📚 A-Level OCR Physics: Last-Minute Revision Notes | A-Level OCR 物理：考前冲刺笔记
This set of concise, exam-focused revision notes covers the key concepts, definitions and equations from the A-Level OCR Physics specification. The notes are designed for quick recap and last-minute preparation, emphasising common pitfalls, essential derivations and examination techniques.
这套简明扼要的考前冲刺笔记涵盖了 A-Level OCR 物理课程的核心概念、定义和公式。笔记专为快速回顾和考前最后准备而设计，重点突出常见易错点、重要推导和应试技巧。
1. Kinematics and Motion Graphs | 运动学与运动图像
Kinematics describes the motion of objects using displacement, velocity and acceleration. The four SUVAT equations apply only when acceleration is constant.
运动学使用位移、速度和加速度描述物体运动。四个 SUVAT 方程仅在加速度恒定时适用。
v = u + at s = ½(u+v)t s = ut + ½at² v² = u² + 2as
Velocity–time graphs have gradients equal to acceleration and areas equal to displacement. A horizontal line on a velocity–time graph indicates constant velocity, and a straight sloping line indicates uniform acceleration.
速度–时间图像的斜率等于加速度，面积等于位移。速度–时间图像上的水平线表示匀速，倾斜直线表示匀加速。
Displacement–time graphs have gradients equal to velocity. A curved displacement–time graph indicates changing velocity; the instantaneous velocity is the gradient of the tangent.
位移–时间图像的斜率等于速度。弯曲的位移–时间图像表示速度在变化；瞬时速度是切线的斜率。
Acceleration of free fall g is approximated as 9.81 m s⁻². In the absence of air resistance, all objects fall with the same acceleration regardless of mass.
自由落体加速度 g 近似为 9.81 m s⁻²。在没有空气阻力的情况下，所有物体不论质量大小都以相同的加速度下落。
2. Forces and Newton’s Laws | 力与牛顿定律
Newton’s First Law states that an object remains at rest or in uniform motion unless acted upon by a resultant force. Inertia is the resistance of an object to changes in its state of motion.
牛顿第一定律指出，除非受到合外力作用，否则物体将保持静止或匀速直线运动状态。惯性是物体抵抗其运动状态改变的性质。
Newton’s Second Law: F = ma, where F is the resultant force, m is mass and a is acceleration. The unit of force is the newton (N). Weight is the gravitational force: W = mg.
牛顿第二定律：F = ma，其中 F 为合外力，m 为质量，a 为加速度。力的单位是牛顿 (N)。重力为：W = mg。
Newton’s Third Law: if body A exerts a force on body B, body B exerts an equal and opposite force on body A. These forces act on different bodies and are of the same type.
牛顿第三定律：如果物体 A 对物体 B 施加一个力，那么物体 B 就会对物体 A 施加一个大小相等、方向相反的力。这两个力作用在不同物体上且属于同一类型。
The moment of a force about a pivot is given by Moment = Fd, where d is the perpendicular distance from the pivot to the line of action of the force. The principle of moments states that for equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments.
力对支点的力矩由 力矩 = Fd 给出，其中 d 为从支点到力作用线的垂直距离。力矩原理指出，处于平衡状态时，顺时针力矩之和等于逆时针力矩之和。
Momentum p = mv. The impulse of a force equals the change in momentum: FΔt = Δ(mv). The law of conservation of momentum states that the total momentum of a closed system remains constant in the absence of external forces.
动量 p = mv。力的冲量等于动量的变化：FΔt = Δ(mv)。动量守恒定律指出，在没有外力作用的封闭系统中，总动量保持不变。
3. Work, Energy and Power | 功、能与功率
Work done is the product of the force and the distance moved in the direction of the force: W = Fx cosθ. The unit of work and energy is the joule (J).
功是力与在力的方向上移动距离的乘积：W = Fx cosθ。功和能量的单位是焦耳 (J)。
Kinetic energy KE = ½mv². Gravitational potential energy GPE = mgh, where h is the vertical height above a reference level. The law of conservation of energy states that energy cannot be created or destroyed, only transferred between stores.
动能 KE = ½mv²。重力势能 GPE = mgh，其中 h 为参考水平面以上的竖直高度。能量守恒定律指出，能量既不能创造也不能消灭，只能在不同能量库之间转移。
Power is the rate of doing work: P = ΔW / Δt. For an object moving at constant velocity against a resistive force, power can also be expressed as P = Fv. The unit of power is the watt (W).
功率是做功的速率：P = ΔW / Δt。对于以恒定速度克服阻力的物体，功率也可以表示为 P = Fv。功率的单位是瓦特 (W)。
Efficiency = (useful energy output / total energy input) × 100%. In any real system, efficiency is always less than 100% due to dissipative forces such as friction.
效率 = (有用能量输出 / 总能量输入) × 100%。在任何实际系统中，由于摩擦等耗散力的存在，效率总是低于 100%。
4. Materials and Hooke’s Law | 材料与胡克定律
Hooke’s Law states that the extension of a spring or wire is proportional to the applied load up to the limit of proportionality: F = kΔL, where k is the spring constant.
胡克定律指出，在比例极限内，弹簧或金属丝的伸长量与施加的载荷成正比：F = kΔL，其中 k 为弹簧常量。
Stress σ = F / A and strain ε = ΔL / L are used to characterise material behaviour independent of dimensions. The Young modulus E = σ / ε gives a measure of stiffness; its unit is pascal (Pa).
应力 σ = F / A 和应变 ε = ΔL / L 用于表征与尺寸无关的材料行为。杨氏模量 E = σ / ε 给出了材料刚度的量度，其单位是帕斯卡 (Pa)。
Elastic strain energy stored in a stretched spring or wire is E = ½FΔL = ½k(ΔL)², which is the area under the force–extension graph up to the limit of proportionality.
储存在被拉伸的弹簧或金属丝中的弹性应变能为 E = ½FΔL = ½k(ΔL)²，这是力–伸长量图上比例极限以下的面积。
Elastic deformation is reversible; plastic deformation causes permanent change. The yield point, ultimate tensile stress and breaking stress are key features of a stress–strain graph for ductile materials.
弹性形变是可逆的；塑性形变会导致永久性变化。屈服点、极限抗拉应力和断裂应力是韧性材料应力–应变图的关键特征。
5. Waves and Optics | 波与光学
Progressive waves transfer energy without transferring matter. For all progressive waves: v = fλ and T = 1 / f.
行波传递能量而不传递物质。对所有行波：v = fλ 且 T = 1 / f。
Transverse waves have oscillations perpendicular to the direction of energy transfer (e.g. electromagnetic waves). Longitudinal waves have oscillations parallel to the direction of energy transfer (e.g. sound).
横波的振动方向与能量传播方向垂直（例如电磁波）。纵波的振动方向与能量传播方向平行（例如声波）。
Refraction is described by Snell’s law: n₁ sin θ₁ = n₂ sin θ₂. The refractive index n = c / v. Total internal reflection occurs when the angle of incidence exceeds the critical angle C, where sin C = 1 / n.
折射由斯涅尔定律描述：n₁ sin θ₁ = n₂ sin θ₂。折射率 n = c / v。当入射角大于临界角 C 时发生全内反射，其中 sin C = 1 / n。
Young’s double-slit experiment demonstrates interference. Fringe spacing: Δx = λD / s. A diffraction grating gives sharp maxima: d sin θ = nλ, where d is the slit spacing.
杨氏双缝实验展示了干涉现象。条纹间距：Δx = λD / s。衍射光栅可产生锐利的极大值：d sin θ = nλ，其中 d 为缝间距。
Stationary waves form when two identical progressive waves travelling in opposite directions superpose. Nodes are points of zero displacement; antinodes are points of maximum amplitude. The distance between adjacent nodes is λ/2.
当两列相同的行波沿相反方向传播并叠加时，会形成驻波。波节是位移为零的点；波腹是振幅最大的点。相邻波节之间的距离为 λ/2。
6. Electricity and Circuits | 电学与电路
Ohm’s law states that the current through a conductor is proportional to the potential difference across it, provided temperature remains constant: V = IR. Resistance is measured in ohms (Ω).
欧姆定律指出，在温度保持恒定的条件下，通过导体的电流与导体两端的电势差成正比：V = IR。电阻的单位是欧姆 (Ω)。
Power in electrical circuits: P = IV = I²R = V² / R. Resistivity relates resistance to geometry: R = ρL / A, where ρ is resistivity.
电路中的电功率：P = IV = I²R = V² / R。电阻率将电阻与几何形状相关联：R = ρL / A，其中 ρ 为电阻率。
Kirchhoff’s first law: total current entering a junction equals total current leaving it (charge conservation). Kirchhoff’s second law: in any closed loop, the sum of e.m.f.s equals the sum of p.d.s (energy conservation).
基尔霍夫第一定律：流入节点的总电流等于流出节点的总电流（电荷守恒）。基尔霍夫第二定律：在任何闭合回路中，电动势之和等于电势差之和（能量守恒）。
A potential divider can provide a variable output voltage: Vout = Vin × R₂ / (R₁ + R₂). Internal resistance r of a cell causes lost volts: V = E − Ir.
分压器可以提供可变的输出电压：Vout = Vin × R₂ / (R₁ + R₂)。电池的内阻 r 会引起路端电压下降：V = E − Ir。
Capacitance C = Q / V. Energy stored in a capacitor: E = ½QV = ½CV² = ½Q² / C. The time constant τ = RC determines charging and discharging rates; after time τ, the charge falls to about 37% of its initial value.
电容 C = Q / V。电容器储存的能量：E = ½QV = ½CV² = ½Q² / C。时间常数 τ = RC 决定充放电速率；经过时间 τ 后，电荷量降至初始值的约 37%。
7. Quantum Physics | 量子物理
Photons are quanta of electromagnetic radiation with energy E = hf. The relationship c = fλ links frequency and wavelength.
光子是电磁辐射的量子，能量为 E = hf。关系式 c = fλ 将频率和波长联系起来。
The photoelectric effect is explained by hf = Φ + KEmax, where Φ is the work function. Electrons are emitted only if the photon frequency exceeds the threshold frequency f₀ = Φ / h. The maximum kinetic energy depends on frequency, not intensity.
光电效应由 hf = Φ + KEmax 解释，其中 Φ 为逸出功。只有当光子频率大于阈值频率 f₀ = Φ / h 时，电子才会被释放。最大动能取决于频率，而非光强。
Electron diffraction provides evidence for wave–particle duality. The de Broglie wavelength is λ = h / p = h / mv. Particles exhibit wave-like behaviour when their de Broglie wavelength is comparable to the spacing of atoms or slits.
电子衍射为波粒二象性提供了证据。德布罗意波长为 λ = h / p = h / mv。当粒子的德布罗意波长与原子或狭缝间距相当时，粒子会表现出波动行为。
Energy levels in atoms are discrete. When an electron jumps from a higher level to a lower level, a photon is emitted with energy equal to the difference: ΔE = E2 − E1 = hf.
原子中的能级是分立的。当电子从高能级跃迁到低能级时，会发射一个光子，其能量等于能级差：ΔE = E2 − E1 = hf。
8. Thermal Physics and Gases | 热物理与气体
Temperature is a measure of the average kinetic energy of particles. Thermal equilibrium occurs when two objects have the same temperature and there is no net heat flow.
温度是粒子平均动能的量度。当两个物体温度相同且没有净热流时，达到热平衡。
Specific heat capacity c: Q = mcΔθ. Specific latent heat L: Q = mL. During a phase change, temperature stays constant while energy is used to break intermolecular bonds.
比热容 c：Q = mcΔθ。比潜热 L：Q = mL。在相变过程中，温度保持恒定，能量用于打破分子间键。
The ideal gas laws can be combined into the equation of state: pV = nRT and pV = NkT, where R = k NA. One mole of any gas at room temperature and pressure occupies 24 dm³.
理想气体定律可合并为状态方程：pV = nRT 和 pV = NkT，其中 R = k NA。在室温和常压下，1 摩尔任何气体的体积为 24 dm³。
The kinetic theory model links macroscopic pressure to microscopic motion: pV = ⅓ N m
分子动理论模型将宏观压强与微观运动联系起来：pV = ⅓ N m
9. Nuclear and Particle Physics | 核与粒子物理
The atom consists of a small, positive nucleus surrounded by electrons. The strong nuclear force holds nucleons together over very short ranges, overcoming electrostatic repulsion between protons.
原子由带正电的小原子核和绕核电子组成。强核力在极短距离内将核子束缚在一起，克服了质子之间的静电排斥力。
Mass–energy equivalence: E = mc². The mass defect is the difference between the mass of a nucleus and the sum of the masses of its separate nucleons. Binding energy = mass defect × c².
质能等价：E = mc²。质量亏损是原子核的质量与其所有独立核子质量之和的差。结合能 = 质量亏损 × c²。
Radioactive decay is spontaneous and random. Activity A = λN. The number of undecayed nuclei follows N = N₀ e−λt. Half-life T½ = ln 2 / λ. Decay types: alpha (helium nucleus), beta-minus (electron and antineutrino), beta-plus (positron and neutrino) and gamma (photon).
放射性衰变是自发的和随机的。活度 A = λN。未衰变核的数目遵循 N = N₀ e
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