📚 Core Formulas and Application Points for A-Level Physics | A-Level物理考点：核心公式梳理与应用要点
A-Level Physics demands not only an understanding of concepts but also the confident application of core formulas across mechanics, electricity, waves, thermal physics, and nuclear physics. This guide compresses the essential equations you must know, highlights their key application points, and warns you about common pitfalls.
A-Level物理不仅要求理解概念，更要求你能够自信地运用力学、电学、波动、热学和原子物理中的核心公式。这篇文章为你浓缩了必须掌握的方程，指出关键的应用要点，并提醒常见误区。
1. Kinematics Equations | 运动学方程
The four constant-acceleration equations connect displacement s, initial velocity u, final velocity v, acceleration a, and time t. They are valid only when acceleration is constant.
四个匀变速运动公式联系到位移 s、初速度 u、末速度 v、加速度 a 和时间 t。它们仅在加速度恒定（匀变速）时成立。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
Application point: Choose the equation with the least unknown quantity. If an object is dropped from rest, u = 0 and a = g = 9.81 m s⁻². When an object reaches its highest point, v = 0.
应用要点：选用未知量最少的方程。物体从静止下落时，u = 0，a = g = 9.81 m s⁻²。物体到达最高点时，v = 0。
Common pitfall: Never use these equations for motion with changing acceleration, such as a pendulum or a mass on a spring.
常见误区：不要在加速度变化的运动中套用这些公式，例如单摆或弹簧上的质量块。
2. Newton’s Laws and Forces | 牛顿定律与力
Newton’s second law is the bridge between force and acceleration. In vector form, the net force equals the product of mass and acceleration.
牛顿第二定律连接了力与加速度。在矢量形式下，合外力等于质量乘以加速度。
F = ma
Weight W = mg
Frictional force ≤ μR
Application point: Resolve forces into horizontal and vertical components before applying F = ma. For a block sliding down an incline, take the direction along the slope as positive.
应用要点：应用 F = ma 前先将力分解为水平和竖直分量。对于沿斜面下滑的物块，取沿斜面向下为正方向。
Common pitfall: Do not confuse weight (force) with mass. Weight is measured in newtons, mass in kilograms.
常见误区：不要混淆重力（力）与质量。重力单位是牛顿，质量单位是千克。
3. Work, Energy, and Power | 功、能与功率
Work is done when a force causes displacement. Energy is the capacity to do work. Power is the rate of doing work.
力使物体发生位移时就做了功。能量是做功的能力。功率是做功的快慢。
W = Fd cos θ
Eₖ = ½mv²
Eₚ = mgh
P = W/t = Fv
Application point: Use the work-energy principle to avoid dealing with acceleration in problems involving variable forces or curved paths. For a non-conservative force (e.g. friction), the total mechanical energy is not conserved.
应用要点：遇到变力或曲线路径问题，使用功能原理可以避免求解加速度。对于非保守力（如摩擦力），总机械能不守恒。
Common pitfall: In the formula W = Fd cos θ, angle θ is between the force and displacement directions. For a cyclist moving horizontally, the vertical normal force does no work because θ = 90°.
常见误区：在 W = Fd cos θ 中，θ 是力与位移方向之间的夹角。水平骑行时，竖直方向的支持力不做功，因为 θ = 90°。
4. Momentum and Impulse | 动量与冲量
Momentum is a vector quantity defined as mass times velocity. Impulse equals the change in momentum. In the absence of external forces, total momentum is conserved.
动量是矢量，定义为质量乘以速度。冲量等于动量的变化量。在没有外力时，总动量守恒。
p = mv
Impulse = FΔt = Δp
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ (elastic or inelastic)
Application point: In collisions, use conservation of momentum for both elastic and inelastic cases. If a collision is perfectly elastic, kinetic energy is also conserved, so you can solve for unknown final velocities.
应用要点：在碰撞中，无论弹性碰撞还是非弹性碰撞，都可用动量守恒。如果碰撞是完全弹性碰撞，则动能也守恒，可据此联立解出未知末速度。
Common pitfall: Momentum is a vector. In two-dimensional collision problems, resolve momentum into x and y components separately.
常见误区：动量是矢量。在二维碰撞问题中，需要分别对 x 和 y 方向应用动量守恒。
5. Circular Motion | 圆周运动
Uniform circular motion requires a net centripetal force directed toward the center of the circle. Although the speed is constant, the velocity direction changes continuously, so there is an acceleration.
匀速圆周运动需要指向圆心的合外力提供向心力。虽然速度大小不变，但速度方向不断改变，因此存在加速度。
a = v²/r = rω²
F = mv²/r = mrω²
ω = 2π/T = 2πf
Application point: For a car on a banked curve, the horizontal component of the normal reaction provides the centripetal force. For a satellite in orbit, the gravitational force provides the centripetal force.
应用要点：汽车在倾斜弯道上行驶时，支持力的水平分力提供向心力。卫星做圆周运动时，万有引力提供向心力。
Common pitfall: Centrifugal force is not a real force in an inertial frame. Never add it to a free-body diagram as an actual force acting on the object.
常见误区：在惯性参考系中，离心力不是真实力。绝不能在受力分析图中把离心力当成实际作用力。
6. Gravitation | 万有引力
Newton’s law of gravitation describes the attractive force between two point masses. For a spherical mass, the gravitational field outside can be treated as if the entire mass were concentrated at the center.
牛顿万有引力定律描述了两质点之间的吸引力。对于球对称质量，外部引力场可以等效为质量集中于球心的质点产生的场。
F = GMm/r²
g = GM/r²
Gravitational potential V = -GM/r
Application point: To find orbital speed of a satellite, set gravitational force equal to mv²/r, yielding v = √(GM/r). The orbital period is T = 2π√(r³/GM).
应用要点：要求卫星的轨道速度，令万有引力等于 mv²/r，即得 v = √(GM/r)。轨道周期 T = 2π√(r³/GM)。
Common pitfall: The gravitational potential at infinity is defined as zero. Potential values near a mass are negative. Do not confuse potential (scalar) with field strength (vector).
常见误区：无穷远处引力势能定义为 0。质量附近的势能为负值。不要混淆引力势（标量）与引力场强（矢量）。
7. Electric Fields and Coulomb’s Law | 电场与库仑定律
Electric charges create electric fields. Coulomb’s law gives the force between two point charges. The electric field strength is force per unit positive charge.
电荷产生电场。库仑定律给出了两点电荷之间的作用力。电场强度是单位正电荷所受的力。
F = kQ₁Q₂/r²
E = F/q
E = kQ/r² (point charge)
V = kQ/r (potential)
Application point: For a uniform electric field between parallel plates, E = V/d, where V is plate potential difference and d is separation. Use energy conservation: charge q moving through potential difference V changes electric potential energy by qV.
应用要点：平行板间的匀强电场 E = V/d，其中 V 是板间电势差，d 是板间距。利用能量守恒：电荷 q 通过电势差 V 时，电势能变化为 qV。
Common pitfall: Electric field direction is from positive to negative. The force on a negative charge is opposite to the field direction.
常见误区：电场方向从正电荷指向负电荷。负电荷所受电场力方向与场强方向相反。
8. Capacitance | 电容
A capacitor stores charge and energy in an electric field. Capacitance is defined as charge stored per unit potential difference.
电容器在电场中储存电荷和能量。电容定义为储存的电荷量跟电势差的比值。
C = Q/V
C = ε₀εᵣA/d (parallel plate)
Energy stored = ½QV = ½CV² = Q²/2C
Application point: When capacitors are connected in parallel, the total capacitance is the sum. In series, the reciprocal of total capacitance equals the sum of reciprocals.
应用要点：电容器并联时，总电容相加。串联时，总电容的倒数等于各电容倒数之和。
Common pitfall: The charging and discharging of capacitors through a resistor follow exponential curves. Use τ = RC as the time constant; after one time constant, the voltage reaches about 63% of its final value.
常见误区：电容器通过电阻充电和放电遵循指数曲线。时间常数 τ = RC；经过一个时间常数后，电压达到最终值的约 63%。
9. Circuit Laws and Resistivity | 电路定律与电阻率
Ohm’s law, Kirchhoff’s laws, and the resistivity equation form the foundation of DC circuit analysis.
欧姆定律、基尔霍夫定律和电阻率公式构成了直流电路分析的基础。
V = IR
R = ρL/A
Kirchhoff’s voltage law: ΣV = 0 around a loop
Kirchhoff’s current law: ΣI = 0 at a junction
Application point: Use the potential divider equation V_out = V_s × R₂/(R₁ + R₂) when two resistors are in series. The current is the same through series components, while voltage is the same across parallel components.
应用要点：两个串联电阻构成分压电路时，输出电压 V_out = V_s × R₂/(R₁ + R₂)。串联元件电流相同，并联元件电压相同。
Common pitfall: Ohm’s law is only valid for components that obey Ohm’s law (constant resistance). For filament lamps and diodes, resistance is not constant and V-I graphs are nonlinear.
常见误区：欧姆定律只对遵循欧姆定律的元件（电阻恒定）成立。对于白炽灯和二极管，电阻并非恒定，V-I 图像是非线性的。
10. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
Moving charges experience a force in a magnetic field. Electromagnetic induction occurs when the magnetic flux linkage through a circuit changes.
运动的电荷在磁场中会受到力的作用。当穿过回路的磁通量发生变化时，会产生电磁感应现象。
F = BIL sin θ (wire in a magnetic field)
F = qvB sin θ (moving charge)
Faraday’s law: EMF ε = -NΔΦ/Δt
Lenz’s law: direction opposes the change causing it
Application point: When a rod of length L moves perpendicular to a uniform magnetic field at speed v, the induced EMF is ε = BLv. Use Lenz’s law to predict the direction of induced current; the minus sign in Faraday’s law reminds you of energy conservation.
应用要点：长为 L 的导体棒垂直磁感线以速度 v 切割磁感线时，感应电动势 ε = BLv。用楞次定律判断感应电流方向；法拉第定律中的负号提示能量守恒。
Common pitfall: Magnetic flux is Φ = BA cos θ, where θ is the angle between the magnetic field and the normal to the area. The flux linkage is NΦ for a coil of N turns.
常见误区：磁通量 Φ = BA cos θ，其中 θ 是磁场方向与面积法线方向的夹角。N 匝线圈的磁通链为 NΦ。
11. Waves and Superposition | 波动与叠加
Waves transfer energy without transferring matter. Key relationships involve wavelength, frequency, and speed. Interference and diffraction arise from the superposition principle.
波动传递能量但不传递物质。关键关系涉及波长、频率和速度。干涉与衍射源于叠加原理。
v = fλ
Path difference for constructive interference = nλ
Path difference for destructive interference = (n + ½)λ
Application point: For a double-slit experiment, bright fringe spacing is Δy = λD/d, where D is the distance to the screen and d is the slit separation. For a diffraction grating, the condition for maxima is d sin θ = nλ.
应用要点：双缝干涉实验中，相邻亮条纹间距 Δy = λD/d，其中 D 是屏到缝的距离，d 是双缝间距。对于光栅，主极大条件为 d sin θ = nλ。
Common pitfall: For waves from two coherent sources, a path difference of a whole number of wavelengths gives constructive interference. A half-wavelength path difference gives destructive interference.
常见误区：两列相干波的路程差为波长的整数倍时干涉加强。路程差为半个波长的奇数倍时干涉相消。
12. Thermal Physics and Ideal Gases | 热学与理想气体
Thermal physics deals with internal energy, heat capacity, and phase changes. The ideal gas equation connects macroscopic quantities: pressure, volume, temperature, and amount of substance.
热学研究内能、热容和物态变化。理想气体方程将宏观量压强、体积、温度与物质的量联系在一起。
Q = mcΔT
Q = mL (latent heat)
PV = nRT (ideal gas equation)
Average kinetic energy of a molecule = (3/2)kT
Application point: In processes like isothermal (constant temperature) change, PV = constant. For adiabatic expansion, no heat enters or leaves the system, so temperature drops as gas does work.
应用要点：在等温过程中，PV 为常数。对于绝热膨胀，系统与外界无热量交换，气体对外做功导致温度降低。
Common pitfall: Always convert temperatures to kelvin in gas law calculations. Celsius temperatures cannot be used directly in PV = nRT.
常见误区：气体定律计算中必须将温度转换为开尔文。摄氏温度不能直接代入 PV = nRT。
13. Atomic and Nuclear Physics | 原子与原子核物理
Nuclear physics equations describe radioactive decay, mass-energy equivalence, and the energy changes in nuclear reactions.
核物理方程描述放射性衰变、质能关系以及核反应中的能量变化。
N = N₀e^(-λt)
A = A₀e^(-λt)
T½ = ln 2 / λ
E = Δmc²
Application point: Use the exponential decay equations to find the activity or number of remaining nuclei. The half-life is the time for half the sample to decay. For nuclear binding energy, calculate the mass defect Δm and multiply by c².
应用要点：用指数衰变方程求剩余核数或活度。半衰期是样品衰变到一半所需的时间。计算核结合能时，先计算质量亏损 Δm，再乘以 c²。
Common pitfall: The decay constant λ has units s⁻¹, but half-life T½ is a time. Do not confuse decay constant with half-life. The equation T½ = ln 2 / λ shows they are inversely related.
常见误区：衰变常数 λ 的单位是 s⁻¹，而半衰期 T½ 是时间。不要混淆二者。T½ = ln 2 / λ 表明它们成反比关系。
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