Year 11 Edexcel Physics: Formula and Theorem Quick Reference | Year 11 Edexcel 物理：公式定理速查手册

📚 Year 11 Edexcel Physics: Formula and Theorem Quick Reference | Year 11 Edexcel 物理：公式定理速查手册

This revision handbook brings together all the essential formulas, definitions, and core theorems you need for the Edexcel Year 11 Physics course. Every concept is explained with clarity, and each equation is presented in a ready‑to‑use format, helping you to build confidence for both written papers and practical applications.

本复习手册汇集了 Edexcel Year 11 物理课程中所有必要的公式、定义和核心定理。每个概念都讲解得很清晰，每条方程都以即查即用的形式呈现，帮助你在笔试和实际应用中建立信心。

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1. Kinematic Equations | 运动学方程

For objects moving with uniform acceleration, the relationships between displacement, initial velocity, final velocity, acceleration, and time are given by the SUVAT equations.

对于匀加速运动的物体，位移、初速度、末速度、加速度和时间之间的关系由 SUVAT 方程组给出。

The first equation links final velocity (v), initial velocity (u), acceleration (a), and time (t):

第一个方程将末速度 (v)、初速度 (u)、加速度 (a) 和时间 (t) 联系起来：

v = u + a t

This shows that the final velocity equals the initial velocity plus the product of acceleration and time.

这表明末速度等于初速度加上加速度与时间的乘积。

The second equation gives displacement (s) in terms of initial velocity, time, and acceleration:

第二个方程用初速度、时间和加速度来表示位移 (s)：

s = u t + ½ a t²

It tells us that displacement is the sum of the distance travelled at constant initial velocity and the extra distance due to acceleration.

它告诉我们，位移等于以恒定初速度运动的距离与因加速度产生的额外距离之和。

Sometimes it is useful to eliminate time. The third equation does this:

有时消去时间会很方便。第三个方程做到了这一点：

v² = u² + 2 a s

This is particularly helpful when you know the initial and final speeds and the acceleration, but not the time taken.

当你知道初速度和末速度以及加速度，但不知道所用时间时，这个方程特别有用。

In free‑fall problems near the Earth’s surface, the acceleration a is replaced by the acceleration due to gravity, g ≈ 9.8 m/s², and the direction of motion must be taken into account.

在地表附近的自由落体问题中，加速度 a 用重力加速度 g ≈ 9.8 m/s² 代替，并且必须考虑运动方向。

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2. Forces and Newton’s Laws | 力与牛顿定律

Newton’s First Law states that an object remains at rest or in uniform motion in a straight line unless acted upon by a resultant force. This property is called inertia.

牛顿第一定律指出，物体将保持静止或匀速直线运动状态，除非受到合外力的作用。这种性质称为惯性。

Newton’s Second Law quantifies the relationship between force, mass, and acceleration:

牛顿第二定律量化了力、质量与加速度之间的关系：

F = m a

The resultant force F (in newtons) equals the product of mass m (in kilograms) and acceleration a (in m/s²). This is a vector equation: the acceleration is in the same direction as the resultant force.

合外力 F（牛顿）等于质量 m（千克）乘以加速度 a（米每二次方秒）。这是一个矢量方程：加速度的方向与合外力的方向相同。

Newton’s Third Law tells us that for every action force there is an equal and opposite reaction force. These forces act on different objects and therefore do not cancel in a free‑body diagram for a single object.

牛顿第三定律告诉我们，每一个作用力都有一个大小相等、方向相反的反作用力。这些力作用在不同的物体上，因此在单个物体的受力图中不会相互抵消。

Weight is the gravitational force on an object and is given by:

重量是作用在物体上的重力，计算公式为：

W = m g

where g is the gravitational field strength (approximately 9.8 N/kg on Earth).

其中 g 是重力场强（地球上约为 9.8 N/kg）。

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3. Momentum | 动量

Momentum is a measure of the quantity of motion of a moving body, defined as the product of mass and velocity:

动量是物体运动量的量度，定义为质量与速度的乘积：

p = m v

Momentum is a vector quantity with the same direction as velocity. Its unit is kg m/s.

动量是一个矢量，方向与速度相同。其单位是 kg m/s。

In a closed system (no external forces), the total momentum before an interaction equals the total momentum after the interaction. This is the principle of conservation of momentum:

在封闭系统（无外力）中，相互作用前的总动量等于相互作用后的总动量。这就是动量守恒定律：

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

Here, u represents initial velocities and v final velocities for two objects with masses m₁ and m₂.

这里，u 代表初速度，v 代表末速度，两个物体的质量分别为 m₁ 和 m₂。

Force is equal to the rate of change of momentum:

力等于动量的变化率：

F = Δp / Δt

This leads directly to the concept of impulse: impulse = F Δt = Δp, which is the change in momentum.

这直接引出了冲量的概念：冲量 = F Δt = Δp，即动量的变化量。

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4. Energy, Work and Power | 能量、功与功率

Work done by a force is the energy transferred when a force moves an object through a distance:

力做的功是力使物体移动一段距离时所传递的能量：

W = F d

provided the force is parallel to the displacement. Work is measured in joules (J).

条件是力与位移方向平行。功的单位是焦耳 (J)。

Gravitational potential energy gained or lost by an object is:

物体获得或失去的重力势能为：

ΔEₚ = m g Δh

Kinetic energy of a moving object is:

运动物体的动能为：

Eₖ = ½ m v²

The principle of conservation of energy states that energy can be transferred usefully, stored, or dissipated, but it cannot be created or destroyed. In many mechanics problems, we assume no energy is lost, so we can equate initial and final total energies.

能量守恒定律指出，能量可以被有效转移、储存或耗散，但不会凭空产生或消失。在许多力学问题中，我们假设没有能量损失，因此可以令初始总能量等于最终总能量。

Power is the rate at which work is done or energy is transferred:

功率是做功或能量转移的速率：

P = W / t

Power can also be expressed for a constant force moving at constant speed: P = F v.

对于以恒定速度运动的恒定力，功率也可以表示为：P = F v。

Efficiency is the ratio of useful output energy (or power) to total input energy (or power), often expressed as a percentage:

效率是有用输出能量（或功率）与总输入能量（或功率）之比，通常以百分比表示：

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

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5. Pressure and Density | 压强与密度

Density is mass per unit volume:

密度是单位体积的质量：

ρ = m / V

The SI unit of density is kg/m³, although g/cm³ is also common.

密度的 SI 单位是 kg/m³，不过 g/cm³ 也很常用。

Pressure is defined as force per unit area:

压强定义为单位面积上的力：

p = F / A

where p is in pascals (Pa), F in newtons, and A in square metres.

其中 p 的单位是帕斯卡 (Pa)，F 是牛顿，A 是平方米。

In a column of liquid, pressure increases with depth due to the weight of the liquid above:

在液柱中，由于上方液体的重量，压强随深度的增加而增加：

p = ρ g h

Here h is the depth below the surface and ρ is the liquid’s density. This equation applies only to static fluids of constant density.

这里 h 是液面下的深度，ρ 是液体密度。该方程仅适用于密度恒定的静止流体。

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6. Wave Properties | 波的性质

For all waves, the speed, frequency, and wavelength are related by:

对于所有波，波速、频率和波长之间的关系为：

v = f λ

where v is wave speed (m/s), f is frequency (Hz), and λ is wavelength (m). This is the wave equation and it applies to both mechanical and electromagnetic waves.

其中 v 是波速 (m/s)，f 是频率 (Hz)，λ 是波长 (m)。这就是波动方程，适用于机械波和电磁波。

The period T of a wave is the time taken for one complete oscillation and is the reciprocal of frequency:

波的周期 T 是完成一次完整振动所需的时间，是频率的倒数：

T = 1 / f

Reflection, refraction, and diffraction are key wave behaviours. Reflection obeys the law: angle of incidence = angle of reflection, measured from the normal. Refraction occurs when waves change speed at a boundary, causing a change in direction unless the wave strikes at normal incidence.

反射、折射和衍射是波的关键行为。反射遵循定律：入射角等于反射角，从法线量起。当波在界面处改变速度时会发生折射，除非波垂直入射，否则方向会改变。

Sound waves are longitudinal and require a medium. Their speed in air is approximately 340 m/s at room temperature.

声波是纵波，需要介质。在室温下，声波在空气中的速度约为 340 m/s。

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7. Electromagnetic Spectrum | 电磁波谱

All electromagnetic waves travel at the speed of light in a vacuum, c = 3.0 × 10⁸ m/s. The wave equation v = f λ still holds, so higher frequency corresponds to shorter wavelength.

所有电磁波在真空中均以光速 c = 3.0 × 10⁸ m/s 传播。波动方程 v = f λ 仍然成立，因此频率越高，波长越短。

The main regions, in order of decreasing wavelength (increasing frequency), are: radio waves, microwaves, infrared, visible light, ultraviolet, X‑rays, gamma rays. Each region has distinct properties and uses.

主要波段按波长递减（频率递增）顺序为：无线电波、微波、红外线、可见光、紫外线、X 射线、伽马射线。每个区域都有独特的性质和用途。

When electromagnetic waves are emitted or absorbed by atoms, changes in electron energy levels are involved. In gamma emission, changes occur in the nucleus.

当原子发射或吸收电磁波时，涉及电子能级的变化。伽马射线的发射则发生在原子核内。

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8. Electricity Basics | 电学基础

Electric current is the rate of flow of electric charge:

电流是电荷流动的速率：

I = ΔQ / Δt

Current I is measured in amperes (A), charge Q in coulombs (C), and time t in seconds. Conventional current flows from positive to negative.

电流 I 的单位是安培 (A)，电荷 Q 的单位是库仑 (C)，时间 t 的单位是秒。常规电流从正极流向负极。

Potential difference (voltage) is the energy transferred per unit charge:

电势差（电压）是单位电荷转移的能量：

V = W / Q

where V is in volts (V), W is energy in joules (J), and Q is charge in coulombs.

其中 V 的单位是伏特 (V)，W 是能量单位焦耳 (J)，Q 是电荷单位库仑。

Resistance is a measure of how much a component opposes the flow of charge. Ohm’s law states that for a metallic conductor at constant temperature, the current is proportional to the potential difference:

电阻是衡量元件对电荷流动阻碍程度的量。欧姆定律指出，对于恒定温度下的金属导体，电流与电势差成正比：

V = I R

Resistance R is measured in ohms (Ω).

电阻 R 的单位是欧姆 (Ω)。

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9. Resistance and Ohm’s Law | 电阻与欧姆定律

The resistance of a wire depends on its length, cross‑sectional area, and the material’s resistivity, but for Edexcel Year 11 you are not required to know the resistivity formula. Instead, you should know that resistance increases with length and decreases with cross‑sectional area.

导线的电阻取决于其长度、横截面积以及材料的电阻率，不过 Edexcel Year 11 不要求掌握电阻率公式。相反，你应知道电阻随长度增加而增大，随横截面积增大而减小。

In series circuits, the total resistance is the sum of individual resistances:

在串联电路中，总电阻等于各电阻之和：

R_total = R₁ + R₂ + …

In parallel circuits, the total resistance is given by:

在并联电路中，总电阻由下式给出：

1/R_total = 1/R₁ + 1/R₂ + …

Knowing how to combine resistances helps you analyse circuit behaviour and calculate currents and voltages using Ohm’s law and the conservation of charge (current) and energy (voltage).

掌握电阻的组合方式有助于分析电路行为，并利用欧姆定律以及电荷（电流）和能量（电压）守恒来计算电流和电压。

Components such as filament lamps and diodes have non‑linear I‑V characteristics. A filament lamp’s resistance increases as the current increases because the metal filament gets hotter. A diode allows current in only one direction.

白炽灯和二极管等元件具有非线性 I‑V 特性。白炽灯的电阻随电流增大而增加，因为金属灯丝变得更热。二极管只允许单向电流通过。

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10. Transformers and Electromagnetic Induction | 变压器与电磁感应

Electromagnetic induction occurs when there is a change in the magnetic field linked with a circuit. This can be caused by moving a magnet relative to a coil or by changing the current in a nearby coil. The induced potential difference depends on the rate of change of the magnetic field.

当与电路链接的磁场发生变化时，就会发生电磁感应。这可以通过相对线圈移动磁铁或改变附近线圈中的电流来实现。感应电动势的大小取决于磁场变化的速率。

Transformers use induction to change the size of an alternating voltage. For an ideal transformer (100% efficient), the relationship between voltages and the number of turns on the primary and secondary coils is:

变压器利用感应来改变交流电压的大小。对于理想变压器（效率 100%），电压与初级和次级线圈匝数之间的关系为：

Vₚ / Vₛ = Nₚ / Nₛ

Also, for an ideal transformer, the primary and secondary currents are related by:

同样，对于理想变压器，初级和次级电流的关系为：

Iₚ Nₚ = Iₛ Nₛ

This means that a step‑up transformer (more secondary turns) increases voltage but decreases current, while a step‑down transformer does the opposite.

这意味着升压变压器（次级匝数更多）升高电压但降低电流，而降压变压器则相反。

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11. Atomic Physics and Radioactive Decay | 原子物理与放射性衰变

The nuclear model of the atom describes a small, dense, positively charged nucleus surrounded by electrons in energy levels. The number of protons (atomic number) defines the element; the total number of protons and neutrons is the mass number.

原子的核式模型描述了一个体积小、密度大、带正电的原子核，周围有处于不同能级的电子。质子数（原子序数）决定了元素种类；质子与中子的总和为质量数。

Radioactive decay is a random process in which an unstable nucleus emits radiation. Three main types of radiation are alpha (α) particles, beta (β) particles, and gamma (γ) rays. Their properties are summarised in the table below.

放射性衰变是一种随机过程，不稳定的原子核会发出辐射。三种主要辐射类型是 α 粒子、β 粒子和 γ 射线。它们的性质总结在下表中。

Property	Alpha (α)	Beta (β⁻)	Gamma (γ)
Nature	Helium nucleus (2p+2n)	Fast electron	Electromagnetic wave
Penetration	Few cm in air; stopped by paper	Few mm Al; stopped by aluminium foil	Several cm of lead; reduced by thick lead
Ionising power	High	Medium	Low

The activity of a radioactive source is the number of decays per second and is measured in becquerels (Bq). The half‑life is the time taken for the activity (or number of radioactive nuclei) to halve. It is a constant for a given isotope.

放射源的活度是每秒衰变次数，单位为贝克勒尔 (Bq)。半衰期是活度（或放射性核数目）减半所需的时间。对于给定的同位素，这是一个常数。

Nuclear equations can be written to show the changes in atomic number and mass number during alpha or beta decay. For example, alpha decay of uranium‑238: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Beta decay of carbon‑14: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e + anti‑neutrino.

可以写出核方程来表示 α 或 β 衰变过程中原子序数和质量数的变化。例如，铀‑238 的 α 衰变：²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He。碳‑14 的 β 衰变：¹⁴₆C → ¹⁴₇N + ⁰₋₁e + 反中微子。

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