A-Level OCR Science: Formula Compendium | A-Level OCR 科学：公式汇总手册

📚 A-Level OCR Science: Formula Compendium | A-Level OCR 科学：公式汇总手册

Mastering A-Level OCR Science involves memorising and applying a wide range of formulas across Physics and Chemistry. This compendium brings together all essential equations in one place for quick revision and exam preparation.

掌握 A-Level OCR 科学课程需要记忆并应用物理和化学的大量公式。本手册将核心方程汇编在一起，便于快速复习和备考。

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1. Kinematics & Motion | 运动学与运动

Average velocity (v) equals displacement (Δs) divided by time interval (Δt).

v = Δs / Δt

平均速度等于位移除以时间间隔。

Acceleration (a) is the rate of change of velocity.

a = Δv / Δt

加速度是速度的变化率。

First SUVAT equation: final velocity (v) = initial velocity (u) + acceleration (a) × time (t).

v = u + a t

第一个匀加速运动方程：末速度 = 初速度 + 加速度 × 时间。

Second SUVAT equation: displacement (s) = ut + ½ a t².

s = u t + ½ a t²

第二个匀加速运动方程：位移 = 初速度 × 时间 + ½ 加速度 × 时间平方。

Third SUVAT equation: v² = u² + 2 a s.

v² = u² + 2 a s

第三个匀加速运动方程：末速度平方 = 初速度平方 + 2 × 加速度 × 位移。

Fourth SUVAT equation: s = ½(u + v) t.

s = ½(u + v) t

第四个匀加速运动方程：位移 = ½ × (初速度 + 末速度) × 时间。

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2. Dynamics & Forces | 动力学与力

Newton’s second law: net force (F) equals mass (m) times acceleration (a).

F = m a

牛顿第二定律：合力等于质量乘以加速度。

Weight (W) is the gravitational force on an object: W = m g, where g is gravitational field strength.

W = m g

重力等于物体质量乘以重力场强度 g。

Linear momentum (p) is the product of mass and velocity.

p = m v

动量等于质量乘以速度。

Impulse (F Δt) equals change in momentum (Δp).

F Δt = Δp

冲量等于动量的变化量。

In a closed system, total momentum is conserved.

Σ p_before = Σ p_after

在封闭系统中，碰撞前的总动量等于碰撞后的总动量。

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3. Work, Energy & Power | 功、能量与功率

Work done (W) by a constant force F acting at an angle θ to displacement s.

W = F s cos θ

恒力做的功：力 × 位移 × 夹角的余弦。

Kinetic energy (Eₖ) of an object of mass m moving at speed v.

Eₖ = ½ m v²

动能等于 ½ × 质量 × 速度平方。

Change in gravitational potential energy (ΔEₚ) = m g Δh.

ΔEₚ = m g Δh

重力势能的变化量等于质量 × 重力场强度 × 高度变化。

Power (P) is the rate of doing work; also P = F v for constant force parallel to velocity.

P = ΔW / Δt = F v

功率等于功除以时间，也等于力乘以速度（力与速度同向）。

Efficiency = useful energy output / total energy input (× 100%).

Efficiency = E_out / E_in

效率 = 有用输出能量 / 总输入能量。

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4. Materials & Hooke’s Law | 材料与胡克定律

Tensile stress (σ) = force per unit cross-sectional area.

σ = F / A

应力（σ）等于力除以横截面积。

Tensile strain (ε) = extension (ΔL) divided by original length (L).

ε = ΔL / L

应变等于伸长量除以原长。

Young modulus (E) = stress / strain (within limit of proportionality).

E = σ / ε

杨氏模量等于应力除以应变（在弹性比例极限内）。

Hooke’s law for a spring: force (F) is proportional to extension (Δx).

F = k Δx

胡克定律：弹簧的力与伸长量成正比，k 为劲度系数。

Elastic potential energy stored in a stretched spring.

E = ½ F Δx = ½ k (Δx)²

弹簧储存的弹性势能：½ × 力 × 伸长量 或 ½ × 劲度系数 × 伸长量平方。

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5. Thermal Physics & Gas Laws | 热物理学与气体定律

Ideal gas equation using moles (n) and molar gas constant (R).

p V = n R T

理想气体状态方程：pV = nRT，T 为热力学温度。

Form using number of molecules (N) and Boltzmann constant (k).

p V = N k T

用分子数 N 和玻尔兹曼常数 k 表示：pV = NkT。

Boyle’s law at constant temperature: p₁V₁ = p₂V₂.

p₁ V₁ = p₂ V₂

玻意耳定律（恒温）：压力与体积成反比。

Charles’s law at constant pressure: V / T = constant.

V₁ / T₁ = V₂ / T₂

查理定律（恒压）：体积与热力学温度成正比。

Pressure law at constant volume: p / T = constant.

p₁ / T₁ = p₂ / T₂

压力定律（恒容）：压力与热力学温度成正比。

First law of thermodynamics: change in internal energy (ΔU) = heat added (q) + work done on system (W).

ΔU = q + W

热力学第一定律：内能变化 = 吸收的热量 + 外界对系统做的功。

Kinetic theory pressure formula: p = ⅓ ρ ⟨c²⟩, where ρ is density and ⟨c²⟩ is mean square speed.

p = ⅓ ρ ⟨c²⟩

分子动力论压强公式：压强 = ⅓ × 密度 × 均方速率。

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6. Waves & Optics | 波与光学

Wave speed (v) equals frequency (f) times wavelength (λ).

v = f λ

波速 = 频率 × 波长。

Period (T) is the reciprocal of frequency.

T = 1 / f

周期 = 1 / 频率。

Refractive index (n) = speed of light in vacuum (c) / speed in medium (v).

n = c / v

折射率等于真空中光速除以介质中光速。

Snell’s law: n₁ sin θ₁ = n₂ sin θ₂, where angles are to the normal.

n₁ sin θ₁ = n₂ sin θ₂

斯涅尔折射定律：入射介质折射率 × 入射角正弦 = 折射介质折射率 × 折射角正弦。

Critical angle (θc) for total internal reflection: sin θc = n₂ / n₁ (n₁ > n₂).

sin θc = n₂ / n₁

全反射临界角：sin θc = 光疏介质折射率 / 光密介质折射率。

Double-slit interference: path difference = nλ, maxima occur at d sin θ = nλ.

d sin θ = n λ

双缝干涉亮纹条件：d 为缝距，d sin θ = nλ（n 为整数）。

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7. Electricity & Circuits | 电学与电路

Electric current (I) is the rate of flow of charge: I = ΔQ / Δt.

I = ΔQ / Δt

电流 = 通过截面的电荷量 / 时间。

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