📚 IB CIE Physics: Formula Handbook | IB CIE 物理公式汇总手册
This comprehensive formula handbook brings together all the essential equations covered in the IB and CIE Physics syllabi. Use it as a quick reference during revision, ensuring you can recall the relationships between physical quantities under timed conditions.
这一全面的公式手册汇集了 IB 和 CIE 物理课程中的所有核心方程。在复习过程中将其用作快速参考，确保你在限时条件下能够准确回忆起物理量之间的关系。
1. Kinematics | 运动学
v = u + at
The first SUVAT equation links final velocity v to initial velocity u, constant acceleration a, and time t.
第一个匀变速运动方程将末速度 v、初速度 u、恒定加速度 a 和时间 t 联系起来。
s = ut + ½at²
Displacement s with constant acceleration is given by the product of initial velocity and time plus half the acceleration multiplied by the square of time.
在恒定加速度下，位移 s 等于初速度与时间的乘积加上加速度与时间平方乘积的一半。
v² = u² + 2as
This time‑independent equation relates final velocity squared to initial velocity squared, acceleration, and displacement.
这个与时间无关的方程将末速度的平方与初速度的平方、加速度和位移联系起来。
2. Dynamics | 动力学
F = ma
Newton’s second law: the net force F acting on a body equals its mass m multiplied by its acceleration a.
牛顿第二定律：作用在物体上的净外力 F 等于物体质量 m 与其加速度 a 的乘积。
Fₙ = μR
The maximum static or kinetic friction force Fₙ is the product of the coefficient of friction μ and the normal reaction force R.
最大静摩擦力或动摩擦力 Fₙ 等于摩擦系数 μ 与法向反作用力 R 的乘积。
p = mv
Linear momentum p is the product of mass and velocity; in an isolated system the total momentum is conserved.
线动量 p 是质量与速度的乘积；在孤立系统中总动量守恒。
3. Work, Energy & Power | 功、能量与功率
W = Fs cosθ
Work done W by a constant force F acting over a displacement s, with θ the angle between force and displacement vectors.
恒力 F 在位移 s 上做的功 W，θ 是力与位移矢量之间的夹角。
KE = ½mv²
Kinetic energy of a body of mass m moving with speed v.
质量为 m、以速率 v 运动的物体的动能。
GPE = mgh
Gravitational potential energy near the Earth’s surface, where g is the acceleration of free fall and h is the vertical height.
地球表面附近的重力势能，其中 g 是自由落体加速度，h 是垂直高度。
P = Fv = W/t
Power P is the rate of doing work; for a constant force moving with velocity v, P equals force times velocity.
功率 P 是做功的速率；对于以速度 v 运动的恒力，功率等于力乘以速度。
4. Circular Motion | 圆周运动
v = ωr
Linear speed v of a point moving in a circle of radius r with angular speed ω.
以角速度 ω 在半径为 r 的圆周上运动的点的线速度 v。
a = v²/r = ω²r
Centripetal acceleration a directed towards the centre of the circle, expressed in terms of speed or angular speed.
指向圆心的向心加速度 a，可以用速率或角速度表示。
F = mv²/r = mω²r
The centripetal force F required to keep a mass m in uniform circular motion.
使质量为 m 的物体保持匀速圆周运动所需的向心力 F。
5. Gravitational Field | 引力场
F = G m₁ m₂ / r²
Newton’s law of gravitation: the force between two point masses m₁ and m₂ separated by a distance r, with the universal gravitational constant G.
牛顿万有引力定律：两个质量分别为 m₁ 和 m₂ 的质点、相距 r 时的引力，G 为万有引力常量。
g = F/m = GM/r²
Gravitational field strength g at a distance r from a point mass M (or a spherical body).
距离点质量 M（或球形天体）r 处的引力场强度 g。
U = – G M m / r
Gravitational potential energy U of two masses separated by distance r, with the zero reference at infinity.
两质量相距 r 时的引力势能 U，以无穷远处为零势能参考。
6. Simple Harmonic Motion | 简谐运动
a = – ω²x
Defining equation of SHM: acceleration a is proportional to displacement x from equilibrium and directed opposite to it.
简谐运动的定义方程：加速度 a 与离开平衡位置的位移 x 成正比，且方向相反。
x = A sin(ωt + φ)
Displacement as a function of time for SHM, with amplitude A, angular frequency ω, and initial phase φ.
简谐运动的位移随时间变化关系，A 为振幅，ω 为角频率，φ 为初相位。
T = 2π/ω = 2π √m/k
Period T of a mass–spring oscillator; for a simple pendulum T = 2π √l/g.
弹簧振子的周期 T；对于单摆 T = 2π √l/g。
7. Thermal Physics | 热物理
Q = mcΔθ
Heat energy Q transferred to raise the temperature of mass m by Δθ, where c is the specific heat capacity.
使质量为 m 的物体温度升高 Δθ 所需传递的热量 Q，c 为比热容。
Q = mL
Latent heat Q required to change the phase of mass m without temperature change, L being the specific latent heat.
使质量为 m 的物质在不发生温度变化的情况下发生相变所需的潜热 Q，L 为比潜热。
pV = nRT = NkT
Ideal gas equation linking pressure p, volume V, amount n (in mol) and temperature T, with R the molar gas constant and k the Boltzmann constant.
理想气体状态方程将压强 p、体积 V、物质的量 n（摩）和温度 T 联系起来，R 为摩尔气体常量，k 为玻尔兹曼常量。
8. Waves | 波动
v = fλ
Wave speed v equals the product of frequency f and wavelength λ.
波速 v 等于频率 f 与波长 λ 的乘积。
nλ = d sinθ
Condition for constructive interference in a double‑slit or diffraction grating: path difference is an integer n multiple of wavelength, with slit spacing d and angle θ to the normal.
双缝或衍射光栅的相长干涉条件：光程差为波长 λ 的整数 n 倍，d 为缝距，θ 为与法线的夹角。
n₁ sinθ₁ = n₂ sinθ₂
Snell’s law of refraction: the product of refractive index n and the sine of the angle to the normal is constant across an interface.
斯涅尔折射定律：折射率 n 与入射角（或折射角）的正弦值的乘积在界面两侧相等。
9. Electric Circuits | 电路
I = ΔQ/Δt
Electric current I is the rate of flow of charge; for a steady current I = Q/t.
电流 I 是电荷流动的速率；对于恒定电流 I = Q/t。
V = IR
Ohm’s law: the potential difference V across a resistor of resistance R is proportional to the current I flowing through it.
欧姆定律：电阻为 R 的电阻器两端的电势差 V 与流过其中的电流 I 成正比。
P = IV = I²R = V²/R
Electrical power P dissipated in a component, expressed in three equivalent forms using current, voltage, and resistance.
元件中消耗的电功率 P，可用电流、电压和电阻以三种等价形式表示。
R = ρL/A
Resistance R of a uniform conductor depends on its resistivity ρ, length L, and cross‑sectional area A.
均匀导体的电阻 R 取决于其电阻率 ρ、长度 L 和横截面积 A。
10. Magnetic Fields | 磁场
F = BIL sinθ
Force on a current‑carrying wire of length L in a magnetic field B; θ is the angle between the current direction and the field.
磁场 B 中长度为 L 的通电直导线所受的力；θ 是电流方向与磁场方向的夹角。
F = qvB sinθ
Magnetic force on a particle with charge q moving with speed v in a magnetic field B; the force is perpendicular to both v and B.
电荷量为 q、以速率 v 在磁场 B 中运动的粒子所受的磁力；力垂直于 v 和 B 所在的平面。
11. Electromagnetic Induction | 电磁感应
ε = – N ΔΦ/Δt
Faraday’s law: induced emf ε in a coil of N turns equals the negative rate of change of magnetic flux Φ through the coil.
法拉第定律：匝数为 N 的线圈中产生的感应电动势 ε 等于穿过线圈的磁通量 Φ 变化率的负值。
Φ = BA cosθ
Magnetic flux Φ through an area A in a uniform field B, with θ the angle between the field and the normal to the area.
均匀磁场 B 中通过面积 A 的磁通量 Φ，θ 为磁场方向与面积法线之间的夹角。
12. Atomic & Nuclear Physics | 原子与核物理
E = mc²
Energy–mass equivalence: a mass m has an equivalent rest energy E, where c is the speed of light in vacuum.
质能等价：质量 m 具有等效的静止能量 E，c 为真空中的光速。
N = N₀ e⁻λᵗ
Radioactive decay law: the number of undecayed nuclei N decreases exponentially with time t, where λ is the decay constant.
放射性衰变定律：未衰变原子核的数目 N 随时间 t 呈指数衰减，λ 为衰变常量。
t₁/₂ = ln 2 / λ
Relationship between half‑life t₁/₂ and the decay constant λ.
半衰期 t₁/₂ 与衰变常量 λ 的关系。
Eₚₕₒₜₒₙ = hf
Energy of a photon of frequency f, with Planck constant h.
频率为 f 的光子的能量，h 为普朗克常量。
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