Formula Summary Handbook | 公式汇总手册

📚 Formula Summary Handbook | 公式汇总手册

Welcome to the ultimate formula summary handbook tailored for IB and CCEA Physics students. This guide consolidates every essential equation across all major topics, from kinematics to quantum physics, ensuring you have a quick reference for revision and exam preparation. Each formula is presented with clear notation, accompanied by concise explanations in both English and Chinese.

欢迎使用针对IB和CCEA物理学生量身打造的公式汇总手册。本指南整合了从运动学到量子物理所有主要领域的关键方程，确保您复习备考时有便捷的参考。每个公式都清晰标注符号，并配有简洁的中英文说明。

1. Kinematics | 运动学

Definition of average speed: average speed is distance travelled divided by time taken.

v = s / t

平均速度定义：平均速度等于路程除以时间。

Definition of average velocity: average velocity is displacement divided by time.

v = Δx / Δt

平均速率定义：平均速率等于位移除以时间。

Instantaneous velocity is the rate of change of displacement.

v = dx / dt

瞬时速度是位移对时间的变化率。

Acceleration is the rate of change of velocity.

a = Δv / Δt

加速度是速度的变化率。

First equation of motion: final velocity = initial velocity + acceleration × time, valid for constant acceleration.

v = u + at

第一运动方程：末速度 = 初速度 + 加速度 × 时间，适用于匀加速运动。

Second equation of motion: displacement = initial velocity × time + half acceleration × time squared.

s = ut + ½at²

第二运动方程：位移 = 初速度×时间 + ½ × 加速度×时间²。

Third equation of motion: final velocity squared = initial velocity squared + 2 × acceleration × displacement.

v² = u² + 2as

第三运动方程：末速度² = 初速度² + 2×加速度×位移。

Fourth equation of motion: displacement = average velocity × time.

s = ½(u+v)t

第四运动方程：位移 = ½（初速度+末速度）× 时间。

For free fall under gravity, the acceleration is g = 9.81 m s⁻², with u = 0 if dropped.

v = gt, s = ½gt², v² = 2gs

自由落体运动，加速度为 g = 9.81 m s⁻²，若释放时初速度为零，适用以上方程。

Projectile motion: horizontal component of velocity remains constant; vertical component follows free‑fall equations with a = −g (upwards positive).

vₓ = u cosθ, vᵧ = u sinθ − gt

抛体运动：水平分速度恒定；竖直分运动遵循自由落体方程，取向上为正时 a = −g。

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2. Newton’s Laws and Dynamics | 牛顿定律与动力学

Newton’s second law: the net force acting on an object equals its mass times its acceleration.

F = ma

牛顿第二定律：物体所受合外力等于质量乘以加速度。

Weight of an object near Earth’s surface is the product of mass and gravitational field strength.

W = mg

物体在地表附近的重力等于质量与重力场强度的乘积。

Frictional force for a moving object is proportional to the normal reaction; static friction varies up to a maximum.

f ≤ μR

滑动摩擦力与正压力成正比，静摩擦力最大值满足此式。

Hooke’s law for a spring: force is proportional to extension within the elastic limit.

F = kx

胡克定律：在弹性限度内，弹簧力与伸长量成正比。

Tension, normal reaction, and applied forces are resolved into components using free‑body diagrams.

ΣFₓ = 0, ΣFᵧ = 0 (equilibrium)

拉力、支持力及其他作用力通过受力图分解；平衡时合力为零。

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3. Work, Energy and Power | 功、能与功率

Work done by a constant force is the product of the force, displacement and the cosine of the angle between them.

W = Fs cosθ

恒力所做的功等于力×位移×两者夹角余弦。

Kinetic energy of a moving object.

KE = ½mv²

物体的动能：½ × 质量 × 速度的平方。

Gravitational potential energy near Earth’s surface.

GPE = mgh

地表附近的重力势能：质量 × 重力加速度 × 高度。

Elastic potential energy stored in a stretched spring.

EPE = ½kx²

弹簧储存的弹性势能：½ × 劲度系数 × 伸长量的平方。

Power is the rate of doing work, or the product of force and velocity when the force is parallel to motion.

P = W/t = Fv

功率是做功的快慢，当力与速度平行时功率 = 力 × 速度。

Principle of conservation of energy: total energy of an isolated system remains constant.

KEᵢ + PEᵢ = KEₑ + PEₑ (no dissipation)

能量守恒定律：孤立系统的总能量保持不变，无耗散时初始动能+势能=末动能+势能。

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4. Momentum and Impulse | 动量与冲量

Linear momentum of an object is the product of mass and velocity.

p = mv

物体的动量 = 质量 × 速度。

Impulse delivered by a force equals the change in momentum.

J = FΔt = Δp

冲量等于力乘作用时间，也等于动量的变化。

Conservation of momentum for a closed system: total momentum before collision equals total momentum after.

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

动量守恒定律：系统碰撞前的总动量等于碰撞后的总动量。

For a perfectly elastic collision, kinetic energy is also conserved; for an inelastic collision, only momentum is conserved.

½m₁u₁² + ½m₂u₂² = ½m₁v₁² + ½m₂v₂² (elastic)

完全弹性碰撞中动能守恒；非弹性碰撞中仅动量守恒。

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5. Circular Motion and Gravitation | 圆周运动与万有引力

Angular velocity is the rate of change of angle; related to frequency.

ω = Δθ / Δt = 2πf

角速度是角度的变化率，等于 2π × 频率。

Linear speed of an object moving in a circle of radius r.

v = ωr

做圆周运动的物体的线速度 = 角速度 × 半径。

Centripetal acceleration directed towards the centre.

a = v²/r = rω²

向心加速度指向圆心，大小为 v²/r 或 rω²。

Centripetal force required to keep a mass moving in a circle.

F = mv²/r = mrω²

维持圆周运动所需的向心力 = 质量 × 向心加速度。

Newton’s law of universal gravitation: force between two point masses.

F = Gm₁m₂ / r²

万有引力定律：两质点间的引力与质量乘积成正比，与距离平方成反比。

Gravitational field strength at a distance from a mass M.

g = GM / r²

距离质量M为r处的引力场强度 g = GM/r²。

Orbital speed of a satellite in a circular orbit.

v = √(GM / r)

卫星在圆形轨道上的运行速度 v = √(GM/r)。

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6. Thermal Physics | 热力学

Heat energy required to change the temperature of a substance, with specific heat capacity c.

Q = mcΔθ

物质温度变化所需热量：质量 × 比热容 × 温度变化。

Heat required to change state at constant temperature, with latent heat L.

Q = mL

相变潜热：质量 × 潜热。

Ideal gas equation linking pressure, volume, temperature and amount of gas.

pV = nRT

理想气体状态方程：压强×体积 = 物质的量×摩尔气体常数×热力学温度。

Boyle’s law for a fixed mass of gas at constant temperature.

p₁V₁ = p₂V₂ (T constant)

玻意耳定律：一定质量气体在温度不变时，压强与体积成反比。

Charles’s law at constant pressure.

V₁/T₁ = V₂/T₂ (p constant)

查理定律：压强不变时，气体体积与热力学温度成正比。

Pressure law at constant volume.

p₁/T₁ = p₂/T₂ (V constant)

压强定律：体积不变时，气体压强与热力学温度成正比。

First law of thermodynamics: change in internal energy equals heat added plus work done on the system (W done on system). For an expanding gas at constant pressure, W = −pΔV.

ΔU = Q + W

热力学第一定律：内能增量 = 吸收的热量 + 外界对系统做的功。对恒压膨胀，系统做功 W = −pΔV。

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7. Simple Harmonic Motion and Waves | 简谐运动与波

Simple harmonic motion acceleration is proportional to displacement and directed towards the equilibrium.

a = −ω²x

简谐运动的加速度与位移成正比且指向平衡位置。

Displacement as a function of time for SHM.

x = A cos(ωt + φ)

简谐运动位移随时间变化：x = A cos(ωt + φ)。

Speed in SHM at a given displacement.

v = ± ω √(A² − x²)

简谐运动中某位移处的速度大小。

Period of a mass‑spring system.

T = 2π √(m/k)

弹簧振子的周期 T = 2π√(m/k)。

Period of a simple pendulum for small angles.

T = 2π √(L/g)

单摆小角度下的周期 T = 2π√(L/g)。

Wave speed is the product of frequency and wavelength.

v = fλ

波速 = 频率 × 波长。

Snell’s law of refraction at a boundary.

n₁ sinθ₁ = n₂ sinθ₂

斯涅耳折射定律。

Critical angle for total internal reflection.

sin C = 1/n

全反射临界角满足 sin C = 1/n。

Double‑slit interference fringe separation.

Δx = λD / a

杨氏双缝干涉条纹间距。

Diffraction grating equation for maxima.

d sinθ = nλ

光栅方程：d sinθ = nλ。

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8. Electric Fields and Circuits | 电场与电路

Coulomb’s law for the force between two point charges.Published by TutorHao | IB Physics Revision Series | aleveler.com

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