📚 A-Level Physics Unit 4: Further Mechanics, Fields and Particles | A-Level 物理 Unit 4：进阶力学、场与粒子物理复习
Unit 4 brings together three big ideas: how objects behave when forces cause acceleration in circles, how electric and magnetic fields store and transfer energy, and how the particle model explains the building blocks of matter. This revision guide covers the key definitions, equations, graphs and typical exam traps.
Unit 4 汇集了三大核心思想：力使物体做圆周运动时的行为、电场与磁场如何储存和传递能量，以及粒子模型如何解释物质的基本组成。本复习指南涵盖关键定义、公式、图像和常见考试陷阱。
1. Momentum and Impulse | 动量与冲量
ity. In any collision or explosion, the total momentum of a closed system remains constant provided no external resultant force acts. This conservation law is especially useful when two objects separate or join.
动量是由 p = mv 定义的矢量，其中 m 为质量，v 为速度。在任何碰撞或爆炸中，只要没有外合力作用，封闭系统的总动量保持不变。当两个物体分离或结合时，这一守恒定律尤其有用。
acting over time. It is given by FΔt and equals the change in momentum Δp = mv − mu. Force–time graphs show impulse as the area under the curve.
冲量衡量力在一段时间内的作用效果。它由 FΔt 给出，等于动量变化量 Δp = mv − mu。力–时间图像中，冲量表示为曲线下的面积。
p = mv ; FΔt = Δp
2. Circular Motion Basics | 圆周运动基础
angle swept out per second, measured in rad s⁻¹. It links to linear speed through v = ωr.
物体以恒定速率做圆周运动时仍会加速，因为其方向不断变化。角速度 ω 是每秒扫过的角度，单位为 rad s⁻¹。它通过 v = ωr 与线速度联系起来。
s force is not a separate force but is provided by tension, friction, gravity or electrostatic attraction.
向心加速度指向圆心，大小为 a = v²/r = ω²r。合向心力为 F = mv²/r = mω²r。该力不是独立的力，而是由张力、摩擦力、重力或静电力提供。
a = v²/r = ω²r ; F = mv²/r = mω²r
3. Electric Fields | 电场
rge q is F = qE, and the work done moving charge across a potential difference is W = qΔV.
两平行板之间的匀强电场场强为 E = V/d，其中 V 为电势差，d 为板间距。电荷 q 所受电场力为 F = qE，将电荷移动通过电势差所做的功为 W = qΔV。
is V = kQ/r. Potential is a scalar, so potentials from multiple charges add algebraically.
在点电荷周围的径向场中，场强为 E = kQ/r²，电势为 V = kQ/r。电势是标量，因此多个电荷产生的电势可代数相加。
E = V/d ; F = qE ; W = qΔV ; V = kQ/r
4. Capacitors and Energy Storage | 电容器与储能
xpressed as U = ½QV = ½CV² = ½Q²/C. This energy is released when the capacitor discharges.
电容定义为每单位电势差储存的电荷量，C = Q/V，单位为法拉。电容器储存的能量可表示为 U = ½QV = ½CV² = ½Q²/C。当电容器放电时，这些能量被释放。
a resistor, the charge, current and potential difference all decay exponentially: V = V₀e−t/RC. The time constant τ = RC is the time taken for the voltage to fall to about 37% of its initial value.
对于通过电阻放电的电容器，电荷、电流和电势差均按指数衰减：V = V₀e−t/RC。时间常数 τ = RC 是电压降至初始值约 37% 所需的时间。
U = ½QV = ½CV² ; V = V₀e−t/RC ; τ = RC
5. Magnetic Fields and Forces | 磁场与力
ductor, the force is F = BIL sinθ, where θ is the angle between the current and the field.
磁场对运动电荷有力的作用。电荷 q 以速度 v 垂直于磁场 B 运动时，力为 F = Bqv。对于载流导体，力为 F = BIL sinθ，其中 θ 为电流与磁场之间的夹角。
centripetal force gives r = mv/Bq. This is the basis of cyclotrons and mass spectrometers.
带电粒子垂直进入匀强磁场时做圆周运动。将磁力等于向心力可得 r = mv/Bq。这是回旋加速器和质谱仪的基础。
F = Bqv ; F = BIL sinθ ; r = mv/Bq
6. Electromagnetic Induction | 电磁感应
Faraday' the induced emf is equal to the rate of change of magnetic flux linkage: ε = N ΔΦ/Δt. Lenz's law gives the direction: the induced current opposes the change that produced it.
法拉第定律指出，感应电动势的大小等于磁链变化率：ε = N ΔΦ/Δt。楞次定律给出方向：感应电流阻碍引起它的变化。
through a field can also generate an emf ε = BLv when it cuts field lines perpendicularly.
磁通量 Φ = BA cosθ，其中 θ 为磁场与面积法线之间的夹角。导体在磁场中运动并垂直切割磁感线时，也可产生电动势 ε = BLv。
ε = N ΔΦ/Δt ; Φ = BA cosθ ; ε = BLv
7. Particle Physics and the Standard Model | 粒子物理与标准模型
The Standard Model classifies matter into quarks and leptons, and describes interactions through gauge bosons such as the photon, W and Z bosons, and gluons. Conservation rules include charge, baryon number, lepton number and strangeness in strong interactions.
标准模型将物质分为夸克和轻子，并通过光子、W 和 Z 玻色子及胶子等规范玻色子描述相互作用。守恒规则包括电荷、重子数、轻子数以及强相互作用中的奇异数。
Hadrons are particles made of quarks: baryons have three quarks
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