📚 IB Physics: Last-Minute Revision Notes | IB 物理：考前冲刺笔记
These concise revision notes cover the most important concepts, equations, and common pitfalls in IB Physics. Whether you are taking Standard Level or Higher Level, use this guide to refresh your memory and boost your confidence before the exam.
这份精炼的考前冲刺笔记涵盖了IB物理中最关键的概念、公式和常见易错点。无论你参加的是标准级别还是高级别，都可以借助这份指南快速温习并增强迎考信心。
1. Kinematics | 运动学
Kinematics describes motion using quantities like displacement, velocity, and acceleration without considering forces. The four SUVAT equations are central, but remember they only apply when acceleration a is constant.
运动学用位移、速度、加速度等物理量描述运动，不涉及力。四条SUVAT方程是核心，但请记住它们只在加速度 a 恒定时成立。
v = u + at s = ut + ½at² v² = u² + 2as s = ½(u + v)t
rd acceleration g = 9.81 m s⁻²) components. The two motions share the same time of flight.
分析抛体运动时，应分解为水平方向（匀速）和竖直方向（恒定向下加速度 g = 9.81 m s⁻²）。两个方向的运动共用相同的飞行时间。
2. Dynamics | 动力学
Newton's laws form the foundation: inertia (1st), force causes acceleration (2nd, F = ma), and action-reaction pairs (3rd). Always draw a free-body diagram and resolve forces. Friction is given by f = μR, where R is the normal reaction force.
牛顿定律是基础：惯性定律（第一定律）、力产生加速度（第二定律，F = ma）以及作用力与反作用力（第三定律）。请务必画出受力分析图并分解力。摩擦力由 f = μR 给出，其中R是法向反作用力。
Momentum p = mv is conserved when no external resultant force acts. Impulse equals change in momentum: FavgΔt = Δp. In collisions, always check direction when calculating momentum.
当没有外力作用时，动量 p = mv 守恒。冲量等于动量的变化量：FavgΔt = Δp。处理碰撞问题时，计算动量务必注意方向。
3. Work, Energy and Power | 功、能和功率
Work done by a constant force is W = Fs cosθ, where θ is the angle between force and displacement. The work–energy theorem links total work to the change in kinetic energy.
恒力所做的功为 W = Fs cosθ，其中θ是力与位移的夹角。功能关系将总功与动能的变化联系起来。
Kinetic energy Eₖ = ½mv², gravitational potential energy Eₚ = mgh (only valid near Earth's surface). Conservation of mechanical energy holds only when non-conservative forces do no net work.
动能 Eₖ = ½mv²，重力势能 Eₚ = mgh（仅适用于地球表面附近）。只有当非保守力不做净功时，机械能才守恒。
Power is the rate of doing work: P = W/t = Fv for constant force and velocity. Efficiency = useful output power / input power.
功率是做功的快慢：P = W/t = Fv（恒力和恒速条件下）。效率 = 有用输出功率 / 输入功率。
4. Circular Motion and Gravitation | 圆周运动与万有引力
An object moving in a circle at constant speed has an acceleration directed towards the centre: a = v²/r = ω²r. The centripetal force is F = mv²/r = mω²r and is always perpendicular to velocity.
做匀速圆周运动的物体具有指向圆心的加速度：a = v²/r = ω²r。向心力为 F = mv²/r = mω²r，其方向始终垂直于速度。
Newton's law of gravitation: F = GMm/r². This provides the centripetal force for orbiting planets and satellites. Gravitational field strength at a point is g = GM/r².
牛顿万有引力定律：F = GMm/r²。它提供行星和卫星轨道运动的向心力。一点的引力场强为 g = GM/r²。
5. Thermal Physics | 热学
Internal energy is the sum of total random kinetic energy and potential energy of particles in a substance. Temperature (T in kelvin) measures the average random kinetic energy per particle.
内能是物质内所有粒子无规则运动的总动能与势能之和。温度（单位开尔文，T）衡量每个粒子的平均无规则动能。
For an ideal gas, pV = nRT and pV = NkBT. The average kinetic energy of a molecule is Eₖ = (3/2)kBT. Remember that ideal gases have no intermolecular forces and point-like molecules.
对于理想气体，有 pV = nRT 和 pV = NkBT。一个分子的平均动能为 Eₖ = (3/2)kBT。牢记理想气体无分子间作用力且分子视为质点。
6. Waves | 波动
rse waves have oscillation perpendicular to energy transfer; longitudinal waves have oscillation parallel.
波的基本属性：频率 f、波长 λ、波速 v = fλ。横波的振动方向垂直于能量传播方向；纵波的振动方向平行于传播方向。
For constructive interference in a double-slit setup: nλ = d sinθ. For single-slit diffraction minima: b sinθ = nλ ing waves form when two identical waves travel in opposite directions; node spacing = λ/2.
双缝干涉加强条件：nλ = d sinθ。单缝衍射暗条纹：b sinθ = nλ，其中b是缝宽。两列完全相同的波相向传播时形成驻波，波节间距 = λ/2。
7. Electric Fields and Circuits | 电场与电路
Coulomb's law: F = kQ₁Q₂/r². Electric field strength E = F/q, and for a point charge E = kQ/r². Field lines point away from positive charges.
库仑定律：F = kQ₁Q₂/r²。电场强度 E = F/q，点电荷产生的电场强度 E = kQ/r²。电场线从正电荷出发。
Ohm's law: V = IR. Power dissipated in a resistor: P = IV = I²R = V²/R. In series circuits, current is the same and voltage divides; in parallel, voltage is the same and current divides.
欧姆定律：V = IR。电阻上的耗散功率：P = IV = I²R = V²/R。串联电路中电流处处相等、电压分压；并联电路中电压相等、电流分流。
Internal resistance r of a cell causes terminal p.d. V = ε - Ir. Electromotive force (emf) ε is the energy supplied per unit charge.
电源内阻r导致路端电压 V = ε - Ir。电动势（emf）ε是电源将其他形式能量转换为电能的非静电力每单位电荷所做的功。
8. Electromagnetic Induction (AHL) | 电磁感应 (HL)
Magnetic flux Φ = BA cosθ. Faraday's law: magnitude of induced emf equals the rate of change of flux linkage, ε = Δ(NΦ)/Δt. Lenz's law states that the induced current opposes the change that produced it.
磁通量 Φ = BA cosθ。法拉第定律：感应电动势的大小等于磁链的变化率，ε = Δ(NΦ)/Δt。楞次定律指出感应电流总是阻碍引起它的变化。
For a conductor of length L moving with velocity v perpendicular to a magnetic field B, motional emf is ε = BLv. The right-hand dynamic rule helps determine the direction of force on a current-carrying conductor in a B-field: F = BIL sinθ.
长度为L的导体以速度v垂直于磁场B运动时，产生的动生电动势为 ε = BLv。右手定则可帮助判断载流导体在磁场中的受力方向：F = BIL sinθ。
9. Quantum and Nuclear Physics | 量子与核物理
Photoelectric effect: photon energy E = hf. The kinetic energy of emitted electrons is Eₖmax = hf - Φ, where Φ is the work function. This confirmed the particle nature of light.
光电效应：光子能量 E = hf。逸出电子的最大动能为 Eₖmax = hf - Φ，其中Φ是逸出功。该效应证实了光的粒子性。
Bohr model: electrons exist in discrete energy levels; photons are emitted or absorbed during transitions: hf = Ehigher - Elower. Nuclear reactions conserve mass-energy: E = mc².
玻尔模型：电子存在于分立的能级中；跃迁时发射或吸收光子：hf = Ehigher - Elower。核反应中质量能量守恒：E = mc²。
Radioactive decay follows exponential law: N = N₀e-λt and activity A = λN. Half-life T½ = ln2/λ. Three types of radiation: alpha (α), beta (β⁻), and gamma (γ).
放射性衰变遵循指数规律：N = N₀e-λt，活度 A = λN。半衰期 T½ = ln2/λ。辐射有三种：α射线、β⁻射线和γ射线。
10. Measurements and Uncertainties | 测量与不确定度
All measurements carry uncertainty. Absolute uncertainty is usually half the smallest scale division unless stated otherwise. Record raw data to a consistent number of decimal places.
所有测量都带有不确定度。绝对不确定度通常取最小刻度值的一半，除非另有说明。记录原始数据时小数位数应保持一致。
When combining uncertainties: add absolute uncertainties when adding or subtracting quantities; add fractional (percentage) uncertainties when multiplying or dividing. If a quantity is raised to a power n, multiply the percentage uncertainty by n.
合成不确定度时：加减运算合并绝对不确定度；乘除运算合并相对（百分比）不确定度。若物理量被乘方n次，则将其百分比不确定度乘以n。
Plot graphs with error bars and use maximum–minimum lines or linear regression to determine slopes and intercepts. Always state final results with a reasonable number of significant figures.
作图时应包含误差棒，并利用最大–最小线或线性回归求出斜率和截距。最终结果需用合理的有效数字位数表示。
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