📚 OCR Year 12 Physics Formula & Theorem Quick Reference | OCR 12年级物理公式定理速查手册
This quick-reference handbook gathers every essential equation, law and definition from the OCR AS-level Physics specification (Year 12). The material is organised by topic so you can rapidly find the relationship you need, together with a concise explanation in both English and Chinese. Use it for revision, problem‑solving and reinforcing your conceptual understanding.
本速查手册汇集了 OCR AS 物理（12年级）大纲中所有核心公式、定律与定义。内容按主题编排，方便你快速查找所需关系式，并配有中英双语简明解释。适合用于复习、解题和巩固概念理解。
1. Kinematics & Motion Graphs | 运动学与运动图像
Kinematics describes how objects move without considering the forces involved. The SUVAT equations are only valid when acceleration is constant.
运动学描述物体如何运动而不考虑受力。SUVAT 方程仅在加速度恒定时适用。
v = u + at
Final velocity v equals initial velocity u plus acceleration a multiplied by time t.
末速度 v 等于初速度 u 加上加速度 a 乘以时间 t。
s = ut + ½at²
Displacement s is obtained from the initial velocity and the time‑squared term.
位移 s 由初速度项和时间平方项得出。
s = ½(u + v)t
Average velocity multiplied by time gives displacement when acceleration is uniform.
加速度均匀时，平均速度乘以时间等于位移。
v² = u² + 2as
Links final speed directly to initial speed and displacement, without requiring time.
将末速度直接与初速度和位移关联，无需时间。
From a displacement–time graph, the gradient gives velocity. From a velocity–time graph, the gradient gives acceleration and the area under the graph gives displacement.
位移–时间图像的斜率代表速度；速度–时间图像的斜率代表加速度，图像下的面积代表位移。
g = 9.81 m s⁻²
The acceleration of free fall near Earth’s surface, g, is taken as 9.81 m s⁻² in OCR examinations.
OCR 考试中，地球表面附近自由落体加速度 g 取 9.81 m s⁻²。
2. Forces, Newton’s Laws & Free‑body Diagrams | 力、牛顿定律与受力分析
Newton’s three laws describe how forces change the motion of an object. A net force produces acceleration, and forces always occur in equal but opposite pairs.
牛顿三定律描述了力如何改变物体的运动状态。合力产生加速度，力总是成对出现且大小相等方向相反。
F = ma
Resultant force F (in N) equals mass m (kg) times acceleration a (m s⁻²).
合力 F（单位 N）等于质量 m（kg）乘以加速度 a（m s⁻²）。
When an object is in equilibrium, the vector sum of all forces is zero, and the vector sum of all moments is zero.
物体处于平衡状态时，所有力的矢量和为零，所有力矩的矢量和也为零。
moment = force × perpendicular distance from pivot
The turning effect of a force depends on the perpendicular distance from the line of action to the pivot.
力的转动效应取决于力的作用线到支点的垂直距离。
weight = mg
Weight is the gravitational force acting on a mass; it points towards the centre of the Earth.
重力是作用在物体质量上的引力，方向指向地心。
A free‑body diagram shows all the forces acting on a single object, drawn as arrows from the object’s centre of mass.
受力分析图展示作用在单个物体上的所有力，箭头从物体质心画出。
3. Work, Energy & Power | 功、能量与功率
Energy is the capacity to do work. The principle of conservation of energy states that energy can be transferred or stored but never created or destroyed.
能量是做功的本领。能量守恒定律指出：能量只能转移或储存，不能凭空产生或消失。
W = Fs cos θ
Work done W is the product of the force F, the displacement s and the cosine of the angle θ between force and displacement directions.
功 W 等于力 F、位移 s 以及力与位移方向夹角 θ 的余弦的乘积。
P = W / t = Fv
Power P is the rate of work done; for a constant force moving at constant speed, P = Fv.
功率 P 是做功的快慢；恒力作用下匀速运动时，P = Fv。
KE = ½mv²
Kinetic energy of a body of mass m travelling at speed v.
质量为 m、速度为 v 的物体的动能。
GPE = mgh
Change in gravitational potential energy for small height changes near Earth’s surface.
地球表面附近，高度变化 h 引起重力势能的变化。
Efficiency is the ratio of useful output energy (or power) to total input energy.
效率是有用输出能量（或功率）与总输入能量之比。
4. Momentum & Impulse | 动量与冲量
Momentum is a vector quantity defined as the product of mass and velocity. In a closed system, total momentum is conserved.
动量是矢量，定义为质量与速度的乘积。在封闭系统中，总动量守恒。
p = mv
Momentum p (kg m s⁻¹) equals mass m times velocity v.
动量 p（单位 kg m s⁻¹）等于质量 m 乘以速度 v。
FΔt = Δp
The impulse FΔt equals the change in momentum. This is the force–time form of Newton’s second law.
冲量 FΔt 等于动量的变化量。这是牛顿第二定律的力–时间形式。
In a collision or explosion with no external forces:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
The total momentum before the event equals the total momentum after.
事件发生前后，系统的总动量保持不变。
Perfectly elastic collisions conserve both kinetic energy and momentum. Inelastic collisions do not conserve kinetic energy.
完全弹性碰撞同时守恒动能和动量；非弹性碰撞动能不守恒。
5. Materials: Hooke’s Law, Stress & Strain | 材料：胡克定律、应力与应变
Materials respond to forces by deforming. Elastic deformation is reversible; plastic deformation is permanent.
材料受力会变形。弹性变形可恢复，塑性变形永久存在。
F = kΔL
Hooke’s law: the extension ΔL is directly proportional to the applied load F, up to the limit of proportionality.
胡克定律：在比例极限内，伸长量 ΔL 与外力 F 成正比。
stress = F / A
Tensile stress is force per unit cross‑sectional area (unit Pa or N m⁻²).
拉应力是单位横截面积所受的力（单位 Pa 或 N m⁻²）。
strain = ΔL / L₀
Tensile strain is the extension per unit original length; it has no units.
拉应变是单位原始长度的伸长量，无单位。
E = stress / strain
The Young modulus E measures a material’s stiffness. It is constant for a given material within the elastic limit.
杨氏模量 E 表示材料的刚度，在弹性极限内对给定材料为常量。
elastic potential energy = ½FΔL = ½kΔL²
The energy stored in a stretched spring or wire within the elastic region.
弹性区域中，拉伸弹簧或金属丝内储存的弹性势能。
6. Electric Current & Charge | 电流与电荷
Electric current is the rate of flow of charge. The direction of conventional current is from positive to negative.
电流是电荷流动的速率，规定正电荷定向移动的方向为电流方向。
I = ΔQ / Δt
Current I (A) is the amount of charge ΔQ (C) passing a point per unit time Δt (s).
电流 I（安培）等于单位时间 Δt（秒）内通过某点的电荷量 ΔQ（库仑）。
Q = I t
For a steady current, total charge transferred equals current multiplied by time.
恒定电流下，总转移电荷等于电流乘以时间。
The elementary charge e = 1.60 × 10⁻¹⁹ C. The charge on an electron is −e; on a proton it is +e.
基本电荷 e = 1.60 × 10⁻¹⁹ C。电子电荷为 −e，质子电荷为 +e。
7. Potential Difference, EMF & Internal Resistance | 电势差、电动势与内阻
Potential difference (p.d.) is the work done per unit charge to move charge between two points. EMF is the total energy supplied per unit charge by a source.
电势差（p.d.）是移送单位电荷在两点间做的功。电动势（EMF）是电源每供一单位电荷所提供的总能量。
V = W / Q
Potential difference V (volts) equals work done W (joules) per unit charge Q (coulombs).
电势差 V（伏特）等于对单位电荷（库仑）所做的功 W（焦耳）。
ε = I(R + r)
EMF ε is equal to the sum of the terminal p.d. (IR) and the lost volts across the internal resistance r.
电动势 ε 等于路端电压 IR 与内阻 r 上的电压损失之和。
V = ε − Ir
Terminal p.d. V drops as current increases because of the internal resistance.
路端电压 V 因内阻的存在随电流增大而下降。
The energy transferred by a component: W = VQ = VIt = I²Rt = V²t / R.
元件消耗的能量：W = VQ = VIt = I²Rt = V²t / R。
8. Ohm’s Law, I‑V Characteristics & Resistivity | 欧姆定律、I-U 特性与电阻率
For an ohmic conductor at constant temperature, the current through it is directly proportional to the potential difference across it.
对于温度恒定的欧姆导体，通过它的电流与两端电压成正比。
R = V / I
Resistance R (Ω) is defined as the ratio of p.d. to current. For an ohmic component this ratio is constant.
电阻 R（欧姆）定义为电压与电流之比。对于欧姆元件，此比值为常数。
I‑V graphs: a resistor gives a straight line through the origin; a filament lamp curves as temperature rises; a diode conducts in only one direction.
I-U 图线：电阻为过原点的直线；灯丝因温度升高而弯曲；二极管仅单向导电。
R = ρL / A
Resistivity ρ (Ω m) links resistance to the length L and cross‑sectional area A of a uniform conductor.
电阻率 ρ（Ω m）将均匀导体的电阻与其长度 L、横截面积 A 联系起来。
For a thermistor, resistance falls as temperature rises (NTC type commonly used). For an LDR, resistance decreases with increasing light intensity.
热敏电阻（NTC 型）阻值随温度升高而下降；光敏电阻阻值随光强增大而减小。
9. Kirchhoff’s Laws & Potential Dividers | 基尔霍夫定律与电位器
Kirchhoff’s rules allow analysis of any DC circuit, regardless of complexity.
基尔霍夫定律可用于分析任意复杂程度的直流电路。
ΣIin = ΣIout
First law: the total current entering a junction equals the total current leaving it — a consequence of charge conservation.
第一定律：流入节点的总电流等于流出节点的总电流——电荷守恒的结果。
Σε = ΣIR
Second law: around any closed loop, the sum of the EMFs equals the sum of the products of current and resistance — a consequence of energy conservation.
第二定律：沿任一闭合回路，电动势的代数和等于各元件上电流与电阻乘积的代数和——能量守恒的表现。
Vout = R₂ / (R₁ + R₂) × Vin
For a potential divider made of two resistors in series, the output voltage across R₂ is a fraction of the input voltage.
由两个电阻串联构成的电位器，R₂ 两端的输出电压为输入电压的一部分。
Potential dividers are used to supply a variable p.d., to interface sensors like thermistors and LDRs, or to set a reference voltage.
电位器用于提供可调电压、连接热敏电阻或光敏电阻等传感器，或设定参考电压。
10. Waves: Properties, Speed & Refraction | 波的性质、波速与折射
A progressive wave transfers energy without transferring matter. Waves can be transverse (oscillation perpendicular to propagation) or longitudinal (oscillation parallel to propagation).
行波传递能量而不传递介质。波分为横波（振动方向与传播方向垂直）和纵波（振动方向与传播方向平行）。
v = f λ
Wave speed v equals frequency f multiplied by wavelength λ.
波速 v 等于频率 f 乘以波长 λ。
T = 1 / f
The period T is the reciprocal of the frequency.
周期 T 与频率互为倒数。
phase difference = (2π × path difference) / λ
The phase relationship between two points depends on the path difference expressed as a fraction of a wavelength.
两点间的相位关系取决于用波长倍数表示的路程差。
n = c / v
The absolute refractive index n of a medium is the ratio of the speed of light in vacuum, c, to the speed in the medium, v.
介质的绝对折射率 n 为真空中光速 c 与该介质中光速 v 之比。
n₁ sin θ₁ = n₂ sin θ₂
Snell’s law: the product of refractive index and sine of the angle (measured from the normal) is constant across a boundary.
斯涅耳定律：折射率与对应角（自法线量起）的正弦乘积在界面处不变。
sin θc = n₂ / n₁ (n₁ > n₂)
The critical angle θc occurs when the angle of refraction is 90°; total internal reflection happens for incident angles greater than θc.
当折射角为 90° 时的入射角称为临界角 θc；入射角大于临界角时发生全反射。
11. Superposition, Stationary Waves & Interference | 叠加、驻波与干涉
The principle of superposition states that when two or more waves meet at a point, the resultant displacement is the vector sum of the individual displacements.
叠加原理指出：两列或多列波在空间某点相遇时，合位移为各列波单独引起的位移的矢量和。
Stationary (standing) waves are formed when two identical progressive waves travelling in opposite directions superpose. Nodes are points of zero displacement; antinodes are points of maximum amplitude.
驻波由两列频率相同、传播方向相反的行波叠加形成。节点位移始终为零，腹点振幅最大。
λ = 2L / n (fixed both ends, n = 1, 2, 3 …)
For a string fixed at both ends, the allowed wavelengths give harmonics with n antinodes.
两端固定的弦线上，允许的波长为 λ = 2L/n，形成 n 个腹点的谐波。
λ = 4L / (2n − 1) (closed pipe, n = 1, 2, 3 …)
For a pipe closed at one end, only odd harmonics are present; the fundamental has λ = 4L.
一端封闭的气柱中仅存在奇数次谐波，基频波长 λ = 4L。
Interference: constructive interference occurs when waves arrive in phase (path difference = nλ), destructive interference when they arrive in anti‑phase (path difference = (n + ½)λ).
干涉：两列波同相相遇时产生相长干涉（路程差为波长的整数倍），反相相遇时产生相消干涉（路程差为半波长的奇数倍）。
12. Quantum Physics: Photons, Photoelectric Effect & Energy Levels | 量子物理：光子、光电效应与能级
Light exhibits both wave and particle behaviour. A photon is a quantum of electromagnetic radiation with energy proportional to frequency.
光具有波粒二象性。光子是电磁辐射的能量子，其能量与频率成正比。
E = hf
Photon energy E equals Planck constant h (6.63 × 10⁻³⁴ J s) times frequency f.
光子能量 E 等于普朗克常数 h（6.63 × 10⁻³⁴ J s）乘以频率 f。
c = f λ
For electromagnetic waves, the speed of light links frequency and wavelength.
电磁波中光速与频率、波长满足 c = fλ。
The photoelectric effect: electrons are emitted from a metal surface when light above a threshold frequency shines on it.
光电效应：当入射光频率超过金属的极限频率时，电子从金属表面逸出。
hf = Φ + KEmax
Einstein’s photoelectric equation: photon energy equals work function Φ plus the maximum kinetic energy of the emitted electron.
爱因斯坦光电方程：光子能量等于逸出功 Φ 与光电子最大动能之和。
eVs = KEmax
The stopping potential Vs multiplied by the elementary charge e gives the maximum kinetic energy in electronvolts (eV).
遏止电压 Vs 乘以基本电荷 e 等于以电子伏特 (eV) 表示的最大动能。
ΔE = hf
When an electron moves between discrete energy levels in an atom, a photon is emitted or absorbed with energy equal to the difference between the levels.
电子在原子分立能级间跃迁时，会发射或吸收光子，光子能量等于能级差。
Electron diffraction provides evidence for the wave nature of particles; the de Broglie wavelength λ = h / p, though often studied in more detail in Year 13, is already introduced here conceptually.
电子衍射验证了粒子的波动性；德布罗意波长 λ = h/p 的概念在 12 年级已作简介，详细内容在 13 年级学习。
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