Year 12 OCR Physics: Formula & Theorem Quick Reference Handbook | Year 12 OCR 物理：公式定理速查手册

📚 Year 12 OCR Physics: Formula & Theorem Quick Reference Handbook | Year 12 OCR 物理：公式定理速查手册

This quick reference handbook covers the essential formulas, laws and theorems for Year 12 OCR A Level Physics (AS content). Each section is presented with clear explanations in both English and Chinese to help you revise efficiently. Use this handbook to consolidate your understanding of mechanics, materials, electricity, waves and quantum physics.

本速查手册涵盖了 Year 12 OCR A Level 物理（AS 部分）的关键公式、定律和定理。每个部分均配有清晰的中英文解释，帮助您高效复习。使用本手册巩固对力学、材料、电学、波动和量子物理的理解。

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1. Quantities and Units | 量与单位

All physical quantities are expressed in terms of SI base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol) and candela (cd). Derived units such as the newton (N) can be broken down into kg m s⁻².

所有物理量均用国际单位制（SI）基本单位表示：米 (m)、千克 (kg)、秒 (s)、安培 (A)、开尔文 (K)、摩尔 (mol) 和坎德拉 (cd)。导出单位如牛顿 (N) 可以分解为 kg m s⁻²。

Prefix	Symbol	Factor
tera	T	10¹²
giga	G	10⁹
mega	M	10⁶
kilo	k	10³
centi	c	10⁻²
milli	m	10⁻³
micro	µ	10⁻⁶
nano	n	10⁻⁹
pico	p	10⁻¹²

Common SI prefixes allow us to express very large or very small numbers concisely. For example, 5.0×10⁻⁶ s = 5.0 µs.

常用的 SI 前缀使我们能够简洁地表示非常大或非常小的数字。例如，5.0×10⁻⁶ s = 5.0 µs。

A vector quantity has both magnitude and direction (e.g. displacement, velocity, force). A scalar has magnitude only (e.g. distance, speed, mass). Vectors can be added by scale drawing or resolved into perpendicular components.

矢量既有大小又有方向（例如位移、速度、力）。标量只有大小（例如距离、速率、质量）。矢量可以通过作图相加，也可以分解为互相垂直的分量。

F_x = F cosθ   F_y = F sinθ

Resolving a vector F into horizontal component F_x and vertical component F_y where θ is the angle to the horizontal.

将矢量 F 分解为水平分量 F_x 和垂直分量 F_y，其中 θ 为与水平方向的夹角。

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2. Kinematics | 运动学

Describing motion involves displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t). The SUVAT equations apply when acceleration is constant.

描述运动涉及位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t)。当加速度恒定时，可使用 SUVAT 方程。

v = u + at

Equation linking final velocity, initial velocity, acceleration and time.

关联末速度、初速度、加速度和时间的方程。

s = ut + ½at²

Displacement as a function of initial velocity, acceleration and time.

位移作为初速度、加速度和时间的函数。

v² = u² + 2as

Relates final velocity squared to initial velocity squared, acceleration and displacement.

关联末速度平方、初速度平方、加速度和位移的方程。

s = ½(u + v)t

Displacement equals average velocity multiplied by time.

位移等于平均速度乘以时间。

For free fall under gravity, the acceleration is g = 9.81 m s⁻² downward. The same SUVAT equations apply with a = g, taking downward as positive.

对于重力作用下的自由落体运动，加速度为 g = 9.81 m s⁻² 竖直向下。以向下为正时，上述 SUVAT 方程中 a = g 依然适用。

Velocity-time graphs: gradient gives acceleration, area under graph gives displacement. Displacement-time graphs: gradient gives velocity.

速度-时间图：斜率表示加速度，图线下的面积表示位移。位移-时间图：斜率表示速度。

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3. Dynamics and Newton’s Laws | 动力学与牛顿定律

Newton’s first law: an object remains at rest or in uniform motion unless acted upon by a resultant force.

牛顿第一定律：若无合外力作用，物体将保持静止或匀速直线运动状态。

ΣF = ma

Newton’s second law: the net force acting on a body is equal to the product of its mass and acceleration.

牛顿第二定律：作用在物体上的合外力等于物体的质量与加速度的乘积。

W = mg

Weight is the gravitational force on a mass, with g the gravitational field strength (9.81 N kg⁻¹ on Earth).

重力是作用在物体上的万有引力，g 为重力场强度（地球上约为 9.81 N kg⁻¹）。

Newton’s third law: when two bodies interact, they exert equal and opposite forces on each other. These forces are of the same type and act on different objects.

牛顿第三定律：两物体相互作用时，彼此施加等大反向的力。这两个力属于同种类型，作用在不同物体上。

Moment of a force about a pivot = force × perpendicular distance from pivot.

力对支点的力矩 = 力 × 支点到力作用线的垂直距离。

Moment = F d⊥

For equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments, and net force is zero.

处于平衡状态时，顺时针力矩之和等于逆时针力矩之和，且合外力为零。

Density ρ = m / V

Density is mass per unit volume, measured in kg m⁻³.

密度是单位体积的质量，单位为 kg m⁻³。

Pressure p = F / A

Pressure is normal force per unit area, measured in pascal (Pa).

压强是单位面积所受的法向力，单位为帕斯卡 (Pa)。

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4. Work, Energy and Power | 功、能与功率

W = Fx cosθ

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

恒力所做的功等于力、位移和两者夹角余弦的乘积。

E_k = ½mv²

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

质量为 m、速度为 v 的物体的动能。

ΔE_p = mgΔh

Change in gravitational potential energy near the Earth’s surface.

地表附近重力势能的变化量。

P = W / t = Fv

Power is the rate of doing work. For a constant force moving at speed v, instantaneous power is Fv.

功率是做功的快慢。若恒力作用的物体以速度 v 运动，其瞬时功率为 Fv。

Efficiency = useful output energy (or power) / total input energy (or power). Efficiency is always less than 1 due to energy dissipation.

效率 = 有用输出能量（或功率）/ 总输入能量（或功率）。由于存在能量耗散，效率始终小于 1。

The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or stored in different forms.

能量守恒定律指出，能量不能被创生或消灭，只能在不同形式之间转移或储存。

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5. Materials | 材料力学

Hooke’s law: F = kx

Within the elastic limit, the extension x of a spring or wire is directly proportional to the applied force F. k is the stiffness constant (N m⁻¹).

在弹性限度内，弹簧或金属丝的伸长量 x 与施加的力 F 成正比。k 为劲度系数（单位 N m⁻¹）。

Elastic strain energy = ½Fx = ½kx²

The work done in stretching a spring is stored as elastic potential energy (area under the force–extension graph).

拉伸弹簧所做的功以弹性势能的形式储存（等于力-伸长图下方的面积）。

Stress = F / A

Tensile or compressive stress is the force per unit cross-sectional area, measured in Pa.

拉伸或压缩应力是单位横截面积所受的力，单位为 Pa。

Strain = x / L

Strain is the extension per unit original length; it has no units.

应变是单位原始长度的伸长量，无量纲。

Young modulus E = stress / strain

The Young modulus is a measure of the stiffness of a material, valid in the linear elastic region.

杨氏模量是衡量材料刚度的量，仅在线性弹性区域有效。

Key points on a stress–strain curve: limit of proportionality, elastic limit, yield point, ultimate tensile strength (UTS). After the UTS, necking occurs before fracture.

应力-应变曲线上的关键点：比例极限、弹性极限、屈服点、抗拉强度 (UTS)。超过 UTS 后出现颈缩，最终断裂。

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6. Momentum | 动量

p = mv

Linear momentum is the product of mass and velocity. It is a vector quantity measured in kg m s⁻¹.

线动量是质量与速度的乘积，为矢量，单位为 kg m s⁻¹。

Impulse = FΔt = Δp

The impulse of a force equals the change in momentum it produces. Area under a force–time graph gives impulse.

力的冲量等于它引起的动量变化。力-时间图下方的面积表示冲量。

Principle of conservation of linear momentum: in a closed system with no external forces, total momentum before an event equals total momentum after.

线动量守恒定律：在无外力的封闭系统中，作用前的总动量等于作用后的总动量。

For two interacting bodies: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. In a perfectly inelastic collision, the bodies stick together and share a common final velocity. In an elastic collision, kinetic energy is conserved.

对于两个相互作用的物体：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。完全非弹性碰撞中，两物体粘在一起并以共同速度运动；弹性碰撞中，动能守恒。

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7. Charge and Current | 电荷与电流

I = ΔQ / Δt

Electric current is the rate of flow of charge, measured in ampere (A) where 1 A = 1 C s⁻¹.

电流是电荷流动的速率，单位是安培 (A)，1 A = 1 C s⁻¹。

Elementary charge e = 1.60 × 10⁻¹⁹ C. The total charge Q = ne, where n is the number of electrons or protons.

基本电荷 e = 1.60 × 10⁻¹⁹ C。总电荷 Q = ne，n 为电子或质子的数目。

Conventional current direction is the flow of positive charge (opposite to electron flow). Charge carriers in metals are free electrons.

常规电流方向规定为正电荷的流动方向（与电子流动方向相反）。金属中的载流子是自由电子。

Kirchhoff’s first law (junction rule): the sum of currents entering a junction equals the sum of currents leaving it (charge conservation).

基尔霍夫第一定律（节点定律）：流入节点的电流之和等于流出节点的电流之和（电荷守恒）。

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8. Circuits and Resistance | 电路与电阻

V = W / Q

Potential difference (p.d.) is the energy transferred per unit charge between two points, measured in volts (V), 1 V = 1 J C⁻¹.

电势差（电压）是两点间转移单位电荷的能量，单位为伏特 (V)，1 V = 1 J C⁻¹。

Ohm’s law: V = IR

Provided temperature is constant, the p.d. across an ohmic conductor is directly proportional to the current. Resistance R is measured in ohm (Ω).

在温度不变的条件下，欧姆导体两端的电压与电流成正比。电阻 R 的单位为欧姆 (Ω)。

R = ρL / A

Resistance depends on resistivity ρ (property of material), length L and cross-sectional area A. Resistivity is measured in Ω m.

电阻取决于电阻率 ρ（材料属性）、长度 L 和横截面积 A。电阻率单位为 Ω m。

P = IV = I²R = V²/R

Electrical power dissipated in a component. Energy transferred E = IVt = Pt, measured in joules (J).

元件消耗的电功率。转移的能量 E = IVt = Pt，单位为焦耳 (J)。

Electromotive force (e.m.f.) ε is the energy supplied per unit charge by a source. For a cell with internal resistance r connected to a load R:

ε = I(R + r)   terminal p.d. V = ε – Ir

电动势 (e.m.f.) ε 是电源向每单位电荷提供的能量。对于内阻为 r 的电池，连接负载 R 时：端电压 V = ε – Ir。

Resistors in series: R_total = R₁ + R₂ + … same current through each. Resistors in parallel: 1/R_total = 1/R₁ + 1/R₂ + … same p.d. across each.

串联电阻：R总 = R₁ + R₂ + …，电流处处相等。并联电阻：1/R总 = 1/R₁ + 1/R₂ + …，各支路端电压相等。

Kirchhoff’s second law (loop rule): around any closed loop, the sum of e.m.f.s equals the sum of p.d.s (energy conservation).

基尔霍夫第二定律（回路定律）：沿任一闭合回路，电动势之和等于电势差之和（能量守恒）。

A potential divider circuit uses two resistors in series to produce a fraction of the input voltage: V_out = V_in × R₂/(R₁ + R₂).

分压电路利用两个串联电阻来获得输入电压的一部分：V出 = V入 × R₂/(R₁ + R₂)。

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9. Waves | 波

v = fλ   f = 1 / T

Wave speed v equals frequency f multiplied by wavelength λ. Frequency is the reciprocal of the period T.

波速 v 等于频率 f 乘以波长 λ。频率是周期 T 的倒数。

Intensity I is proportional to amplitude² (I ∝ A²). For a point source, intensity decreases with the square of distance (inverse square law) if no absorption.

强度 I 与振幅的平方成正比 (I ∝ A²)。对于点波源，如果无吸收，强度随距离的平方反比减小。

Phase difference can be measured in radians or degrees. Two points are in phase if their phase difference is a multiple of 2π radians.

相位差可用弧度或度衡量。若两点相位差为 2π 弧度的整数倍，则它们同相。

Refraction is described by Snell’s law: n₁ sinθ₁ = n₂ sinθ₂, where n is the absolute refractive index n = c/v.

折射可用斯涅尔定律描述：n₁ sinθ₁ = n₂ sinθ₂，其中绝对折射率 n = c/v。

Critical angle sin C = n₂ / n₁ (for n₁ > n₂)

Total internal reflection occurs when the angle of incidence exceeds the critical angle C, only when light travels from a denser to a less dense medium.

全反射发生的条件是入射角大于临界角 C，且光从光密介质射向光疏介质。

Transverse waves (e.g. all EM waves, waves on a string) oscillate perpendicularly to the direction of energy transfer. Longitudinal waves (e.g. sound) oscillate parallel to energy transfer.

横波（例如所有电磁波、弦上的波）的振动方向与能量传播方向垂直。纵波（例如声波）的振动方向与传播方向平行。

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