📚 SAT II Physics Formula Summary | SAT II 物理常用公式汇总
The SAT II Physics test covers a broad range of topics, from mechanics to modern physics. Mastering the essential formulas is crucial for solving problems quickly and accurately. This guide provides a concise English-Chinese summary of the key equations you need to know, organized by topic, with explanations to help you apply them effectively.
SAT II 物理考试涵盖从力学到现代物理的广泛内容。掌握核心公式对于快速准确地解题至关重要。本指南按主题整理了你需要掌握的关键方程，并提供英中双语解释，帮助你有效运用这些公式。
1. Kinematics | 运动学
Kinematics describes motion without reference to forces. The following equations apply to constant acceleration along a straight line. Remember to define a coordinate system and treat vectors carefully.
运动学描述运动而不涉及力。以下方程适用于匀加速直线运动。记得定义坐标系，并谨慎处理矢量。
The first equation links final velocity, initial velocity, acceleration, and time: v = v₀ + a t. Here, v is final velocity, v₀ is initial velocity, a is constant acceleration, and t is time.
第一个方程联立末速度、初速度、加速度和时间：v = v₀ + a t。这里 v 是末速度，v₀ 是初速度，a 是恒加速度，t 是时间。
Displacement involves a quadratic term: Δx = v₀ t + ½ a t². This equation is useful when you know initial velocity and acceleration and need the distance traveled.
位移包含二次项：Δx = v₀ t + ½ a t²。当已知初速度和加速度且需要求行程距离时，该方程很有用。
Another form eliminates time: v² = v₀² + 2 a Δx. This is handy for problems where time is not given.
另一种形式消去了时间：v² = v₀² + 2 a Δx。在未给出时间的问题中，这个公式很方便。
For average velocity under constant acceleration, you can use vavg = (v₀ + v) / 2, and then Δx = vavg t. Remember, these simplify only for constant acceleration.
对于匀加速运动中的平均速度，可用 vavg = (v₀ + v) / 2，然后 Δx = vavg t。请记住，这些简化仅适用于匀加速。
2. Newton's Laws and Forces | 牛顿定律与力
Dynamics connects forces to motion. Newton's second law is the cornerstone: the net force equals mass times acceleration.
动力学将力与运动联系起来。牛顿第二定律是基石：合力等于质量乘以加速度。
Fnet = m a
Always draw a free-body diagram and resolve forces into components. The weight of an object near Earth's surface is Fg = m g, with g ≈ 9.8 m/s² downward.
务必画出受力分析图并分解力。物体在地球表面附近的重力为 Fg = m g，g 约 9.8 m/s² 向下。
Friction is often proportional to the normal force N: kinetic friction fk = μ_k N, static friction ranges up to a maximum fs ≤ μ_s N. On an inclined plane, the normal force is typically N = m g cosθ.
摩擦力通常与法向力 N 成正比：动摩擦力 fk = μ_k N，静摩擦力最大可达 fs ≤ μ_s N。在斜面上，法向力通常为 N = m g cosθ。
For an object moving in a circle, the net centripetal force is given by Fc = m v² / r. This is not a new force but the net force toward the center.
对于做圆周运动的物体，向心力由 Fc = m v² / r 给出。这不是一种新的力，而是指向圆心的合力。
3. Work, Energy, and Power | 功、能与功率
Energy concepts simplify many problems. Work done by a constant force is the product of force, displacement, and the cosine of the angle between them.
能量概念简化了许多问题。恒力做功等于力、位移及其夹角余弦的乘积。
W = F d cosθ
Kinetic energy is KE = ½ m v². The work-energy theorem states that the net work equals the change in kinetic energy: Wnet = ΔKE.
动能为 KE = ½ m v²。动能定理指出净功等于动能的变化：Wnet = ΔKE。
Gravitational potential energy near Earth's surface is PE_g = m g h, where h is the height relative to a chosen reference. Spring potential energy is PE_s = ½ k x², with k the spring constant and x the displacement from equilibrium.
地表附近的重力势能为 PE_g = m g h，h 是相对于选定参考点的高度。弹性势能为 PE_s = ½ k x²，k 为劲度系数，x 为偏离平衡位置的位移。
Mechanical energy is conserved if only conservative forces (gravity, springs) do work: KE_i + PE_i = KE_f + PE_f.
若只有保守力（重力、弹力）做功，机械能守恒：KE_i + PE_i = KE_f + PE_f。
Power is the rate of doing work: P = W / t. For a constant force acting on a moving object, P = F v cosθ. The average power can also be written as P = F vavg if the force and velocity are parallel.
功率是做功的快慢：P = W / t。对于作用于运动物体的恒力，P = F v cosθ。若力与速度平行，平均功率也可写为 P = F vavg。
4. Momentum and Collisions | 动量与碰撞
Momentum helps analyze interactions, especially collisions. Linear momentum p = m v. Impulse equals the change in momentum: J = Favg Δt = Δp.
动量有助于分析相互作用，尤其是碰撞。线动量 p = m v。冲量等于动量的变化：J = Favg Δt = Δp。
In a closed system with no external forces, total momentum is conserved: p_initial = pfinal. This applies to both elastic and inelastic collisions.
在无外力的封闭系统中，总动量守恒：p_initial = pfinal。这适用于弹性碰撞和非弹性碰撞。
For a perfectly inelastic collision, objects stick together and move with a common velocity: m₁ v₁ + m₂ v₂ = (m₁ + m₂) vf. Kinetic energy is not conserved, but momentum is.
完全非弹性碰撞中，物体粘在一起以共同速度运动：m₁ v₁ + m₂ v₂ = (m₁ + m₂) vf。动能不守恒，但动量守恒。
In an elastic collision, both momentum and kinetic energy are conserved. For one-dimensional elastic collisions, relative velocity of approach equals relative velocity of separation: v₁ - v₂ = -(v₁' - v₂').
在弹性碰撞中，动量和动能均守恒。一维弹性碰撞的接近速度与分离速度大小相等、方向相反：v₁ - v₂ = -(v₁' - v₂')。
5. Circular Motion and Gravitation | 圆周运动与引力
Uniform circular motion involves a centripetal acceleration directed toward the center. Its magnitude is ac = v² / r = ω² r, where ω is angular speed in rad/s. The relationship between linear and angular velocity is v = ω r.
匀速圆周运动具有指向圆心的向心加速度，大小为 ac = v² / r = ω² r，其中 ω 为角速度（rad/s）。线速度与角速度的关系为 v = ω r。
The period T of one revolution is T = 2πr / v = 2π / ω. Frequency f is the inverse: f = 1 / T.
转动周期 T 为 T = 2πr / v = 2π / ω。频率 f 为其倒数：f = 1 / T。
Newton's law of universal gravitation describes the attractive force between two point masses: Fg = G m₁ m₂ / r², with G = 6.67 × 10⁻¹¹ N·m²/kg².
牛顿万有引力定律描述两质点间的引力：Fg = G m₁ m₂ / r²，G = 6.67 × 10⁻¹¹ N·m²/kg²。
For a satellite in circular orbit, the centripetal force is provided by gravity, yielding orbital speed v = √G M / r and period T = 2π √r³ / G M. The gravitational field strength g at a distance r from mass M is g = G M / r².
对于圆轨道卫星，向心力由引力提供，可得轨道速度 v = √G M / r 和周期 T = 2π √r³ / G M。距离质量 M 为 r 处的引力场强为 g = G M / r²。
6. Simple Harmonic Motion | 简谐运动
In simple harmonic motion (SHM), the restoring force is proportional to displacement and opposite in direction: F = -k x. The motion is sinusoidal.
简谐运动（SHM）中，回复力与位移成正比且方向相反：F = -k x。运动呈正弦曲线。
The period of a mass-spring system is T = 2π √m / k, independent of amplitude. For a simple pendulum with small amplitude, T = 2π √L / g, where L is the length.
弹簧振子的周期为 T = 2π √m / k，与振幅无关。对于小振幅单摆，T = 2π √L / g，L 为摆长。
The angular frequency ω is ω = 2πf = 2π / T = √k / m for a spring, and ω = √g / L for a pendulum. The displacement as a function of time can be written x = A cos(ωt + φ) or x = A sin(ωt + φ), depending on initial conditions.
角频率 ω 为 ω = 2πf = 2π / T = √k / m（弹簧），以及 ω = √g / L（单摆）。位移随时间变化可表示为 x = A cos(ωt + φ) 或 x = A sin(ωt + φ)，取决于初始条件。
Energy in SHM continuously transforms between kinetic and potential. The total energy is constant: Etotal = ½ k A² = ½ m vmax².
简谐运动中的能量在动能和势能间不断转换。总能量恒定：Etotal = ½ k A² = ½ m vmax²。
7. Waves and Optics | 波与光学
Waves transfer energy without transferring matter. The wave speed relates frequency and wavelength: v = f λ. For a periodic wave, the period T = 1/f.
波传递能量而不传递物质。波速联系频率和波长：v = f λ。对于周期波，周期 T = 1/f。
The speed of a wave on a string depends on tension and linear density: v = √FT / μ, where μ is mass per unit length. Sound waves in air are longitudinal; their speed is about 340 m/s at room temperature.
弦上波速取决于张力和线密度：v = √FT / μ，μ 是单位长度的质量。空气中的声波是纵波；常温下波速约为 340 m/s。
When waves meet, they interfere. Standing waves on a string fixed at both ends have nodes at the ends, and the resonant wavelengths are λ_n = 2L / n ,3...). For a pipe open at both ends, standing sound waves have antinodes at the ends, and λ_n = 2L / n; for a pipe closed at one end, λ_n = 4L / n with n odd.
波相遇时发生干涉。两端固定的弦上的驻波在两端为波节，共振波长为 λ_n = 2L / n（n = 1,2,3...）。两端开口的管中驻波在开口端为波腹，λ_n = 2L / n；一端封闭的管，λ_n = 4L / n，n 为奇数。
In optics, the law of reflection states that the angle of incidence equals the angle of reflection. Snell's law governs refraction: n₁ sinθ₁ = n₂ sinθ₂ refraction n = c / v_material. For total internal reflection, the critical angle satisfies sinθ_c = n₂ / n₁ (n₁ > n₂).
在光学中，反射定律指出入射角等于反射角。折射由斯涅尔定律描述：n₁ sinθ₁ = n₂ sinθ₂。折射率 n = c / v_material。全内反射的临界角满足 sinθ_c = n₂ / n₁（n₁ > n₂）。
Thin lens equation relates object distance do, image distance di, and focal length f: 1/do + 1/di = 1/f. The sign convention: positive f for converging lens, negative for diverging. Magnification is M = - di / do.
薄透镜方程联系物距 do、像距 di 和焦距 f：1/do + 1/di = 1/f。符号约定：凸透镜 f 为正，凹透镜为负。放大率为 M = - di / do。
8. Electric Forces and Fields | 电场力与电场
Electric charges exert forces on each other. Coulomb's law gives the force between two point charges: F = k q₁ q₂ / r² k = 8.99 × 10⁹ N·m²/C². The force is repulsive for like charges, attractive for opposites.
电荷间相互施力。库仑定律给出两点电荷间的力：F = k q₁ q₂ / r²，k = 8.99 × 10⁹ N·m²/C²。同号电荷相斥，异号相吸。
The electric field E at a point is the force per unit test charge: E = F / q. The field due to a point charge q is E = k q / r², directed radially away from a positive charge.
某点的电场 E 是单位检验电荷所受的力：E = F / q。点电荷 q 产生的电场为 E = k q / r²，方向由正电荷向外径向。
Electric potential energy for two charges is U = k q₁ q₂ / r. The electric potential (voltage) is potential energy per unit charge: V = U / q. Potential due to a point charge is V = k q / r.
两点电荷的电势能为 U = k q₁ q₂ / r。电势（电压）是单位电荷的电势能：V = U / q。点电荷产生的电势为 V = k q / r。
In a uniform electric field (e.g., between parallel plates), E = V / d, where d is the separation. The work done by the field when a charge moves through a potential difference ΔV is W = q ΔV.
在匀强电场中（如平行板间），E = V / d，d 为间距。电荷通过电势差 ΔV 时电场做的功为 W = q ΔV。
9. Electric Circuits | 电路
Current is the rate of flow of charge: I = ΔQ / Δt. Ohm's law relates voltage, current, and resistance: V = I R. Resistance depends on material and geometry: R = ρ L / A, where ρ is resistivity.
电流是电荷流动的速率：I = ΔQ / Δt。欧姆定律联系电压、电流和电阻：V = I R。电阻取决于材料和几何形状：R = ρ L / A，ρ 为电阻率。
Power dissipated in a resistor can be expressed as P = I V = I² R = V² / R. In series circuits, current is constant, and resistors add: Req = R₁ + R₂ + .... In parallel circuits, voltage is constant, and the reciprocal equivalent resistance is 1/Req = 1/R₁ + 1/R₂ + ....
电阻消耗的功率可表示为 P = I V = I² R = V² / R。串联电路中电流恒定，电阻相加：Req = R₁ + R₂ + ...。并联电路中电压恒定，等效电阻的倒数为 1/Req = 1/R₁ + 1/R₂ + ...。
Capacitance is the ability to store charge: C = Q / V. For a parallel-plate capacitor, C = ε₀ A / d, with ε₀ the permittivity of free space. The energy stored in a capacitor is Uc = ½ Q V = ½ C V² = ½ Q² / C.
电容是储存电荷的能力：C = Q / V。平行板电容器的电容为 C = ε₀ A / d，ε₀ 是真空介电常数。电容中储存的能量为 Uc = ½ Q V = ½ C V² = ½ Q² / C。
Kirchhoff's rules help analyze complex circuits: the junction rule states that the sum of currents entering a junction equals the sum leaving (ΣIin = ΣIout e loop rule says the sum of potential differences around any closed loop is zero (ΣV = 0).
基尔霍夫定律有助于分析复杂电路：节点电流定律指出流入节点的电流之和等于流出节点的电流之和（ΣIin = ΣIout）。回路电压定律指出沿任何闭合回路的电势差之和为零（ΣV = 0）。
10. Magnetism | 磁学
Moving charges and currents create magnetic fields. The force on a charge moving in a magnetic field is given by the Lorentz force: F = q v B sinθ, where θ is the angle between velocity and field. The direction is perpendicular to both v and B (right-hand rule for positive charge).
运动的电荷和电流产生磁场。运动电荷在磁场中所受的力由洛伦兹力给出：F = q v B sinθ，θ 是速度与磁场间的夹角。力的方向垂直于 v 和 B（正电荷用右手定则）。
A current-carrying wire of length L in a uniform magnetic field experiences a force F = I L B sinθ, where θ is the angle between the wire and B. The direction again follows the right-hand rule.
长为 L 的通电导线在匀强磁场中所受的力为 F = I L B sinθ，θ 是导线与 B 的夹角，方向同样遵循右手定则。
The magnetic field around a long straight wire carrying current I at distance r is B = μ₀ I / (2π r), with μ₀ = 4π × 10⁻⁷ T·m/A. For a solenoid, the interior field is nearly uniform: B = μ₀ n I, where n is the number of turns per unit length.
长直通电导线产生的磁场，在距离 r 处的大小为 B = μ₀ I / (2π r)，μ₀ = 4π × 10⁻⁷ T·m/A。螺线管内部磁场近似均匀：B = μ₀ n I，n 是单位长度的匝数。
11. Thermodynamics | 热力学
Temperature measures average kinetic energy of particles. The Celsius and Kelvin scales are related by T(K) = T(°C) + 273.15. Thermal expansion: length change ΔL = α L₀ ΔT; volume change ΔV = β V₀ ΔT, where β ≈ 3α for solids.
温度衡量粒子平均动能。摄氏温标与开氏温标的关系为 T(K) = T(°C) + 273.15。热膨胀：长度变化 ΔL = α L₀ ΔT；体积变化 ΔV = β V₀ ΔT，对固体 β ≈ 3α。
Heat transfer depends on mass and specific heat: Q = m c ΔT. During phase changes, temperature remains constant and Q = m L, where L is latent heat (fusion or vaporization).
热传递取决于质量和比热容：Q = m c ΔT。相变过程中温度不变，Q = m L，L 为潜热（熔化热或汽化热）。
The ideal gas law is P V = n R T, where n is number of moles and R = 8.31 J/(mol·K). It can also be written as P V = N kB T, with kB Boltzmann's constant. For a fixed amount of gas, combined gas law: P₁V₁/T₁ = P₂V₂/T₂.
理想气体定律为 P V = n R T，n 为摩尔数，R = 8.31 J/(mol·K)。也可写成 P V = N kB T，kB 为玻尔兹曼常数。对于一定量的气体，有联合气体定律：P₁V₁/T₁ = P₂V₂/T₂。
The first law of thermodynamics is energy conservation: ΔU = Q - W he system. For an isochoric process, W = 0; for an isothermal process, ΔU = 0 (ideal gas).
热力学第一定律即能量守恒：ΔU = Q -
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