📚 IB & OCR Science: Essential Formulae Handbook | IB OCR 科学：公式汇总手册
This handbook consolidates the most important equations from IB and OCR science syllabi, spanning physics and chemistry. Whether you are preparing for IB Physics, OCR A-Level Physics, or combined science assessments, this quick-reference guide will help you memorise and apply key formulae.
本手册整理了来自 IB 和 OCR 科学大纲的最重要公式，涵盖物理和化学。无论你正在备考 IB 物理、OCR A-Level 物理，还是综合科学考试，这份快速参考指南都将帮助你记忆和运用关键公式。
1. Kinematics | 运动学
The equations of uniformly accelerated motion form the backbone of classical mechanics.
匀加速运动的方程是经典力学的基础。
v = u + at
Relates final velocity v to initial velocity u, constant acceleration a and time t.
将末速度 v、初速度 u、恒定加速度 a 和时间 t 联系起来。
s = ut + ½ at²
Displacement s as a function of time; note the ½ factor before acceleration.
位移 s 作为时间的函数；注意加速度前的 ½ 因子。
v² = u² + 2as
Links final speed squared directly to displacement without requiring time.
将末速度的平方直接与位移联系起来，无需时间。
s = ½ (u + v) t
Average velocity form, useful when the total time and the velocities are known.
平均速度形式，当已知总时间和速度时非常有用。
2. Dynamics & Forces | 动力学与力
Newton’s laws provide the core relationships between force, mass and motion.
牛顿定律给出了力、质量和运动之间的核心关系。
F = m a
Net force equals mass times acceleration; always remember vector direction.
合力等于质量乘以加速度；始终谨记矢量方向。
W = m g
Weight is the gravitational force acting on a mass near a planet’s surface.
重量是作用在行星表面附近的质量上的引力。
p = m v
Linear momentum is the product of mass and velocity; conserved in isolated systems.
线性动量是质量和速度的乘积；在孤立系统中守恒。
F Δt = Δp
Impulse equals change in momentum; the basis for crash-safety calculations.
冲量等于动量的变化；是碰撞安全计算的基础。
F = −k x
Hooke’s law for a spring: restoring force is proportional to extension x, with spring constant k.
弹簧的胡克定律：回复力与伸长量 x 成正比，比例系数为劲度系数 k。
3. Work, Energy & Power | 功、能量与功率
Energy and work are scalar quantities that simplify many mechanical problems.
能量和功是标量，能简化许多力学问题。
W = F s cos θ
Work done by a constant force; θ is the angle between force and displacement.
恒力所做的功；θ 是力与位移之间的夹角。
Eₖ = ½ m v²
Kinetic energy depends on the square of speed.
动能取决于速度的平方。
Eₚ = m g h
Gravitational potential energy near Earth’s surface, where h is the vertical height.
地球表面附近的重力势能，其中 h 为竖直高度。
Eₚₑ = ½ k x²
Elastic potential energy stored in a stretched or compressed spring.
储存在拉伸或压缩弹簧中的弹性势能。
P = W / t = F v
Power is the rate of doing work; for constant velocity motion, P = F v.
功率是做功的速率；对于匀速运动，P = F v。
4. Thermal Physics | 热物理
Thermal processes link macroscopic measurements with microscopic behaviour.
热过程将宏观测量与微观行为联系起来。
ΔU = Q − W
First law of thermodynamics: increase in internal energy equals heat added minus work done by the system (IB sign convention).
热力学第一定律：内能的增加等于加入的热量减去系统对外做的功（IB 符号约定）。
p V = n R T
Ideal gas law; R = 8.31 J mol⁻¹ K⁻¹. Use SI units throughout.
理想气体状态方程；R = 8.31 J mol⁻¹ K⁻¹。全程使用国际单位制。
Eₖ = (3/2) k_B T
Average kinetic energy of a gas particle; k_B = 1.38 × 10⁻²³ J K⁻¹.
气体粒子的平均动能；k_B = 1.38 × 10⁻²³ J K⁻¹。
Q = m c ΔT
Heat required to change temperature; c is specific heat capacity.
改变温度所需的热量；c 为比热容。
5. Waves & Optics | 波与光学
Wave phenomena are described by frequency, wavelength and speed relationships.
波动现象可通过频率、波长和速度之间的关系来描述。
v = f λ
Wave speed equals frequency times wavelength; applies to all progressive waves.
波速等于频率乘以波长；适用于所有行波。
n₁ sin θ₁ = n₂ sin θ₂
Snell’s law of refraction; θ is measured from the normal to the surface.
斯涅耳折射定律；θ 从法线开始测量。
d sin θ = n λ
Young’s double‑slit interference condition for maxima; n is order number.
杨氏双缝干涉极大条件；n 为级数。
θ ≈ λ / a
Angular width of central maximum in single‑slit diffraction; a is slit width.
单缝衍射中央极大的角宽度；a 为缝宽。
1/f = 1/u + 1/v
Thin‑lens equation; u is object distance, v is image distance, f is focal length.
薄透镜公式；u 为物距，v 为像距，f 为焦距。
6. Electricity | 电学
Electric circuits are analysed using conservation laws and material properties.
电路分析利用守恒定律和材料特性。
I = ΔQ / Δt
Electric current is the rate of charge flow; unit ampere.
电流是电荷流动的速率；单位为安培。
V = I R
Ohm’s law for a resistor at constant temperature.
恒定温度下电阻器的欧姆定律。
R = ρ L / A
Resistance depends on resistivity ρ, length L and cross‑sectional area A.
电阻取决于电阻率 ρ、长度 L 和横截面积 A。
P = I V = I² R = V² / R
Power dissipated in a component; use the form most convenient for the data.
元件消耗的功率；根据已知数据选用最方便的形式。
ε = I (R + r)
EMF ε of a source equals terminal voltage plus the drop across internal resistance r.
电源的电动势 ε 等于端电压加上内阻 r 上的压降。
7. Magnetism & Electromagnetism | 磁学与电磁学
Magnetic forces and induction are central to motors and generators.
磁力和电磁感应是电动机和发电机的核心。
F = B I L sin θ
Force on a current‑carrying conductor in a magnetic field; θ between current and B.
载流导体在磁场中所受的力；θ 为电流与 B 的夹角。
F = q v B sin θ
Lorentz force on a moving charge
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