📚 Year 9 SQA Physics Formula & Theorem Quick Reference Handbook | SQA九年级物理公式定理速查手册
This handbook brings together all the key formulas and theorems you will encounter in Year 9 SQA Physics. Use it for quick revision, homework checks and exam preparation. Each entry gives the equation, explains the symbols and units, and highlights the underlying concept in clear, bilingual notes.
本手册汇总了SQA九年级物理中你将遇到的所有核心公式和定理。可用于快速复习、作业对照和考试准备。每个条目给出方程式，解释符号与单位，并以清晰的双语说明突出基本概念。
1. Speed and Velocity | 速率与速度
Speed is the distance travelled per unit of time. For an object moving at constant speed, the formula is:
v = d / t
where v is the speed (m/s), d is the distance travelled (m) and t is the time taken (s). Velocity is a vector quantity – it is speed in a given direction. When an object moves in a straight line at constant velocity, the same formula applies, but you must assign a positive or negative direction.
速率是单位时间内移动的距离。对于匀速运动的物体，公式为：
v = d / t
其中 v 是速率（米/秒），d 是移动的距离（米），t 是所用时间（秒）。速度是矢量，即带有方向的速率。当物体沿直线匀速运动时，同一公式也适用，但需要规定正负方向。
To convert from metres per second (m/s) to kilometres per hour (km/h), multiply by 3.6.
从米/秒 (m/s) 转换为千米/小时 (km/h)，需乘以 3.6。
2. Acceleration | 加速度
Acceleration is the rate of change of velocity. When acceleration is uniform, it is given by:
a = (v – u) / t
where a is the acceleration (m/s²), v is the final velocity (m/s), u is the initial velocity (m/s), and t is the time taken (s). Since velocity is a vector, acceleration also has direction. Deceleration (negative acceleration) occurs when an object slows down.
加速度是速度的变化率。当加速度恒定时，公式为：
a = (v – u) / t
其中 a 是加速度（米/秒²），v 是末速度（米/秒），u 是初速度（米/秒），t 是所用时间（秒）。因为速度是矢量，加速度也有方向。物体减速时加速度为负值，称为减速度。
0. If an object moves on a straight track and its speed increases by 5 m/s every second, its acceleration is 5 m/s².
从静止开始运动的物体 u = 0。若物体在直轨道上运动，速度每秒增加 5 m/s，则加速度为 5 m/s²。
3. Newton’s Laws of Motion | 牛顿运动定律
First Law (Inertia): An object remains at rest or moves with constant velocity unless acted upon by an unbalanced force.
第一定律（惯性）： 除非受到不平衡力的作用，物体将保持静止或匀速直线运动状态。
Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
F = m a
where F is the resultant force (N), m is the mass (kg), and a is the acceleration (m/s²). This is the most important equation of motion.
第二定律： 物体的加速度与作用在其上的合外力成正比，与物体的质量成反比。
F = m a
其中 F 是合力（牛顿），m 是质量（千克），a 是加速度（米/秒²）。这是最重要的运动方程。
Third Law: For every action there is an equal and opposite reaction. Forces always come in pairs acting on two different bodies.
第三定律： 每一个作用力都有一个大小相等、方向相反的反作用力。力总是成对出现，作用在两个不同的物体上。
4. Weight and Mass | 重量与质量
Weight is the force of gravity acting on a mass. It is calculated by:
W = m g
ss is the amount of matter and does not change; weight depends on the gravitational field.
重量是作用在物体上的重力。计算公式为：
W = m g
其中 W 是重量（牛顿），m 是质量（千克），g 是引力场强度（牛/千克）。地球表面 g约为 9.8 N/kg。质量是物体所含物质的多少，不随位置改变；重量则取决于引力场。
pproximately 5 × 9.8 = 49 N on Earth, but only about 8 N on the Moon (where g ≈ 1.6 N/kg).
一个质量为 5 kg 的物体在地球上的重量约为 5 × 9.8 = 49 N，但在月球上仅有约 8 N（月球 g 约 1.6 N/kg）。
5. Work, Energy and Power | 功、能与功率
Work done is the energy transferred when a force moves an object. When the force and displacement are in the same direction:
W = F d
where W is work done (J), F is the constant force (N), and d is the distance moved in the direction of the force (m).
功是力使物体移动时所传递的能量。当力与位移方向相同时：
W = F d
其中 W 是功（焦耳），F 是恒定的力（牛顿），d 是沿力方向移动的距离（米）。
Gravitational potential energy gained or lost when an object changes height:
ΔEp = m g Δh
where ΔEp is the change in gravitational potential energy (J), m is mass (kg), g is gravitational field strength (N/kg), and Δh is the change in height (m).
重力势能的变化与高度变化有关：
ΔEp = m g Δh
其中 ΔEp 是重力势能的变化（焦），m 是质量（kg），g 是引力场强度（N/kg），Δh 是高度变化（米）。
Power is the rate at which energy is transferred or work is done:
P = E / t or P = W / t
where P is power (W, watts), E is energy transferred (J), W is work done (J), and t is time (s). 1 watt equals 1 joule per second.
功率是能量传递或做功的速率：
P = E / t 或 P = W / t
其中 P 是功率（瓦特），E 是传递的能量（焦），W 是做功（焦），t 是时间（秒）。1 瓦 = 1 焦/秒。
6. Density and Pressure | 密度与压力
Density is the mass per unit volume of a substance:
ρ = m / V
c metre, but grams per cubic centimetre (g/cm³) is also widely used. 1 g/cm³ = 1000 kg/m³.
密度是物质单位体积的质量：
ρ = m / V
其中 ρ 是密度（千克/米³），m 是质量（kg），V 是体积（m³）。密度的国际单位是千克每立方米，但也广泛使用克每立方厘米 (g/cm³)。1 g/cm³ = 1000 kg/m³。
Pressure is the force acting per unit area when a force is applied over a surface:
P = F / A
the area (m²). 1 Pa = 1 N/m². Large forces applied over small areas produce high pressure.
压力（压强）是作用在单位面积上的力：
P = F / A
其中 P 是压强（帕斯卡），F 是垂直于表面的力（牛顿），A 是面积（米²）。1 Pa = 1 N/m²。大力作用在小面积上会产生高压强。
7. Electric Current and Charge | 电流与电荷
Electric current is the rate of flow of electric charge. It is defined by:
I = Q / t
where I is current (A, ampere), Q is the charge (C, coulomb), and t is time (s). Charge is carried by electrons in a metal conductor. One coulomb is the amount of charge passing a point in a circuit when a current of 1 A flows for 1 s.
电流是电荷流动的速率。定义式为：
I = Q / t
其中 I 是电流（安培），Q 是电荷（库仑），t 是时间（秒）。在金属导体中，电荷由电子携带。1 库仑是 1 A 电流在 1 s 内通过某截面的电荷量。
Voltage (potential difference) measures the energy transferred per unit charge between two points:
V = E / Q or V = W / Q
where V is voltage (V, volt), E or W is energy transferred or work done (J), and Q is charge (C). 1 volt means 1 joule of energy is transferred per coulomb of charge.
电压（电势差）衡量单位电荷在两点间转移的能量：
V = E / Q 或 V = W / Q
其中 V 是电压（伏特），E 或 W 是转移的能量或做的功（焦），Q 是电荷（库仑）。1 伏特表示每库仑电荷转移 1 焦耳的能量。
8. Ohm’s Law and Resistance | 欧姆定律与电阻
Ohm’s Law states that the current through a conductor is directly proportional to the voltage across it, provided the temperature and other physical conditions remain constant:
V = I R
where V is the voltage (V), I is the current (A), and R is the resistance (Ω, ohm). Resistance is a measure of how much a component opposes the flow of current. Resistors that obey Ohm’s Law are called ohmic conductors.
欧姆定律表明，在温度和其它物理条件不变的情况下，通过导体的电流与导体两端的电压成正比：
V = I R
其中 V 是电压（伏），I 是电流（安），R 是电阻（欧姆）。电阻衡量元件对电流阻碍作用的大小。遵从欧姆定律的电阻称为欧姆导体。
The resistance of a component can also be calculated from measured voltage and current:
R = V / I
A typical I–V graph for an ohmic resistor is a straight line passing through the origin.
也可以通过测量的电压和电流计算电阻：
R = V / I
欧姆电阻的 I–V 图是一条通过原点的直线。
9. Series and Parallel Circuits | 串联与并联电路
Understanding how current, voltage and resistance behave in different circuit arrangements is essential. For series circuits:
了解电流、电压和电阻在不同电路连接方式中的行为至关重要。串联电路中：
The current is the same at all points: Itotal = I₁ = I₂ = I₃
各处电流相等：I总 = I₁ = I₂ = I₃
The total voltage is the sum of the p.d.s across each component: Vtotal = V₁ + V₂ + V₃
总电压等于各元件两端电压之和：V总 = V₁ + V₂ + V₃
The total resistance is the sum of individual resistances:
Rtotal = R₁ + R₂ + R₃
总电阻等于各电阻之和。
For parallel circuits:
并联电路中：
The current from the source splits at junctions: Itotal = I₁ + I₂ + I₃
干路电流在节点处分流：I总 = I₁ + I₂ + I₃
The voltage across each parallel branch is the same: Vtotal = V₁ = V₂ = V₃
各支路两端电压相等：V总 = V₁ = V₂ = V₃
The total resistance is found using:
1 / Rtotal = 1 / R₁ + 1 / R₂ + 1 / R₃
总电阻用倒数求和公式计算。
10. The Wave Equation | 波速公式
All waves (light, sound, water) share a basic relationship linking speed, frequency and wavelength:
v = f λ
sing a point per second; the period T is the time for one complete wave, given by T = 1/f.
所有波（光、声、水波）都遵守一个基本关系，将波速、频率和波长联系起来：
v = f λ
其中 v 是波速（米/秒），f 是频率（赫兹），λ 是波长（米）。频率是每秒通过某点的完整波的数量；周期 T 是完成一次完整振动所需的时间，T = 1/f。
speed is 2 × 0.5 = 1 m/s. This equation works for longitudinal and transverse waves alike.
如果水波的波长为 2 m，频率为 0.5 Hz，则波速为 2 × 0.5 = 1 m/s。该公式对纵波和横波均适用。
11. Hooke’s Law | 胡克定律
For many elastic objects, such as springs, the extension is directly proportional to the applied force, provided the proportional limit is not exceeded:
F = k x
where F is the applied force (N), x is the extension—the increase in length from the original position (m), and k is the spring constant (N/m). A larger spring constant means a stiffer spring that is harder to stretch.
对于许多弹性物体（如弹簧），在比例极限内，伸长量与所施加的力成正比：
F = k x
其中 F 是施加的力（牛顿），x 是伸长量（米），k 是劲度系数（牛/米）。劲度系数越大，弹簧越硬，越难拉伸。
Hooke’s Law can be verified by adding known weights to a spring and measuring the extension. The force-extension graph is a straight line through the origin until the elastic limit is reached.
胡克定律可通过在弹簧上加已知质量的砝码并测量伸长量来验证。力-伸长量图是一条通过原点的直线，直到到达弹性极限为止。
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