📚 Year 13 OCR Physics: Formulae & Theorems Quick Reference Handbook | 公式定理速查手册
Welcome to your ultimate quick reference handbook for Year 13 OCR Physics. This guide condenses all the essential formulas and theorems from Modules 5 and 6, covering topics from circular motion and thermal physics to nuclear and medical physics. Use it to reinforce your understanding and ace your exams.
欢迎使用 Year 13 OCR 物理终极速查手册。本指南浓缩了模块5和6的所有核心公式和定理，涵盖从圆周运动、热物理到核物理和医学物理的各个主题。用它来巩固你的理解，并在考试中取得优异成绩。
1. Circular Motion | 圆周运动
Angular speed ω is the rate of change of angle with time, measured in rad s⁻¹. It is related to frequency f and period T.
角速度 ω 是角度随时间的变化率，单位为弧度每秒 (rad s⁻¹)。它与频率 f 和周期 T 相关。
ω = Δθ/Δt = 2πf = 2π/T
speed v of an object moving in a circle of radius r is linked to angular speed by v = ωr.
做圆周运动的物体线速度 v 与角速度之间的关系为 v = ωr。
v = ωr
l acceleration a always points to the centre of the circle, with magnitude a = v²/r = ω²r.
向心加速度 a 始终指向圆心，大小为 a = v²/r = ω²r。
a = v²/r = ω²r
rce required to maintain circular motion is F = mv²/r = mω²r, directed towards the centre.
维持圆周运动所需的向心力为 F = mv²/r = mω²r，方向指向圆心。
F = mv²/r = mω²r
2. Simple Harmonic Motion | 简谐运动
SHM occurs when the acceleration a of a particle is directly proportional to its displacement x from equilibrium and directed opposite to the displacement.
当物体的加速度 a 与其离开平衡位置的位移 x 成正比并且方向相反时，物体做简谐运动。
a = –ω²x
The period of a mass-spring system depends on mass m and spring constant k, while for a simple pendulum it depends on length l and g.
弹簧振子的周期取决于质量 m 和劲度系数 k，而单摆的周期取决于摆长 l 和重力加速度 g。
T = 2π√m/k (mass-spring)
T = 2π√l/g (pendulum)
from equilibrium can be written as x = A cos(ωt) or x = A sin(ωt). The maximum speed is vmax = ωA and the speed at displacement x is v = ±ω√A² – x².
位移可表示为 x = A cos(ωt) 或 x = A sin(ωt)。最大速度为 vmax = ωA，任意位移处的速度为 v = ±ω√A² – x²。
vmax = ωA
v = ±ω√A² – x²
The total energy in SHM is conserved and given by Etotal = ½mω²A². Kinetic and potential energies vary with displacement.
简谐运动的总能量守恒，Etotal = ½mω²A²。动能和势能随位移变化。
Etotal = ½mω²A²
Ek = ½mω²(A² – x²)
Ep = ½mω²x²
3. Gravitational Fields | 引力场
Newton's law of gravitation states that the force between two point masses M and m separated by distance r is attractive and proportional to the product of their masses.
牛顿万有引力定律指出，两个质点 M 和 m 相距 r 时，引力与它们的质量乘积成正比。
F = –(GMm)/r²
The gravitational field strength g at a point is the force per unit mass acting on a small test mass placed there.
引力场强度 g 是作用在单位试探质量上的引力。
g = F/m = GM/r²
Gravitational potential V is the work done per unit mass to bring a test mass from infinity to that point; it is negative around a central mass.
引力势 V 是把单位质量从无穷远移动到该点所做的功，在中心质量周围为负值。
V = –GM/r
The escape velocity from a body of mass M and radius r is the minimum speed needed to leave its gravitational field.
从天体表面逃逸所需的最小速度为逃逸速度。
vesc = √2GM/r
For satellites in circular orbits, Kepler's third law links orbital period T and radius r: T² ∝ r³.
对于圆轨道卫星，开普勒第三定律给出 T² ∝ r³。
T² = (4π²/GM) r³
4. Astrophysics and Cosmology | 天体物理与宇宙学
The luminosity L of a star is the total energy radiated per second. For a black-body, it is given by the Stefan-Boltzmann law.
恒星的光度 L 是每秒辐射的总能量。对于黑体，由斯特藩-玻尔兹曼定律给出。
L = σAT⁴ (σ = 5.67×10⁻⁸ W m⁻² K⁻⁴)
Wien' aw relates the peak wavelength λ_max of black-body radiation to its surface temperature T.
维恩位移定律将黑体辐射的峰值波长 λ_max 与其表面温度 T 联系起来。
λ_max T = 2.898×10⁻³ m K
ines is approximated by Δλ/λ ≈ v/c (blue shift when approaching, red shift when receding).
当相对速度 v 远小于 c 时，谱线的多普勒频移近似为 Δλ/λ ≈ v/c（接近时蓝移，远离时红移）。
Δλ/λ ≈ v/c
Hubble's law describes the expansion of the Universe: the recessional velocity v of a galaxy is proportional to its distance d away from us.
哈勃定律描述宇宙膨胀：星系远离我们的速度 v 与其距离 d 成正比。
v = H₀ d
A crude estimate for the age of the Universe t can be obtained from the Hubble constant H₀.
宇宙年龄 t 的粗略估计可由哈勃常数 H₀ 得出。
t ≈ 1/H₀
5. Thermal Physics | 热物理
For an ideal gas, the equation of state links pressure p, volume V, amount of substance n and temperature T.
对于理想气体，物态方程联系了压强 p、体积 V、物质的量 n 和温度 T。
