Training Zones | 心率与训练区间
Target heart rate zones are calculated from maximum heart rate (HRmax). The simple formula is:
目标心率区间根据最大心率（HRmax）计算，简单公式如下：
HRmax = 220 - Age (years)
A 15-year-old's HRmax = 205 bpm. The aerobic training zone is typically 60-80% of HRmax, so 123-164 bpm. For anaerobic training, 80-90% is used.
15岁青少年的最大心率 = 205次/分。有氧训练区间通常是最大心率的60-80%，即123-164次/分；无氧训练则使用80-90%。
The Karvonen formula uses resting heart rate and heart rate reserve for more precise zones:
卡沃宁公式使用安静心率和心率储备来计算更精确的区间：
Target HR = Resting HR + (Intensity % × (HRmax - Resting HR))
For accurate aerobic prescription, fitness professionals often apply this method.
健身专业人士常采用此方法进行精准的有氧训练处方。
10. Body Mass Index (BMI) | 体重指数
BMI is a simple measure of body composition based on mass and height. It is used to classify underweight, healthy weight, overweight and obesity.
BMI是根据体重与身高评估身体成分的简易指标，用于分类过轻、正常、超重和肥胖。
BMI = Mass (kg) ÷ (Height (m))²
s within the healthy range (18.5-24.9). However, BMI does not distinguish muscle from fat.
70千克、1.75米的人，BMI为70 ÷ (1.75)² = 22.9，属于健康范围（18.5-24.9）。但BMI无法区分肌肉与脂肪。
11. Levers and Mechanical Advantage | 杠杆与机械效益
Levers in the body consist of effort, fulcrum and load. The mechanical advantage (MA) tells us whether a lever favours speed or force.
人体杠杆由动力、支点和阻力组成。机械效益（MA）告诉我们杠杆是省力还是省时。
Mechanical Advantage = Effort arm ÷ Load arm
- MA > 1: the lever can move a large load with little effort (force advantage).
- MA < 1: a large effort moves a small load quickly over a large range (speed advantage).
- MA > 1：杠杆可用较小的力移动大阻力（省力杠杆）。
- MA < 1：需较大力，但可快速移动小阻力并产生大范围运动（速度杠杆）。
In a second-class lever like a calf raise, the effort arm is longer than the load arm, giving MA > 1. In a third-class lever like a bicep curl, MA < 1, favouring speed and range of motion.
在例如提踵的第二类杠杆中，动力臂长于阻力臂，MA > 1；在肱二头肌弯举的第三类杠杆中，MA < 1，有利于速度和运动范围。
12. Cardiac Output and Key Relationships | 心输出量与关键关系
The volume of blood pumped by the heart per minute is cardiac output (Q). It is determined by stroke volume and heart rate.
心脏每分钟泵出的血量称为心输出量（Q），由每搏输出量和心率决定。
Cardiac Output (L/min) = Stroke Volume (L) × Heart Rate (bpm)
Q ≈ 5 L/min (70 bpm × 0.070 L). A fit athlete can exceed 35 L/min during maximal exercise.
运动时每搏输出量和心率均增加，显著提升心输出量。未经训练者安静时心输出量约5升/分（70次/分 × 0.070升）。优秀运动员在最大运动时超过35升/分。
Other important physiological relationships to remember:
需记住的其他重要生理关系：
- Minute Ventilation (VE) = Tidal Volume × Breathing Rate — the volume of air breathed in and out per minute.
- 每分通气量 = 潮气量 × 呼吸频率——每分钟吸入或呼出的空气量。
- Energy expenditure (kcal) ≈ METs × Body mass (kg) × Duration (hours) — useful for interpreting physical activity guidelines.
- 能量消耗（千卡）≈ 代谢当量（METs）× 体重（kg）× 时间（小时）——有助于理解体力活动指南。
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