AS Physics: Formula Summary Handbook | AS 物理：公式汇总手册

📚 AS Physics: Formula Summary Handbook | AS 物理：公式汇总手册

AS Physics requires a solid grasp of key formulas across topics such as mechanics, waves, electricity, and nuclear physics. This handbook provides a concise yet comprehensive reference for all essential equations, along with definitions and typical applications. Use it to reinforce your understanding, master derivations, and become confident in solving exam questions.

AS 物理需要牢固掌握力学、波动、电学和核物理等主题中的关键公式。本手册为所有必考公式提供了简明而全面的参考，并附有定义与典型应用。用它来巩固理解、掌握推导过程，并在解题时游刃有余。

1. Kinematics | 运动学

v = u + at

This equation connects final velocity (v) with initial velocity (u), constant acceleration (a), and time (t). It is used when an object moves with uniform acceleration, for example in free fall or along an inclined plane.

该方程将末速度(v)与初速度(u)、恒定加速度(a)和时间(t)联系起来。当物体做匀加速运动时（例如自由落体或沿斜面运动）使用此公式。

s = ut + ½at²

Displacement (s) is expressed in terms of initial velocity, time, and acceleration. This is the second SUVAT equation, ideal when final velocity is unknown and you know u, a, and t.

位移(s)用初速度、时间和加速度表示。这是第二个SUVAT方程，当不知道末速度但已知u、a和t时使用。

v² = u² + 2as

This equation is useful when time is not involved. It binds final velocity squared to initial velocity squared, acceleration, and displacement.

当不涉及时间时，该方程非常有用。它将末速度的平方与初速度的平方、加速度和位移联系起来。

s = ½(u + v)t

Average velocity multiplied by time gives displacement. This formula is handy when both initial and final velocities are known along with time.

平均速度乘以时间得出位移。当已知初速度、末速度和时间时，这个公式很方便。

s = vt − ½at²

The fifth SUVAT equation expresses displacement using final velocity, acceleration, and time. It is less common but can solve problems where u is not needed.

第五个SUVAT方程利用末速度、加速度和时间表示位移。虽然不常用，但在不需要初速度的情况下可以解决问题。

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2. Dynamics | 动力学

F = ma

Newton’s second law: the net force acting on an object equals its mass multiplied by its acceleration. The direction of acceleration is the same as the net force. This law is fundamental in analysing forces in linear motion.

牛顿第二定律：作用在物体上的合力等于其质量乘以加速度。加速度的方向与合力方向相同。该定律是分析线性运动中受力的基础。

W = mg

Weight (W) is the gravitational force on a mass (m) in a gravitational field of strength g. Near Earth’s surface, g ≈ 9.81 m s⁻².

重量(W)是质量为m的物体在重力场强度g中所受的力。在地球表面附近，g ≈ 9.81 m s⁻²。

F ≤ μR

The frictional force F is at most the coefficient of static friction μ multiplied by the normal reaction R. When an object is at the point of sliding, F = μR. For a surface with no relative motion, the inequality applies.

摩擦力F最大等于静摩擦系数μ乘以正压力R。当物体处于滑动临界点时，F = μR。在没有相对运动的表面上，适用不等号。

T = mg − ma (or within a system)

When analysing problems involving pulleys or lifts, the tension T in a string can be found from Newton’s second law applied to connected masses. The exact form depends on the setup.

在分析涉及滑轮或电梯的问题时，绳子中的张力T可以通过对连接物体应用牛顿第二定律求出。具体形式取决于装置。

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3. Work, Energy and Power | 功、能与功率

W = Fs cosθ

Work done by a constant force F over a displacement s, where θ is the angle between the force and the displacement. Work is a scalar, measured in joules (J). When the force is parallel to displacement, W = Fs.

恒力F在位移s上所做的功，其中θ为力与位移之间的夹角。功是标量，单位为焦耳(J)。当力与位移平行时，W = Fs。

E_k = ½mv²

Kinetic energy is the energy an object possesses due to its motion. It depends linearly on mass and quadratically on speed.

动能是物体因运动而具有的能量。它与质量成正比，与速度的平方成正比。

ΔE_p = mgΔh

Change in gravitational potential energy near Earth’s surface equals the object’s weight multiplied by the vertical height change. This is valid when g is constant.

地球表面附近重力势能的变化等于物体的重力乘以垂直高度的变化。当g恒定时此式成立。

P = W/t = Fv

Power is the rate of doing work or transferring energy. For a constant force moving an object at constant speed v, the instantaneous power is Fv. Power is measured in watts (W).

功率是做功或传递能量的速率。对于以恒定速度v移动物体的恒力，瞬时功率为Fv。功率的单位是瓦特(W)。

Efficiency = (useful output / total input) × 100%

Efficiency describes how much of the input energy is converted into useful output. It is always less than 100% due to dissipative forces like friction.

效率描述输入能量中有多少转化为有用输出。由于摩擦等耗散力，效率始终低于100%。

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4. Momentum and Impulse | 动量与冲量

p = mv

Linear momentum is the product of mass and velocity. It is a vector quantity and is conserved in isolated systems where no external forces act.

线动量是质量与速度的乘积。它是矢量，在没有外力作用的孤立系统中守恒。

F = Δp/Δt

Newton’s second law in momentum form: the resultant force equals the rate of change of momentum. This form is particularly useful when dealing with variable mass or collisions.

动量形式的牛顿第二定律：合力等于动量的变化率。在处理变质量或碰撞问题时，这种形式特别有用。

Impulse = FΔt = Δp

Impulse is defined as the product of average force and the time for which it acts, and it equals the change in momentum. Impulse–momentum theorem is central to analysing collisions.

冲量定义为平均力与其作用时间的乘积，等于动量的变化。冲量-动量定理是分析碰撞问题的核心。

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Conservation of momentum for two colliding objects: the total momentum before collision equals the total momentum after, provided no external resultant force acts.

两个物体碰撞时的动量守恒：只要没有外部合力作用，碰撞前的总动量等于碰撞后的总动量。

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5. Materials | 材料

σ = F/A

Stress (σ) is the force applied per unit cross‑sectional area. Its unit is pascal (Pa) or N m⁻². Stress can be tensile or compressive.

应力(σ)是单位横截面积上所施加的力。单位为帕斯卡(Pa)或N m⁻²。应力可分为张应力和压应力。

ε = ΔL/L₀

Strain (ε) is the extension per unit original length. It is a dimensionless ratio and has no units.

应变(ε)是单位原始长度的伸长量。它是一个无量纲比值，没有单位。

E = σ/ε

Young modulus (E) is the ratio of tensile stress to tensile strain within the elastic limit. It measures the stiffness of a material. A high E means the material is resistant to deformation.

杨氏模量(E)是弹性限度内张应力与张应变之比。它衡量材料的刚度。E值高表示材料抵抗形变的能力强。

E = (F/A)/(ΔL/L₀) = FL₀/(AΔL)

The experimental formula for Young modulus, obtained by combining the definitions. It shows the linear relationship between load and extension for wires and rods in the elastic region.

杨氏模量的实验公式，由定义合并得到。它显示了弹性区域内金属丝和杆件的载荷与伸长量之间的线性关系。

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6. Waves | 波动

v = fλ

Wave speed (v) equals frequency (f) multiplied by wavelength (λ). This relationship holds for all types of waves: mechanical, electromagnetic, transverse, and longitudinal.

波速(v)等于频率(f)乘以波长(λ)。这种关系适用于所有类型的波：机械波、电磁波、横波和纵波。

f = 1/T

Frequency is the reciprocal of the period T. It is the number of complete oscillations per second, measured in hertz (Hz).

频率是周期T的倒数。它是每秒完整振动的次数，以赫兹(Hz)为单位。

nλ = d sinθ (for double‑slit interference)

In Young’s double‑slit experiment, constructive interference occurs when the path difference is an integer multiple of the wavelength. d is the slit separation, θ the angle to the fringe, and n the order number. For small angles, sinθ ≈ tanθ = x/D, leading to λ = ax/D.

在杨氏双缝实验中，当光程差为波长的整数倍时发生相长干涉。d为双缝间距，θ为条纹对应的角度，n为级数。对于小角度，sinθ ≈ tanθ = x/D，于是 λ = ax/D。

nλ = 2d sinθ (for a diffraction grating)

For a transmission grating with slit spacing d, maxima occur at angles θ given by this equation. It is key to measuring wavelengths of light and for spectral analysis.

对于缝间距为d的透射光栅，极大值出现在满足此方程的角度θ处。这是测量光波长和光谱分析的关键公式。

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7. Electricity | 电学

I = ΔQ/Δt

Electric current I is the rate of flow of charge. It is measured in amperes (A). In a metallic conductor, charge carriers are electrons.

电流I是电荷流动的速率，以安培(A)为单位。在金属导体中，载流子是电子。

V = W/Q

Potential difference (voltage) between two points is the work done per unit charge to move a charge between those points. It is measured in volts (V).

两点之间的电势差（电压）是将单位电荷从一点移动到另一点所做的功，以伏特(V)为单位。

V = IR

Ohm’s law for a metallic conductor at constant temperature: voltage across a resistor is directly proportional to the current through it. R is the resistance measured in ohms (Ω).

恒定温度下金属导体的欧姆定律：电阻两端的电压与通过它的电流成正比。R是电阻，以欧姆(Ω)为单位。

P = IV = I²R = V²/R

Power dissipated in a circuit element. The three equivalent forms are derived using Ohm’s law and are used depending on which quantities are known.

电路元件中耗散的功率。根据欧姆定律可推导出三个等价形式，根据已知量选用。

R_series = R₁ + R₂ + …

Resistors in series add linearly. The same current flows through each, and the total voltage is the sum of individual voltages.

串联电阻线性相加。流过每个电阻的电流相同，总电压等于各电压之和。

1/R_parallel = 1/R₁ + 1/R₂ + …

For resistors in parallel, the reciprocal of the total resistance is the sum of reciprocals of individual resistances. The voltage across each is the same.

对于并联电阻，总电阻的倒数等于各电阻倒数之和。每个电阻两端的电压相同。

R = ρL/A

Resistance of a uniform wire: ρ is the resistivity (Ω m), L is length, and A is cross‑sectional area. Resistivity depends on the material and temperature.

均匀导线的电阻：ρ为电阻率(Ω m)，L为长度，A为横截面积。电阻率取决于材料和温度。

emf = V + Ir

For a cell with internal resistance r, the electromotive force emf equals the terminal voltage V plus the voltage drop across the internal resistance (Ir). V = emf − Ir when current flows.

对于具有内阻r的电池，电动势emf等于端电压V加上内阻上的压降(Ir)。当有电流时，V = emf − Ir。

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8. Quantum and Nuclear Physics | 量子与核物理

E = hf

Photon energy E equals Planck’s constant h (6.63 × 10⁻³⁴ J s) multiplied by the frequency f. This quantised energy is the basis for the photoelectric effect and atomic spectra.

光子能量E等于普朗克常数h(6.63 × 10⁻³⁴ J s)乘以频率f。这种量子化的能量是光电效应和原子光谱的基础。

c = fλ

For electromagnetic waves in vacuum, the speed of light c = 3.00 × 10⁸ m s⁻¹ relates frequency and wavelength. Combined with E = hf, we get E = hc/λ.

对于真空中的电磁波，光速c = 3.00 × 10⁸ m s⁻¹ 将频率与波长联系起来。结合E = hf，可得E = hc/λ。

hf = Φ + E_{k max}

Einstein’s photoelectric equation: the energy of an incident photon is used to overcome the work function Φ and to give the emitted electron its maximum kinetic energy. It explains the threshold frequency f₀ = Φ/h.

爱因斯坦光电方程：入射光子的能量用于克服逸出功Φ，并给予发射电子最大动能。它解释了截止频率f₀ = Φ/h。

λ = h/p

De Broglie wavelength of a particle with momentum p = mv. It demonstrates the wave–particle duality of matter; electrons can exhibit diffraction.

动量为p = mv的粒子的德布罗意波长。它证明了物质的波粒二象性；电子可以发生衍射。

E = mc²

Mass–energy equivalence: a mass m has an equivalent rest energy E. In nuclear reactions, mass defect Δm leads to energy release ΔE = Δm c².

质能等价：质量m具有等价的静止能量E。在核反应中，质量亏损Δm导致能量释放ΔE = Δm c²。

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9. Circular Motion | 圆周运动

ω = Δθ/Δt = 2πf

Angular velocity ω is the rate of change of angular displacement. It is related to the frequency of rotation f by ω = 2πf. The unit is rad s⁻¹.

角速度ω是角位移的变化率。它与旋转频率f的关系为ω = 2πf，单位为rad s⁻¹。

v = ωr

The linear speed v of an object moving in a circle of radius r is linked to angular velocity by this simple relation.

沿半径为r的圆周运动的物体，其线速度v与角速度之间由这个简单关系式联系。

a = v²/r = ω²r

Centripetal acceleration: for uniform circular motion, the acceleration is directed towards the centre of the circle. It can be expressed in terms of linear speed or angular velocity.

向心加速度：对于匀速圆周运动，加速度指向圆心。它可以用线速度或角速度表示。

F = mv²/r = mω²r

Centripetal force is the net force causing centripetal acceleration. It is always directed towards the centre and is responsible for keeping an object in circular motion.

向心力是产生向心加速度的合力。它始终指向圆心，是使物体保持圆周运动的力。

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