📚 Pre-U OCR Sport: Formula & Theorem Quick Reference Handbook | Pre-U OCR 体育：公式定理速查手册
This handbook compiles essential formulas, principles and theorems from the OCR Pre-U Sport Science specification. It is designed as a rapid revision tool to help you recall key quantitative relationships and theoretical models that underpin athletic performance, biomechanics and exercise physiology. Use it to reinforce your understanding and tackle exam questions with confidence.
本手册汇集了 OCR Pre-U 体育科学课程中的核心公式、原理和定理，旨在作为快速复习工具，帮助你回忆支撑运动表现、生物力学和运动生理学的关键量化关系及理论模型。用它来巩固理解，自信应对考试题目。
1. Newton’s Laws of Motion | 牛顿运动定律
Newton’s First Law (inertia) states that an object will remain at rest or in uniform motion in a straight line unless acted upon by a net external force. In sprinting, athletes must overcome inertia to accelerate out of the blocks.
牛顿第一定律（惯性定律）指出，如果没有净外力作用，物体将保持静止或匀速直线运动状态。在短跑中，运动员必须克服惯性才能从起跑器上加速。
Newton’s Second Law quantifies this effect: force equals mass times acceleration (F = m a). It explains how a greater force application yields a higher acceleration, assuming mass remains constant.
牛顿第二定律量化了这一效应：力等于质量乘以加速度（F = m a）。它解释了在质量不变的情况下，更大的作用力如何产生更大的加速度。
F = m a
Newton’s Third Law, the action–reaction principle, is fundamental in locomotion: for every force an athlete exerts on the ground, the ground exerts an equal and opposite force, driving the body forward.
牛顿第三定律，即作用力与反作用力原理，是运动的基础：运动员对地面施加的每一个力，地面都会产生大小相等、方向相反的力，推动身体向前。
2. Momentum and Impulse | 动量与冲量
Linear momentum (p) is the product of mass and velocity: p = m v. It is a vector quantity conserved in closed systems when no external forces act.
线动量（p）是质量与速度的乘积：p = m v。它是一个矢量，在无外力作用的封闭系统中守恒。
The impulse-momentum theorem states that the impulse applied to an object equals the change in its momentum: Impulse = F Δt = Δp = m(v_f – v_i).
冲量-动量定理指出，施加于物体的冲量等于其动量的变化量：冲量 = F Δt = Δp = m(v_f – v_i)。
Impulse = F Δt = m(vf – vi)
In tackling or striking, increasing the time over which the force is applied reduces the peak force and helps control momentum transfer, thereby lowering injury risk.
在擒抱或击球中，增加力的作用时间可减小峰值力并有助于控制动量传递，从而降低受伤风险。
3. Projectile Motion | 抛体运动
Projectile motion under constant gravity, neglecting air resistance, can be described by three key equations. The range (horizontal displacement) of a projectile launched at velocity v and angle θ is:
在忽略空气阻力、恒定重力作用下的抛体运动可由三个关键方程描述。以速度 v 和角度 θ 抛射的物体的水平射程为：
R = v² sin(2θ) / g
The maximum height reached is given by:
最大高度为：
H = v² sin²θ / (2g)
And the total time of flight is:
总飞行时间为：
T = 2v sinθ / g
These relationships explain optimal release angles in long jump, shot put and javelin. A 45° launch angle maximises range in a vacuum; in reality, air resistance and release height alter the optimal angle.
这些关系解释了跳远、铅球和标枪中的最佳出手角度。真空中 45° 发射角可获得最大射程；现实中，空气阻力和出手高度会改变最优角度。
4. Bernoulli’s Principle and Magnus Effect | 伯努利原理与马格努斯效应
Bernoulli’s Principle states that an increase in fluid velocity occurs simultaneously with a decrease in pressure. For steady, horizontal flow the relationship simplifies to:
伯努利原理指出，流体速度增加时压力会减小。对于稳定的水平流动，该关系可简化为：
P + ½ρv² = constant
The Magnus effect explains the curved flight of a spinning ball. A rotating ball drags air faster on one side, creating a pressure difference that produces a lift force perpendicular to the motion. The lift force can be expressed as:
马格努斯效应解释了旋转球的弯曲飞行轨迹。旋转球使一侧空气流速更快，产生压力差，从而形成垂直于运动方向的升力。升力可表示为：
FL = ½ ρ v² A CL
where CL is the lift coefficient, which varies with spin rate. In football, tennis and baseball, athletes deliberately impart spin to manipulate the ball’s trajectory.
其中 CL 为升力系数，随转速变化。在足球、网球和棒球中，运动员有意识地施加旋转来控制球的飞行轨迹。
5. Drag and Lift Forces | 阻力与升力
Drag is the force that opposes an object’s motion through a fluid. The drag force equation is fundamental in sports where air or water resistance is significant:
阻力是物体在流体中运动时与之相反的力。阻力方程在空气或水阻力显著的运动中至关重要：
Fd = ½ ρ Cd A v²
where A is the frontal cross-sectional area and Cd is the drag coefficient. Similarly, the general lift force is FL = ½ ρ CL A v².
其中 A 为正面横截面积，Cd 为阻力系数。同样地，一般升力为 FL = ½ ρ CL A v²。
Reducing frontal area and streamlining body position, as seen in cycling time trials and speed skating, minimises drag and maximises speed. The Reynolds number (Re = ρ v L / μ) determines whether flow is laminar or turbulent, influencing drag characteristics on balls, limbs and equipment.
减小正面面积并流线化身体姿势，如同自行车计时赛和速度滑冰中所见，可最小化阻力并最大化速度。雷诺数（Re = ρ v L / μ）决定了流动是层流还是湍流，影响球、肢体和器材的阻力特性。
6. Angular Motion | 角运动
Angular velocity and angular acceleration describe rotational movement:
角速度和角加速度描述旋转运动：
ω = Δθ / Δt
α = Δω / Δt
Centripetal force, necessary to keep a body moving in a circular path, is given by:
维持物体做圆周运动所需的向心力为：
Fc = m v² / r = m ω² r
Torque (moment of force) quantifies the turning effect: τ = F × d, where d is the perpendicular distance from the axis of rotation. In gymnastics and diving, athletes manipulate angular momentum (L = I ω, where I is moment of inertia) by altering body configuration to control spin and somersault rates.
力矩（力的转动效应）量化了转动作用：τ = F × d，其中 d 为到转轴的垂直距离。在体操和跳水中，运动员通过改变身体姿态来控制转动惯量 I，进而操控角动量（L = I ω），以调整旋转和空翻的速率。
7. Work, Energy and Power | 功、能和功率
Work done is defined as the product of force and displacement in the direction of the force: W = F d cosθ. Kinetic energy and gravitational potential energy are core to analysing movement:
功定义为力与在力的方向上位移的乘积：W = F d cosθ。动能和重力势能是分析运动的核心：
KE = ½ m v²
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply