📚 SAT2 Physics 800 Score Knowledge Checklist | SAT2物理800分知识点清单
Although the SAT Subject Test in Physics has been discontinued by the College Board, the depth and breadth of its syllabus still represent an excellent standard for mastering high‑school physics. This checklist distils every essential concept, formula, and graph interpretation skill needed to secure a perfect 800. Use it alongside past papers to identify weak spots and sharpen your problem‑solving speed.
虽然美国大学理事会的 SAT 学科物理考试已经停办，但其考纲的深度和广度依然是精通高中物理的绝佳标杆。这份清单提炼了冲击满分 800 所需的每一个核心概念、公式和图像解读技巧。配合真题使用，能帮你精准定位薄弱环节，提升解题速度。
1. Kinematics | 运动学
Master the vector nature of displacement, velocity, and acceleration. Understand the difference between average and instantaneous quantities. The four constant‑acceleration equations (SUVAT) must be second nature: v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u + v)t. Always define a positive direction before solving.
掌握位移、速度和加速度的矢量本质。分清平均量与瞬时量的区别。四个匀加速直线运动公式必须烂熟于心：v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u + v)t。解题前务必先规定正方向。
Graphs are crucial: slope of an x‑t graph gives velocity; slope of a v‑t graph gives acceleration; area under a v‑t graph gives displacement. For projectiles, split motion into horizontal (constant velocity) and vertical (constant acceleration g = 9.8 m/s² downwards). The trajectory is parabolic, and time of flight depends only on the vertical component.
图像分析是关键：x‑t 图的斜率表示速度；v‑t 图的斜率表示加速度；v‑t 图下的面积表示位移。处理抛体运动时，分解为水平（匀速）和竖直（匀加速 g = 9.8 m/s² 向下）两个独立分量。轨迹为抛物线，飞行时间仅由竖直分量决定。
2. Dynamics & Newton’s Laws | 动力学与牛顿定律
Newton’s First Law: an object maintains constant velocity unless a net external force acts. Second Law: F_net = ma. Third Law: forces come in equal‑and‑opposite pairs acting on different bodies. Distinguish mass (scalar, inertia) from weight (vector, W = mg).
牛顿第一定律：物体在不受合外力时保持匀速运动。第二定律：F_net = ma。第三定律：作用力与反作用力大小相等、方向相反，作用在不同物体上。严格区分质量（标量，惯性）和重量（矢量，W = mg）。
Free‑body diagrams are non‑negotiable. On an inclined plane, resolve weight into mg sin θ (parallel) and mg cos θ (perpendicular). Friction comes in two types: static (f_s ≤ μ_s N) and kinetic (f_k = μ_k N). The direction of friction always opposes relative motion or impending motion. For pulleys and coupled systems, treat the whole system to find acceleration, then isolate a body to find tension.
必须画受力分析图。斜面上分解重力：mg sin θ（平行斜面）和 mg cos θ（垂直斜面）。摩擦力分两种：静摩擦力（f_s ≤ μ_s N）与动摩擦力（f_k = μ_k N），方向总是阻碍相对运动或运动趋势。处理滑轮与连接体时，先用整体法求加速度，再隔离单个物体求张力。
3. Work, Energy & Power | 功、能与功率
Work done by a constant force: W = F d cos θ. The work‑energy theorem states that the net work equals the change in kinetic energy: W_net = ΔK = ½m(v² − u²). Distinguish conservative forces (gravity, spring force, electrostatic) where work is path‑independent and a potential energy function exists.
恒力做功：W = F d cos θ。功能定理：合外力所做的功等于动能的变化量：W_net = ΔK = ½m(v² − u²)。区分保守力（重力、弹簧力、静电力）做功与路径无关，可引入势能函数。
Gravitational potential energy: U_g = mgh (near Earth’s surface). Elastic potential energy: U_s = ½k x². Conservation of mechanical energy (K + U = constant) holds when only conservative forces do work. Power is the rate of doing work: P = W/t = F v cos θ, measured in watts (W).
重力势能：U_g = mgh（近地表）。弹性势能：U_s = ½k x²。当只有保守力做功时，机械能守恒（K + U = 定值）。功率是做功的速率：P = W/t = F v cos θ，单位为瓦特（W）。
4. Momentum & Impulse | 动量与冲量
Linear momentum: p = m v, a vector. Impulse J = Δp = F_avg Δt. The area under a force‑time graph equals impulse. Momentum is conserved in a system with no net external force. Collisions are classified as elastic (both momentum and kinetic energy conserved) or inelastic (momentum conserved, some kinetic energy lost). A perfectly inelastic collision yields maximum kinetic energy loss with objects sticking together.
线动量：p = m v，矢量。冲量 J = Δp = F_avg Δt。力‑时间图像下的面积等于冲量。系统合外力为零时动量守恒。碰撞分弹性碰撞（动量与动能均守恒）和非弹性碰撞（动量守恒，部分动能损失）。完全非弹性碰撞中物体粘在一起，动能损失最大。
For two‑dimensional collisions, resolve momentum into x and y components and apply conservation in each direction. The centre of mass of a system moves as if all mass were concentrated there and all external forces acted at that point. Explosions are reverse perfectly inelastic collisions: momentum is conserved while kinetic energy increases.
处理二维碰撞时，将动量分解为 x、y 分量并分别在每个方向应用守恒。系统质心的运动等同于全部质量集中于此且所有外力作用于此。爆炸可视为完全非弹性碰撞的逆过程：动量守恒而动能增加。
5. Circular Motion & Gravitation | 圆周运动与万有引力
Uniform circular motion involves a centripetal acceleration a_c = v²/r = ω² r, always directed toward the centre. The net force providing this acceleration is F_c = m v²/r. This is not a new kind of force; it arises from tension, gravity, friction, or the normal force. Be prepared to analyse objects at the top and bottom of a vertical circle.
匀速圆周运动具有向心加速度 a_c = v²/r = ω² r，始终指向圆心。提供该加速度的合力为 F_c = m v²/r。这不是一种新的力，而是来源于张力、重力、摩擦力或支持力。需会分析物体在竖直圆轨道最高点和最低点的受力。
Newton’s Law of Universal Gravitation: F_g = G M m / r², where r is centre‑to‑centre distance. The gravitational field strength g = GM/r². For orbits, equate gravitational force to centripetal force to derive v = √(GM/r), T² ∝ r³ (Kepler’s Third Law). Apparent weightlessness in orbit results from being in free fall, not from zero gravity.
牛顿万有引力定律：F_g = G M m / r²，其中 r 为质心间距。引力场强度 g = GM/r²。轨道运动中，令引力等于向心力可推出 v = √(GM/r)，T² ∝ r³（开普勒第三定律）。轨道中的视重为零是由于自由落体，而非引力消失。
6. Simple Harmonic Motion | 简谐运动
SHM arises when the restoring force is proportional to displacement and opposite in direction: F = −k x. Angular frequency ω = √(k/m) for a spring‑mass system, and ω = √(g/L) for a simple pendulum (small angles). The period T = 2π/ω = 2π√(m/k) for the spring, and T = 2π√(L/g) for the pendulum. Period depends only on system properties, not amplitude.
简谐运动产生的条件是回复力与位移成正比且方向相反：F = −k x。弹簧振子的角频率 ω = √(k/m)，单摆（小角度）ω = √(g/L)。弹簧振子周期 T = 2π/ω = 2π√(m/k)，单摆周期 T = 2π√(L/g)。周期只取决于系统固有属性，与振幅无关。
Energy in SHM continually transforms between kinetic and potential, but the total mechanical energy E = ½k A² remains constant (where A is amplitude). Displacement, velocity, and acceleration as functions of time (x = A cos(ωt + φ)) lead to sinusoidal graphs. Recognise the phase relationships: velocity leads displacement by π/2, acceleration is π out of phase with displacement.
简谐运动中的能量在动能与势能间持续转换，但总机械能 E = ½k A² 保持不变（A 为振幅）。位移、速度和加速度的时间函数（x = A cos(ωt + φ)）形成正弦图像。认清相位关系：速度超前位移 π/2，加速度与位移反相（π）。
7. Waves & Sound | 波与声
Waves transfer energy without net transport of matter. Transverse (particle motion perpendicular to wave direction, e.g. light, string waves) and longitudinal (parallel, e.g. sound). Key quantities: frequency f, period T = 1/f, wavelength λ, wave speed v = f λ. For a wave on a string, v = √(Tension/μ) where μ is linear density.
波传递能量而不净输运物质。横波（质点振动垂直于波传播方向，如光、弦波）和纵波（质点振动平行于传播方向，如声波）。关键量：频率 f、周期 T = 1/f、波长 λ、波速 v = f λ。弦上波速 v = √(张力/μ)，μ 为线密度。
Superposition leads to constructive (in phase) and destructive (out of phase) interference. Standing waves form on a string fixed at one or both ends: for two fixed ends, λ_n = 2L/n, f_n = n v/(2L), where n = 1,2,3… For sound in pipes: open‑open pipes have same harmonics as strings; closed‑open pipes have only odd harmonics λ_n = 4L/n (n odd). Beat frequency f_beat = |f₁ − f₂|. The Doppler effect shifts perceived frequency: f’ = f (v_sound ± v_observer)/(v_sound ∓ v_source).
叠加产生相长（同相）和相消（反相）干涉。两端固定的弦上形成驻波：λ_n = 2L/n，f_n = n v/(2L)，n = 1,2,3…。管中声波：两端开口管与弦相同；一端封闭一端开口管只有奇次谐波，λ_n = 4L/n（n 为奇数）。拍频 f_beat = |f₁ − f₂|。多普勒效应改变接收频率：f’ = f (v_sound ± v_observer)/(v_sound ∓ v_source)。
8. Electrostatics & Circuits | 静电与电路
Coulomb’s Law: F = k q₁ q₂ / r², where k ≈ 9×10⁹ N·m²/C². Electric field E = F/q, and for a point charge E = k q/r². Electric potential energy U = k q₁ q₂ / r, and potential V = U/q. For a uniform field between parallel plates, V = E d. Remember that electric field lines point from positive to negative, and equipotential surfaces are perpendicular to them.
库仑定律：F = k q₁ q₂ / r²，k ≈ 9×10⁹ N·m²/C²。电场强度 E = F/q，点电荷电场 E = k q/r²。电势能 U = k q₁ q₂ / r，电势 V = U/q。平行板匀强电场中 V = E d。牢记电场线由正指向负，等势面与之垂直。
Ohm’s Law: V = I R. Resistance R = ρ L/A, where ρ is resistivity. Power dissipated: P = I V = I² R = V²/R. For resistors in series: R_eq = R₁ + R₂ + …, same current. In parallel: 1/R_eq = 1/R₁ + 1/R₂ + …, same voltage. Kirchhoff’s laws: junction rule (ΣI_in = ΣI_out), loop rule (ΣV around any closed loop = 0). Capacitance C = Q/V, parallel‑plate capacitance C = ε₀ A/d. Time constant for RC circuit: τ = R C. After one time constant, a charging capacitor reaches 63% of full voltage.
欧姆定律：V = I R。电阻 R = ρ L/A，ρ 为电阻率。功耗：P = I V = I² R = V²/R。串联电阻：R_eq = R₁ + R₂ + …，电流相同；并联：1/R_eq = 1/R₁ + 1/R₂ + …，电压相同。基尔霍夫定律：节点规则（ΣI入 = ΣI出），回路规则（任一闭合回路 ΣV = 0）。电容 C = Q/V，平行板电容 C = ε₀ A/d。RC 电路时间常数 τ = R C。经一个时间常数，充电电容达满电压的 63%。
9. Magnetism & Electromagnetism | 磁与电磁
Magnetic force on a moving charge: F = q v B sin θ (direction given by the right‑hand rule). Force on a current‑carrying wire: F = I L B sin θ. The path of a charged particle in a uniform B field is circular with radius r = m v/(q B). Magnetic fields are produced by moving charges: a long straight wire creates B = μ₀ I/(2π r); a solenoid creates a nearly uniform field inside, B = μ₀ n I.
运动电荷在磁场中的受力：F = q v B sin θ（方向用右手定则）。电流导线受力：F = I L B sin θ。带电粒子在匀强磁场中做圆周运动，半径 r = m v/(q B)。磁场由运动电荷产生：长直导线产生 B = μ₀ I/(2π r)；螺线管内部产生近似匀强场 B = μ₀ n I。
Electromagnetic induction: changing magnetic flux induces an emf. Faraday’s Law: ε = −N ΔΦ/Δt. Lenz’s Law determines direction: the induced current opposes the change in flux. A simple generator converts mechanical energy into electrical energy by rotating a coil in a magnetic field. The induced emf is sinusoidal: ε = N B A ω sin(ωt). Transformers rely on mutual inductance: V_s/V_p = N_s/N_p, and for an ideal transformer P_p = P_s.
电磁感应：变化的磁通量产生感应电动势。法拉第定律：ε = −N ΔΦ/Δt。楞次定律决定方向：感应电流反抗磁通量的变化。简单发电机通过线圈在磁场中旋转将机械能转换为电能，感应电动势为正弦形：ε = N B A ω sin(ωt)。变压器依赖互感：V_s/V_p = N_s/N_p，理想变压器 P_p = P_s。
10. Geometric & Wave Optics | 几何光学与波动光学
Law of reflection: angle of incidence equals angle of reflection. For spherical mirrors, the mirror equation: 1/f = 1/d_o + 1/d_i, with f = R/2. Sign conventions are essential: concave mirrors have positive f, convex negative; d_o always positive; d_i positive for real images (same side as object for mirrors). Magnification m = −d_i/d_o = h_i/h_o. Ray diagrams for real/virtual, upright/inverted images must be familiar.
反射定律：入射角等于反射角。球面镜方程：1/f = 1/d_o + 1/d_i，焦距 f = R/2。符号规则至关重要：凹面镜 f 为正，凸面镜 f 为负；d_o 恒正；实像 d_i 为正（镜同侧）。放大率 m = −d_i/d_o = h_i/h_o。必须能画出实像、虚像、正立、倒立的光路图。
Refraction: Snell’s Law n₁ sin θ₁ = n₂ sin θ₂. Index of refraction n = c/v. Total internal reflection occurs when light moves from a higher to lower n at an angle greater than the critical angle: sin θ_c = n₂/n₁. Thin lens equation is identical to mirror equation. Convex lenses are converging, concave diverging. Lens power in dioptres: P = 1/f (f in metres).
折射定律：n₁ sin θ₁ = n₂ sin θ₂。折射率 n = c/v。当光从光密介质射向光疏介质且入射角大于临界角时发生全反射：sin θ_c = n₂/n₁。薄透镜方程与球面镜方程相同。凸透镜会聚，凹透镜发散。透镜屈光度：P = 1/f（f 以米为单位）。
Wave optics: Young’s double‑slit interference gives bright fringes at d sin θ = m λ (m = 0, ±1, ±2…). For a single slit, minima occur at a sin θ = m λ. The width of the central maximum is inversely proportional to slit width. Thin‑film interference results from phase changes upon reflection; use the conditions for constructive and destructive interference depending on the wavelength in the film (λ_n = λ/n).
波动光学：杨氏双缝干涉亮纹满足 d sin θ = m λ (m = 0, ±1, ±2…)。单缝衍射暗纹满足 a sin θ = m λ。中央亮纹宽度与缝宽成反比。薄膜干涉由反射时的相位突变引起，根据膜中波长（λ_n = λ/n）应用干涉加强和减弱条件。
11. Heat & Thermodynamics | 热学与热力学
Temperature measures average random kinetic energy of particles. Scales: K = °C + 273. Thermal expansion: linear ΔL = α L₀ ΔT, volume ΔV = β V₀ ΔT, with β ≈ 3α for solids. Specific heat Q = m c ΔT. Latent heat Q = m L (L_f for fusion, L_v for vaporisation) occurs at constant temperature. In calorimetry, ΣQ = 0 for an isolated system.
温度衡量粒子无规则运动的平均动能。温标：K = °C + 273。热膨胀：线膨胀 ΔL = α L₀ ΔT，体膨胀 ΔV = β V₀ ΔT，对固体 β ≈ 3α。比热容 Q = m c ΔT。相变潜热 Q = m L（L_f 熔化热，L_v 汽化热）在恒温下进行。量热学中，孤立系统 ΣQ = 0。
The ideal gas law: P V = n R T, where R = 8.31 J/(mol·K). Alternative form: P V = N k_B T, with k_B = 1.38×10⁻²³ J/K. The kinetic theory links macroscopic and microscopic: pressure P = (1/3) ρ v²_rms, and average kinetic energy per molecule (3/2) k_B T. The First Law of Thermodynamics: ΔU = Q − W, where W is work done by the gas. Thermodynamic processes: isothermal (ΔU = 0, Q = W), adiabatic (Q = 0, ΔU = −W), isovolumetric (W = 0), isobaric (W = P ΔV).
理想气体状态方程：P V = n R T，R = 8.31 J/(mol·K)。也可写为 P V = N k_B T，k_B = 1.38×10⁻²³ J/K。气体动理论联系宏观与微观：压强 P = (1/3) ρ v²_rms，分子平均动能 (3/2) k_B T。热力学第一定律：ΔU = Q − W，W 为气体对外做功。热力学过程：等温（ΔU = 0，Q = W）、绝热（Q = 0，ΔU = −W）、等容（W = 0）、等压（W = P ΔV）。
The Second Law: entropy of an isolated system never decreases. Efficiency of a heat engine: e = W/Q_H = 1 − Q_C/Q_H. Maximum Carnot efficiency: e_Carnot = 1 − T_C/T_H (temperatures in kelvins). Refrigerators and heat pumps move heat from cold to hot with work input; coefficient of performance COP = Q_C/W.
热力学第二定律：孤立系统的熵永不减少。热机效率：e = W/Q_H = 1 − Q_C/Q_H。最大卡诺效率：e_Carnot = 1 − T_C/T_H（温度用开尔文）。冰箱与热泵通过做功将热量从低温输运到高温，制冷系数 COP = Q_C/W。
12. Modern Physics | 现代物理
Wave‑particle duality: light behaves as both a wave (interference, diffraction) and as particles called photons with energy E = h f = hc/λ. The photoelectric effect: electrons are ejected from a metal when photon energy exceeds the work function φ. Einstein’s equation: K_max = h f − φ. Stopping potential V_s = K_max/e. No emission occurs below the threshold frequency, regardless of intensity.
波粒二象性：光既表现出波动性（干涉、衍射），又表现出粒子性（光子），光子能量 E = h f = hc/λ。光电效应：光子能量大于金属逸出功 φ 时电子被击出。爱因斯坦方程：K_max = h f − φ，截止电压 V_s = K_max/e。低于截止频率时无论多强光强都无法产生光电子。
Atomic models: Rutherford’s nuclear model, then Bohr’s model with quantised orbits: angular momentum L = n (h/2π). Energy levels for hydrogen: E_n = −13.6 eV / n². Emission and absorption spectra arise from electron transitions, ΔE = E_final − E_initial = h f. The Balmer series corresponds to transitions to n = 2 (visible). Wave nature of matter: de Broglie wavelength λ = h/p = h/(mv).
原子模型：卢瑟福有核模型，接着玻尔引入量子化轨道：角动量 L = n (h/2π)。氢原子能级：E_n = −13.6 eV / n²。电子跃迁产生发射光谱与吸收光谱，ΔE = E终 − E初 = h f。巴耳末系对应跃迁至 n = 2（可见光）。物质波：德布罗意波长 λ = h/p = h/(mv)。
Nuclear physics: the nucleus consists of protons and neutrons. Mass defect and binding energy: E = (Δm)c², where Δm is the mass difference between the nucleus and its separate nucleons. Types of decay: alpha (⁴₂He nucleus), beta‑minus (electron and antineutrino), beta‑plus (positron and neutrino), gamma (high‑energy photon). In any nuclear reaction, mass‑energy, charge, and nucleon number are conserved. Calculate half‑life from activity decay: N = N₀ (1/2)^(t/T₁/₂).
核物理：原子核由质子和中子组成。质量亏损和结合能：E = (Δm)c²，Δm 是核子与单独核子的质量差。衰变类型：α 衰变（⁴₂He 核）、β⁻ 衰变（电子及反中微子）、β⁺ 衰变（正电子及中微子）、γ 衰变（高能光子）。任何核反应中，质能、电荷与核子数均守恒。由活度变化计算半衰期：N = N₀ (1/2)^(t/T₁/₂)。
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