Year 13 OCR Physics: Formulae & Theorems Quick Reference Handbook

📚 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

The linear 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

Centripetal 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

The net centripetal force 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)

Displacement from equilibrium can be written as x = A cos(ωt) or x = A sin(ωt). The maximum speed is v_max = 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 v_max = ωA，任意位移处的速度为 v = ±ω√(A² – x²)。

v_max = ωA
v = ±ω√(A² – x²)

The total energy in SHM is conserved and given by E_total = ½mω²A². Kinetic and potential energies vary with displacement.

简谐运动的总能量守恒，E_total = ½mω²A²。动能和势能随位移变化。

E_total = ½mω²A²
E_k = ½mω²(A² – x²)
E_p = 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。

v_esc = √(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’s displacement law 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

For relative velocities v much smaller than c, the Doppler shift of spectral lines 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。

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Year 13 OCR Physics: Formulae & Theorems Quick Reference Handbook | 公式定理速查手册