📚 SQA Physics Year 11: Formula & Theorem Quick Reference Handbook | SQA 物理 11 年级：公式定理速查手册
This handbook summarises all essential formulae and theorems needed for the SQA National 5 Physics course (Year 11). It serves as a quick revision guide to help you memorise and apply key relationships across topics such as kinematics, dynamics, energy, electricity, waves, heat, pressure and nuclear radiation. Each formula is presented with its variables clearly defined, followed by a concise explanation in Chinese. Use this alongside your data booklet to master problem-solving in your exam.
本手册汇总了 SQA National 5 物理课程（11 年级）所需的所有关键公式与定理。它可作为快速复习指南，帮助你记忆并运用运动学、动力学、能量、电学、波动、热学、压强与核辐射等主题中的重要关系式。每个公式均列出变量含义，并附有简洁的中文解释。请结合数据手册使用，以便在考试中熟练解题。
1. Kinematics | 运动学
v = u + a t
Relates final velocity v to initial velocity u, constant acceleration a and time t. It is the first equation of motion for uniform acceleration.
将末速度 v 与初速度 u、恒定加速度 a 和时间 t 联系起来。这是匀加速运动的第一个运动方程。
s = u t + ½ a t²
Calculates displacement s when an object accelerates uniformly from initial velocity u over time t. The term ½ a t² accounts for the additional distance due to acceleration.
计算物体从初速度 u 开始匀加速运动、经过时间 t 后的位移 s。½ a t² 项表示因加速度而增加的额外距离。
v² = u² + 2 a s
Links final velocity v, initial velocity u, acceleration a and displacement s without using time. Very useful when time is not given.
将末速度 v、初速度 u、加速度 a 和位移 s 联系起来，不含时间变量。在未给出时间时非常有用。
s = v̄ t and v̄ = (u + v) / 2
For uniform acceleration, average velocity v̄ equals (u+v)/2. Displacement is then the product of average velocity and time. Often used when acceleration is known but constant velocity is not assumed throughout.
对于匀加速运动，平均速度 v̄ = (u+v)/2。位移等于平均速度乘以时间。当加速度恒定但不适用于全程匀速时常用。
v = d / t
Defines constant speed v as distance d divided by time t. For uniform motion, this also gives the magnitude of velocity.
定义恒定速率 v 为距离 d 除以时间 t。对于匀速运动，这也给出了速度的大小。
2. Dynamics & Momentum | 动力学与动量
F = m a
Newton's second law: resultant force F equals mass m multiplied by acceleration a. The unit of force is the newton (N).
牛顿第二定律：合外力 F 等于质量 m 乘以加速度 a。力的单位是牛顿 (N)。
W = m g
Weight W is the gravitational force on a mass m in a gravitational field of strength g (on Earth g ≈ 9.8 N/kg or 9.8 m/s²).
重量 W 是质量为 m 的物体在重力场强度 g 下所受的重力（地球表面 g 约 9.8 N/kg 或 9.8 m/s²）。
p = m v
Momentum p is the product of mass m and velocity v. It is a vector quantity, conserved in all isolated collisions and explosions.
动量 p 等于质量 m 与速度 v 的乘积。它是矢量，在所有孤立碰撞和爆炸中守恒。
Total p before = Total p after
The principle of conservation of momentum: in the absence of external forces, the total momentum of a system remains constant. Use it to find unknown velocities in collisions.
动量守恒定律：在无外力作用时，系统的总动量保持不变。可用其求解碰撞中的未知速度。
3. Energy, Work & Power | 能量、功与功率
Eₖ = ½ m v²
Kinetic energy Eₖ is the energy of motion. It depends on mass m and the square of speed v.
动能 Eₖ 是物体运动具有的能量，取决于质量 m 和速度 v 的平方。
E₝ = m g h
Gravitational potential energy E gained when lifting a mass m through a vertical height h in a gravitational field g.
重力势能 E 是将质量 m 的物体在重力场 g 中竖直抬高 h 后所获得的能量。
W = F d
Work done W when a constant force F moves an object through a distance d in the direction of the force. Work is a scalar measured in joules (J).
做功 W 等于恒力 F 与物体沿力方向移动距离 d 的乘积。功是标量，单位为焦耳 (J)。
P = E / t or P = W / t
e of energy transfer or work done per unit time. Measured in watts (W), where 1 W = 1 J/s.
功率 P 是能量传递或做功的速率，即单位时间内的能量或功。单位为瓦特 (W)，1 W = 1 J/s。
Efficiency = Useful power output / Total power input
Efficiency is often expressed as a percentage. For National 5, use the ratio of useful power (or energy) to total input.
效率通常用百分数表示。在 National 5 课程中，用有用功率（或能量）与总输入的比值。
4. Electricity | 电学
Q = I t
Charge Q transferred is the product of current I and time t. Charge is measured in coulombs (C), current in amperes (A).
电荷量 Q 等于电流 I 与时间 t 的乘积。电荷单位是库仑 (C)，电流单位是安培 (A)。
V = I R
Ohm's law: the voltage V across a resistor is equal to the current I through it multiplied by its resistance R. Resistance is measured in ohms (Ω).
欧姆定律：电阻两端的电压 V 等于通过它的电流 I 乘以其电阻 R。电阻单位为欧姆 (Ω)。
P = I V
power P is given by the product of current I and voltage V. This can be combined with Ohm's law to give P = I² R and P = V² / R.
电功率 P 等于电流 I 与电压 V 的乘积。结合欧姆定律可得 P = I² R 和 P = V² / R。
E = P t
time t. In practical circuits, E = I t V and is measured in joules (J) or kilowatt-hours.
电能 E 等于功率 P 乘以时间 t。在实际电路中，E = I t V，单位为焦耳 (J) 或千瓦时。
Rₛ = R₁ + R₂ + ... (series)
Total resistance in series is the sum of individual resistances. The current is the same through all components.
串联总电阻等于各电阻值之和，串联电路中电流处处相等。
1 / Rₛ = 1 / R₁ + 1 / R₂ + ... (parallel)
For resistors in parallel, the reciprocal of the total resistance equals the sum of the reciprocals of individual resistances. The voltage across each branch is the same.
对于并联电阻，总电阻的倒数等于各支路电阻倒数之和，并联电路各支路电压相等。
5. Waves | 波动
v = f λ
The wave equation: wave speed v equals frequency f multiplied by wavelength λ. Applies to all types of wave: sound, light, water waves.
波动方程：波速 v 等于频率 f 乘以波长 λ。适用于所有类型的波，如声波、光波、水波。
f = 1 / T
Frequency f is the number of complete waves per second; period T is the time for one complete wave. They are reciprocals. Unit of frequency is hertz (Hz), period in seconds (s).
频率 f 是每秒完整波的个数；周期 T 是一个完整波所需的时间。频率与周期互为倒数，频率单位为赫兹 (Hz)，周期单位为秒 (s)。
6. Heat & Temperature | 热与温度
Eₙ = c m ΔT
Heat energy Eₙ required to change the temperature of mass m by ΔT, where c is the specific heat capacity of the material (J kg⁻¹ °C⁻¹ or J kg⁻¹ K⁻¹). No change of state occurs.
改变质量 m 的物体温度 ΔT 所需热量 Eₙ = c m ΔT，其中 c 是物质的比热容（J kg⁻¹ °C⁻¹ 或 J kg⁻¹ K⁻¹）。此过程无物态变化。
Eₙ = m l
Heat energy needed to change the state of mass m at constant temperature. l is the specific latent heat (fusion or vaporisation). For melting l is latent heat of fusion; for boiling it is latent heat of vaporisation.
在温度不变时改变质量 m 的物态所需热量 Eₙ = m l， l 为比潜热（熔化潜热或汽化潜热）。熔化时用熔化潜热，沸腾时用汽化潜热。
7. Pressure & Density | 压强与密度
p = F / A
s the force F acting per unit area A. The SI unit is the pascal (Pa), where 1 Pa = 1 N/m².
压强 p 定义为作用在单位面积 A 上的力 F。国际单位是帕斯卡 (Pa)，1 Pa = 1 N/m²。
p = ρ g h
Pressure at a depth h in a fluid of density ρ in a gravitational field g. This pressure is additional to atmospheric pressure.
在密度为 ρ 的液体中，深度 h 处的压强为 p = ρ g h，是物体所受的液体产生的压强（不计大气压）。
ρ = m / V
Density ρ (rho) is mass m per unit volume V. Units are kg/m³ or g/cm³. An object floats if its density is less than the fluid's density.
密度 ρ 是单位体积 V 内的质量 m，单位为 kg/m³ 或 g/cm³。物体密度小于液体密度时将上浮。
8. Nuclear Radiation | 核辐射
A = N / t
decays N per unit time t. The unit is the becquerel (Bq), where 1 Bq = 1 decay per second.
放射源的活度 A 等于单位时间 t 内的衰变次数 N，单位为贝克勒尔 (Bq)，1 Bq = 1 次衰变/秒。
D = E / m
is the energy E absorbed per unit mass m of tissue. Measured in grays (Gy), 1 Gy = 1 J/kg.
吸收剂量 D 等于每单位质量的组织吸收的能量 E，单位为戈瑞 (Gy)，1 Gy = 1 J/kg。
H = D × wₑ
Equivalent dose H accounts for the biological effect of different radiations. wₑ is the radiation weighting factor (e.g., 1 for beta/gamma, 20 for alpha). H is measured in sieverts (Sv).
当量剂量 H 考虑了不同辐射的生物效应，wₑ 为辐射权重因子（如 β/γ 为 1，α 为 20），单位为希沃特 (Sv)。
Half-life (t½): A = A₀ (½)ⁿ where n = t / t½
After n half-lives, the remaining activity A is the initial activity A₀ multiplied by ½ to the power n. The same expression works for remaining number of undecayed nuclei or mass of a radioisotope.
经过 n 个半衰期后，剩余活度 A = A₀ (½)ⁿ，其中 n = t / t½。该式同样适用于剩余未衰变核素数目或放射性同位素质量。
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