Revision Village IB Physics Formula Booklet 2025: Concept Analysis | Revision Village IB物理公式手册2025 概念解析

📚 Revision Village IB Physics Formula Booklet 2025: Concept Analysis | Revision Village IB物理公式手册2025 概念解析

The Revision Village IB Physics Formula Booklet 2025 is a compact yet comprehensive reference that brings together every essential equation needed for the IB Diploma Programme. Rather than simply listing symbols, this article dives into the physical concepts behind the formulas, explaining what each term means, when to apply it, and how it connects to the broader syllabus. By pairing every English explanation with a Chinese translation, we aim to help bilingual learners build deep conceptual understanding and exam confidence.

Revision Village IB 物理公式手册 2025 是一本精炼而又全面的参考资料，将国际文凭课程所需的每一条核心公式汇集在一起。本文并不只是罗列符号，而是深入探析公式背后的物理概念，解释每一项术语的意义、应用条件以及与整体大纲的关联。通过为每一条英文解释配上对应的中文翻译，我们希望帮助双语学习者建立深刻的概念理解与应试信心。

1. Measurements and Uncertainties | 测量与不确定度

All physical measurements carry uncertainty, and IB Physics places strong emphasis on quantifying and propagating these uncertainties. The absolute uncertainty Δx represents the range within which the true value is expected to lie, typically taken as half the smallest scale division or the standard deviation of repeated readings. When two quantities are added or subtracted, their absolute uncertainties add linearly. For multiplication or division, the fractional uncertainty (Δx/x) of the result roughly equals the sum of the fractional uncertainties of the inputs. Raising a measurement to a power n multiplies its fractional uncertainty by |n|. Mastering these rules allows students to evaluate the reliability of experimental data and to justify the number of significant figures in final results.

所有物理测量都带有不确定度，IB 物理高度重视不确定度的量化和传递。绝对不确定度 Δx 代表真实值可能落入的范围，通常取最小刻度的一半或重复读数的标准差。当两个量相加或相减时，它们的绝对不确定度直接相加；对于乘除运算，结果的相对不确定度（Δx/x）约等于各输入量相对不确定度之和。将测得量进行 n 次方运算会使其相对不确定度扩大 |n| 倍。掌握这些规则能让学生评估实验数据的可靠性，并合理解释最终结果的有效数字位数。

If y = a ± b → Δy = Δa + Δb

If y = a × b or a ÷ b → Δy/y ≈ Δa/a + Δb/b

2. Kinematics | 运动学

The suvat equations describe uniformly accelerated motion along a straight line. They connect initial velocity u, final velocity v, acceleration a, displacement s, and time t. It is crucial to remember that these equations are only valid when acceleration is constant in both magnitude and direction. The sign convention must be applied consistently: usually one direction is taken as positive. The equation v = u + at expresses how velocity changes linearly with time; s = ut + ½at² gives the displacement from the initial position; and v² = u² + 2as links velocity to displacement without explicit time. In projectile motion, the horizontal and vertical components are treated independently, with constant horizontal velocity and constant downward acceleration g.

匀变速直线运动的五个基本方程联系着初速度 u、末速度 v、加速度 a、位移 s 和时间 t。必须记住，这些方程仅在加速度大小和方向均恒定时才成立。正负号规则需要始终一致地进行约定，通常将某一方向规定为正。方程 v = u + at 表明速度随时间线性变化；s = ut + ½at² 给出从出发点开始的位移；而 v² = u² + 2as 则将速度与位移直接联系起来，不必显式包含时间。在抛体运动中，水平与竖直分量独立处理，水平方向保持匀速，竖直方向受恒定向下的重力加速度 g 作用。

v = u + a t

s = u t + ½ a t²

v² = u² + 2 a s

3. Dynamics and Energy | 动力学与能量

Newton’s second law, F_net = m a, tells us that the net force acting on an object equals the product of its mass and acceleration. The net force is the vector sum of all individual forces. When an object moves with constant velocity, the net force is zero — this is the essence of translational equilibrium. The dot product definition of work, W = F s cosθ, shows that only the force component along the displacement does work. Kinetic energy E_k = ½ m v² quantifies the energy of motion, while gravitational potential energy near Earth’s surface is ΔE_p = m g Δh. The work–energy theorem states that the total work done on an object equals its change in kinetic energy. Power P = F v describes the rate of doing work, linking force and instantaneous velocity.

牛顿第二定律 F_净 = m a 指出，作用在物体上的合力等于物体质量与加速度的乘积，合力是所有独立力的矢量和。当物体匀速运动时合力为零，这就是平动平衡的本质。功的点积定义 W = F s cosθ 表明，只有沿位移方向的分力才会做功。动能 E_k = ½ m v² 定量地表示了运动的能量，而地面附近的重力势能变化为 ΔE_p = m g Δh。功能原理说明，对物体所做的总功等于其动能的变化量。功率 P = F v 描述了做功的快慢，把力与瞬时速度联系起来。

F_net = m a

W = F s cos θ

E_k = ½ m v²

P = F v

4. Circular Motion and Gravitation | 圆周运动与万有引力

Uniform circular motion requires a net inward force — the centripetal force F_c = m v²/r = m ω² r. Even though the speed is constant, the velocity continuously changes direction, so there is an inward acceleration a_c = v²/r. The concept of centripetal force is not a new force but the resultant of real forces (tension, friction, gravity) directed towards the centre. Newton’s law of gravitation F = G M m / r² describes the attractive force between two point masses. In a gravitational field, the field strength g equals the force per unit mass, and near a planet’s surface it is approximately constant. The orbital motion of satellites can be understood by equating gravitational force to the required centripetal force, leading to relationships between orbital period, radius and mass of the central body.

匀速圆周运动需要一个指向圆心的净力——向心力 F_c = m v²/r = m ω² r。尽管速率不变，但速度的方向不断改变，因此存在向心加速度 a_c = v²/r。向心力不是一种新的力，而是将真实存在的力（如拉力、摩擦力、引力）中指向圆心的分量合成的结果。牛顿万有引力定律 F = G M m / r² 描述了两个质点间的吸引力。引力场中，引力场强度 g 等于单位质量所受的力，靠近行星表面时可视为常数。卫星的轨道运动可以通过将万有引力等同于所需的向心力来理解，从而推导出轨道周期、半径和中心天体质量之间的关系。

F_c = m v² / r

a_c = v² / r = ω² r

F = G M m / r²

g = F / m

5. Thermal Physics | 热物理

Temperature measures the average random kinetic energy of particles, while heat refers to energy transferred due to a temperature difference. The specific heat capacity c quantifies the energy needed to raise the temperature of 1 kg of a substance by 1 K: Q = m c ΔT. During a phase change, the temperature remains constant even though heat is being added; the latent heat L gives the energy per unit mass: Q = m L. For an ideal gas, the equation of state p V = n R T links pressure, volume, absolute temperature, and amount of gas. The average kinetic energy of a gas molecule is directly proportional to the absolute temperature: E_k,avg = (3/2) k_B T, where k_B is the Boltzmann constant. These fundamental equations help explain phenomena ranging from calorimetry to the behaviour of gases under different conditions.

温度衡量的是粒子平均随机动能的大小，而热量则是指由于温度差而传递的能量。比热容 c 表示使 1 kg 物质温度升高 1 K 所需的能量：Q = m c ΔT。在物态变化过程中，即使继续加热，温度也保持不变，此时潜热 L 给出单位质量相变所需的能量：Q = m L。对于理想气体，状态方程 p V = n R T 将压强、体积、绝对温度和气体的物质的量联系起来。气体分子的平均动能与绝对温度成正比：E_k,avg = (3/2) k_B T，其中 k_B 为玻尔兹曼常数。这些基本方程能解释从量热实验到不同条件下气体行为的一系列现象。

Q = m c ΔT

Q = m L

p V = n R T

E_k,avg = (3/2) k_B T

6. Wave Phenomena | 波动现象

All waves transfer energy without net movement of matter. The wave equation v = f λ links wave speed v, frequency f, and wavelength λ. For light, the refractive index n = c / v explains the bending of rays at a boundary: Snell’s law is n₁ sinθ₁ = n₂ sinθ₂. Interference occurs when coherent waves superpose: constructive interference gives maximum amplitude when the path difference is nλ, while destructive interference gives minima at (n + ½)λ. In single-slit diffraction, the first minimum occurs at an angle θ given by b sinθ = λ, where b is the slit width. The double-slit formula s = λ D / d gives the fringe spacing s in terms of wavelength, slit separation d, and screen distance D. These relationships form the backbone of IB wave optics and are crucial for understanding experiments such as Young’s double-slit.

所有波动都传递能量而不带来物质的净移动。波速方程 v = f λ 将波速 v、频率 f 和波长 λ 联系起来。对于光，折射率 n = c / v 解释了光线在界面处的偏折：斯涅尔定律为 n₁ sinθ₁ = n₂ sinθ₂。当相干波叠加时会发生干涉：路程差为波长整数倍时出现相长干涉，振幅最大；路程差为 (n + ½)λ 时出现相消干涉，振幅最小。在单缝衍射中，第一级极小所在的角位置满足 b sinθ = λ，其中 b 为缝宽。双缝干涉的条纹间距公式 s = λ D / d 表达了波长、双缝间距 d 和屏幕距离 D 对条纹间距的影响。这些关系构成了 IB 波动光学的核心，对理解杨氏双缝等重要实验至关重要。

v = f λ

n₁ sin θ₁ = n₂ sin θ₂

b sin θ = λ

s = λ D / d

7. Electricity and Circuits | 电学与电路

Electric current I is the rate of flow of charge: I = Δq / Δt. Ohm’s law for a resistor at constant temperature is V = I R, but it describes a proportionality, not a definition. Resistance depends on geometry and material: R = ρ L / A, where ρ is resistivity. Power dissipated in a circuit element can be expressed in multiple equivalent forms: P = I V = I² R = V² / R. Kirchhoff’s current law states that the sum of currents entering a junction equals the sum leaving; Kirchhoff’s voltage law states that the algebraic sum of potential differences around any closed loop is zero. Internal resistance r of a cell causes the terminal p.d. to be less than the emf ε: V = ε − I r. These equations enable complete circuit analysis for series, parallel, and mixed configurations.

电流 I 是电荷流动的速率：I = Δq / Δt。恒定温度下电阻器的欧姆定律为 V = I R，但这描述的是一个比例关系而非定义。电阻取决于几何形状和材料：R = ρ L / A，其中 ρ 为电阻率。电路元件消耗的功率可以表示为多种等效形式：P = I V = I² R = V² / R。基尔霍夫电流定律指出，流入某节点的电流之和等于流出该节点的电流之和；基尔霍夫电压定律指出，任意闭合回路中电势差的代数和为零。电池的内阻 r 导致端电压小于电动势 ε：V = ε − I r。这些公式足以对串联、并联和混联电路进行完整的分析。

I = Δq / Δt

V = I R

R = ρ L / A

P = I V = I² R = V² / R

V = ε − I r

8. Magnetism and Electromagnetic Induction | 磁学与电磁感应

A charged particle moving through a magnetic field experiences a force perpendicular to both velocity and field: F = q v B sinθ. This force provides the centripetal force for circular motion in a uniform field. For a current-carrying wire of length L, the magnetic force is F = B I L sinθ. Magnetic flux Φ through an area is B A cosθ, and flux linkage is NΦ. Faraday’s law states that the induced emf equals the rate of change of flux linkage: ε = −N ΔΦ/Δt (the negative sign shows Lenz’s law). The magnitude of motional emf for a conductor moving perpendicular to a field is ε = B L v. These ideas underpin generators, transformers, and the operation of many electromagnetic devices, linking changing magnetic fields to induced currents.

带电粒子在磁场中运动会受到一个垂直于速度和磁场方向的力：F = q v B sinθ，这个力在匀强磁场中作为向心力导致粒子做圆周运动。对于长度为 L 的电流导线，所受的磁力为 F = B I L sinθ。穿过某一面积的磁通量 Φ 等于 B A cosθ，磁链为 NΦ。法拉第定律指出，感应电动势等于磁链的变化率：ε = −N ΔΦ/Δt（负号体现了楞次定律）。当导体垂直于磁场切割磁感线时，动生电动势的大小为 ε = B L v。这些概念是发电机、变压器以及众多电磁装置运行的基础，将变化的磁场与感应电流紧密地联系起来。

F = q v B sin θ

F = B I L sin θ

Φ = B A cos θ

ε = −N ΔΦ / Δt

ε = B L v

9. Atomic, Nuclear and Particle Physics | 原子、核与粒子物理

The energy of a photon is directly proportional to its frequency: E = h f. The photoelectric effect can be explained by Einstein’s equation h f = φ + E_k,max, where φ is the work function of the metal. Matter also exhibits wave-like behaviour, with the de Broglie wavelength λ = h / p. In nuclear physics, the decay law N = N₀ e^−λt describes the exponential decrease of undecayed nuclei, where λ is the decay constant. The half-life T_½ relates to λ by T_½ = ln2 / λ. Mass–energy equivalence is given by E = m c², and the mass defect in a nucleus represents the binding energy that holds nucleons together. The unified atomic mass unit u corresponds to about 931.5 MeV/c², enabling easy energy calculations in nuclear reactions.

光子的能量与其频率成正比：E = h f。光电效应可以通过爱因斯坦方程 h f = φ + E_k,max 解释，其中 φ 为金属的逸出功。物质同样表现出波动性，德布罗意波长 λ = h / p。在核物理中，衰变定律 N = N₀ e^−λt 描述了未衰变原子核数目随时间指数减少的规律，λ 为衰变常量。半衰期 T_½ 与 λ 的关系为 T_½ = ln2 / λ。质能等价关系由 E = m c² 给出，原子核中的质量亏损对应着将核子结合在一起的结合能。统一的原子质量单位 u 约等于 931.5 MeV/c²，这使得核反应中的能量计算变得十分简便。

E = h f

h f = φ + E_k,max

λ = h / p

N = N₀ e^{−λ t}

E = m c²

10. Relativity and Quantum Physics (HL) | 相对论与量子物理 (HL)

Special relativity introduces the Lorentz factor γ = 1/√(1 − v²/c²). Time intervals and lengths are not absolute: proper time Δt₀ measured in the rest frame is dilated to Δt = γ Δt₀ for a moving observer; length contraction reduces the length of a moving object to L = L₀ / γ. Relativistic momentum is p = γ m₀ v, and the total energy of a particle is E = γ m₀ c². The Heisenberg uncertainty principle sets fundamental limits on simultaneous knowledge of certain pairs of quantities, such as position and momentum: Δx Δp ≥ h / 4π. In quantum physics, the wavefunction ψ encodes the probability amplitude, and the square of its magnitude gives the probability density. Tunnelling probability depends exponentially on the barrier width and height. These higher-level concepts reveal the non-intuitive reality at very high speeds and very small scales.

狭义相对论引入了洛伦兹因子 γ = 1/√(1 − v²/c²)。时间间隔与长度并非绝对：在静止系中测得的固有时间 Δt₀ 对于运动观察者而言会被延长为 Δt = γ Δt₀；长度收缩使运动物体的长度缩短为 L = L₀ / γ。相对论动量形式为 p = γ m₀ v，粒子的总能量为 E = γ m₀ c²。海森堡不确定性原理对同时确定某些物理量对如位置和动量设置了基本限制：Δx Δp ≥ h / 4π。量子物理中，波函数 ψ 编码了概率幅，其模平方为概率密度。隧穿概率与势垒宽度和高度呈指数依赖。这些高水平的概念揭示了极高速和极微小尺度下反直觉的物理本质。

γ = 1 / √(1 − v²/c²)

Δt = γ Δt₀

L = L₀ / γ

E = γ m₀ c²

Δx Δp ≥ h / 4π

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