📚 A-Level CCEA Physics Formula Summary Handbook | A-Level CCEA 物理公式汇总手册
This concise handbook brings together all the essential formulas you need for the CCEA A-Level Physics course, organised by topic for quick revision. Each equation is presented with a short explanation of its meaning, helping you understand how and when to use it in problem-solving.
这本简明的公式手册汇集了 CCEA A-Level 物理课程中所有必备公式，按主题分类，方便快速复习。每个公式都配有简短的含义解释，帮助你理解如何以及何时在解题中应用它们。
1. Kinematics and Motion | 运动学与运动
The SUVAT equations describe uniformly accelerated motion along a straight line. They link initial velocity u, final velocity v, acceleration a, displacement s, and time t.
SUVAT 方程描述沿直线的匀加速运动，关联初速度 u、末速度 v、加速度 a、位移 s 和时间 t。
v = u + at
This gives the final velocity after time t under constant acceleration.
该式给出恒加速下经过时间 t 后的末速度。
s = ut + ½at²
It calculates displacement when both initial velocity and acceleration are known.
该式用于已知初速度和加速度时计算位移。
s = ½(u + v)t
Average velocity multiplied by time gives displacement, useful when acceleration is not given directly.
平均速度乘以时间得到位移，在未直接给出加速度时很有用。
v² = u² + 2as
This relation eliminates time, connecting velocities, acceleration and displacement.
此关系式消去了时间，将速度、加速度和位移联系起来。
For projectile motion, horizontal and vertical components are treated independently. The horizontal velocity is constant, while vertically the object undergoes free-fall acceleration g.
对于抛体运动，水平与竖直分量独立处理。水平速度恒定，而竖直方向物体作自由落体加速 g。
v = u + at
y = u_yt + ½gt²
x = uₓt
2. Dynamics and Forces | 动力学与力
Newton’s second law states that the resultant force on an object equals the rate of change of its momentum. For constant mass, it simplifies to F = ma.
牛顿第二定律指出合外力等于物体动量的变化率。对于质量恒定情形，简化为 F = ma。
F = ma
Weight is the force of gravity on a mass: W = mg, where g is the gravitational field strength.
重量是质量所受的重力：W = mg，其中 g 为重力场强度。
W = mg
Momentum p is the product of mass and velocity. The impulse of a force equals the change in momentum.
动量 p 是质量与速度的乘积。力的冲量等于动量的变化。
p = mv
FΔt = Δp = mv – mu
The principle of conservation of momentum states that total momentum before collision equals total momentum after collision, provided no external resultant force acts.
动量守恒原理指出，只要没有合外力作用，碰撞前的总动量等于碰撞后的总动量。
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
For a perfectly elastic collision, kinetic energy is conserved and the relative speed of approach equals the relative speed of separation.
对于完全弹性碰撞，动能守恒，且接近的相对速率等于分离的相对速率。
v₂ – v₁ = u₁ – u₂
3. Work, Energy and Power | 功、能与功率
Work done by a constant force is the product of the force component in the direction of motion and the displacement.
恒力做功等于力在运动方向上的分量与位移的乘积。
W = Fd cosθ
Kinetic energy is the energy due to motion; gravitational potential energy depends on height above a reference level.
动能是由运动产生的能量；重力势能取决于相对于参考平面的高度。
Eₖ = ½mv²
ΔEₚ = mgΔh
Elastic potential energy stored in a stretched spring obeys Hooke’s law up to the limit of proportionality.
拉伸弹簧中储存的弹性势能在比例极限内遵循胡克定律。
E = ½kx²
Power is the rate of doing work; when a constant force moves an object at steady speed, power is force times velocity.
功率是做功的速率；恒力使物体匀速运动时，功率等于力乘以速度。
P = W / t = Fv
Efficiency compares useful output with total input. The forms may be work, energy or power.
效率比较有用输出与总输入，可用功、能量或功率之比表示。
η = (useful output / total input) × 100%
4. Circular Motion | 圆周运动
Angular velocity ω measures the rate of rotation. It relates to linear speed v and radius r.
角速度 ω 衡量旋转的快慢，它与线速率 v 和半径 r 相关联。
ω = Δθ / Δt
v = ωr
An object moving in a circle experiences centripetal acceleration directed towards the centre, even if its speed is constant.
即使速率恒定，做圆周运动的物体也有指向圆心的向心加速度。
a = v² / r = ω²r
The resultant force providing this acceleration is the centripetal force.
提供该加速度的合外力即为向心力。
F = mv² / r = mω²r
Period T is the time for one complete revolution, linked to angular velocity and frequency f.
周期 T 是旋转一圈所需的时间，与角速度和频率 f 相关。
T = 2π / ω = 1 / f
5. Simple Harmonic Motion | 简谐运动
In SHM the restoring force is proportional to displacement from equilibrium and acts towards it, giving acceleration a = –ω²x.
在简谐运动中，恢复力与离开平衡位置的位移成正比并指向平衡位置，加速度 a = –ω²x。
F = –kx
a = –ω²x
Displacement, velocity and acceleration vary sinusoidally; the form depends on the starting condition.
位移、速度和加速度随时间呈正弦变化，具体形式取决于初始条件。
x = A cos(ωt) or x = A sin(ωt)
vmax = ωA
amax = ω²A
For a mass-spring system, the period depends on mass m and spring constant k; for a simple pendulum it depends on length l and g.
对于弹簧振子，周期取决于质量 m 和劲度系数 k；对于单摆，周期取决于摆长 l 和重力场强度 g。
T = 2π√(m/k)
T = 2π√(l/g)
Total energy in SHM is constant (neglecting damping) and proportional to the square of the amplitude.
简谐运动的总能量（忽略阻尼）是恒定的，与振幅的平方成正比。
Etotal = ½kA²
6. Thermal Physics and Gases | 热学与气体
The absolute temperature in kelvin relates to Celsius by T = θ + 273.15, though 273 is often sufficient for calculations.
开尔文绝对温度与摄氏度的关系为 T = θ + 273.15，在计算中通常使用 273 已足够。
The ideal gas equation combines pressure p, volume V, number of moles n, and temperature T.
理想气体状态方程联系了压强 p、体积 V、摩尔数 n 和温度 T。
pV = nRT
Using the number of molecules N, the equation becomes pV = NkT, where k is the Boltzmann constant.
若用分子数 N，方程变为 pV = NkT，其中 k 为玻尔兹曼常数。
pV = NkT
The first law of thermodynamics states that the increase in internal energy equals the heat supplied minus the work done by the system.
热力学第一定律表明，内能的增加等于供给系统的热量减去系统对外做的功。
ΔU = Q – W
Heating a substance without phase change uses specific heat capacity c; during a change of state the latent heat L applies.
无相变时加热使用比热容 c；发生相变时使用潜热 L。
Q = mcΔθ
Q = mL
For an ideal monatomic gas, the average kinetic energy per molecule is directly proportional to the absolute temperature.
对于理想单原子气体，分子平均动能与绝对温度成正比。
Eₖ = (3/2) kT
7. Electric Fields and Circuits | 电场与电路
Coulomb’s law gives the force between two point charges in a vacuum.
库仑定律给出真空中两点电荷之间的作用力。
F = kQq / r²
Electric field strength E is force per unit positive charge; potential V is work done per unit charge.
电场强度 E 是单位正电荷所受的力；电势 V 是单位电荷所做的功。
E = F / q
V = W / q
In a uniform field between parallel plates, field strength is the potential gradient.
在平行板间的匀强电场中，场强等于电势梯度。
E = V / d
Capacitance C is charge stored per unit voltage. The energy stored in a capacitor can be expressed in three equivalent forms.
电容 C 是单位电压下储存的电荷。电容器储存的能量有三种等效表达式。
C = Q / V
E = ½QV = ½CV² = Q² / (2C)
Resistance R depends on resistivity ρ, length L and cross-sectional area A. Ohm’s law links potential difference, current and resistance.
电阻 R 取决于电阻率 ρ、长度 L 和横截面积 A。欧姆定律关联电势差、电流和电阻。
R = ρL / A
V = IR
Electrical power can be calculated using any pair of V, I and R.
电功率可用 V、I 和 R 的任意两两组合计算。
P = IV = I²R = V² / R
Resistors in series add directly; for parallel the reciprocal rule applies. A potential divider provides a fraction of the input voltage.
串联电阻直接相加；并联使用倒数规则。分压器提供输入电压的一部分。
Rseries = R₁ + R₂ + …
1/Rparallel = 1/R₁ + 1/R₂ + …
Vout = Vin × R₂ / (R₁ + R₂)
8. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
A current-carrying conductor in a magnetic field experiences a force given by Fleming’s left-hand rule. The magnitude depends on the angle between current and field.
磁场中的载流导线会受到由左手定则确定的力，其大小取决于电流与磁场之间的夹角。
F = BIL sinθ
A charged particle moving through a magnetic field experiences a force perpendicular to both velocity and field, causing circular motion.
运动电荷在磁场中受到垂直于速度和磁场方向的力，从而产生圆周运动。
F = Bqv sinθ
Magnetic flux Φ measures the total field threading through a given area. When this flux changes, an emf is induced (Faraday’s law).
磁通量 Φ 衡量穿过给定面积的总磁场。当磁通量变化时，会产生感应电动势（法拉第定律）。
Φ = BA cosθ
ε = –N ΔΦ/Δt
For a straight conductor moving perpendicularly through a uniform field, the induced emf is simple.
直导线在匀强磁场中垂直切割磁感线时，感应电动势简单为：
ε = Blv
An ideal transformer changes voltages according to the turns ratio; for 100% efficiency, input and output power are equal.
理想变压器按匝数比改变电压；理想效率下输入与输出功率相等。
Vs / Vp = Ns / Np
VpIp = VsIs
9. Quantum
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