📚 Physics Conceptual Clarifications for IB & WJEC | IB与WJEC物理概念辨析
Understanding physics requires distinguishing similar yet fundamentally different concepts. Whether you are preparing for the IB Diploma or WJEC A-level Physics, certain pairs of terms often lead to confusion. This article clarifies key conceptual pitfalls to strengthen your foundation across topics like mechanics, electricity, and modern physics.
理解物理学需要区分相似但在本质上不同的概念。无论你是在准备IB文凭课程还是WJEC A-level物理，总有一些成对的术语容易混淆。本文梳理力学、电学与现代物理中的关键概念误区，帮助你夯实基础。
1. Speed and Velocity | 速率与速度
Speed is a scalar quantity that measures how fast an object moves, defined as the distance travelled per unit time. Velocity, on the other hand, is a vector that specifies both the speed and the direction of motion. In equations, average speed is total distance divided by time, whereas average velocity is total displacement divided by time.
速率是标量，衡量物体运动的快慢，定义为单位时间内通过的路程。速度则是矢量，同时描述运动的快慢和方向。在公式中，平均速率等于总路程除以时间，而平均速度等于总位移除以时间。
For a car completing a circular lap and returning to the start, its average speed is positive, but its average velocity is zero because displacement is zero. This distinction is vital in IB and WJEC questions on motion graphs and uniformly accelerated motion.
对于一辆汽车绕环形跑道一周回到起点，其平均速率为正，但平均速度为零，因为位移为零。这一区别在IB和WJEC关于运动图像与匀加速运动的问题中至关重要。
vₐᵥₑ = Δs/Δt, vₐᵥₑ = Δx/Δt
2. Mass and Weight | 质量与重量
Mass is a measure of the amount of matter in an object and is an intrinsic property that does not depend on location. It is a scalar measured in kilograms. Weight is the gravitational force acting on a mass and is a vector directed towards the centre of the gravitating body, measured in newtons.
质量是物体所含物质的量度，是物体的内禀属性，不随位置改变，为标量，单位是千克。重量是作用在质量上的引力，是矢量，方向指向引力体中心，单位是牛顿。
On Earth, weight W = mg, with g ≈ 9.8 m s⁻². On the Moon, an astronaut’s mass remains unchanged but their weight reduces to about one-sixth. Students often confuse the two, especially when using balances that measure weight but display ‘mass’ under terrestrial conditions.
在地球上，重量 W = mg，g ≈ 9.8 m s⁻²。在月球上，宇航员的质量不变，但重量减小到约六分之一。学生常混淆二者，尤其因为天平测量的是重量，却在地球环境下显示为“质量”。
3. Momentum and Kinetic Energy | 动量与动能
Momentum (p = mv) is a vector quantity describing the ‘quantity of motion’ and is conserved in isolated systems regardless of the type of collision. Kinetic energy (KE = ½mv²) is a scalar representing energy due to motion; it is only conserved in perfectly elastic collisions.
动量 (p = mv) 是矢量，描述“运动的量”，在孤立系统中无论何种碰撞均守恒。动能 (KE = ½mv²) 是标量，表示由于运动而具有的能量；仅在完全弹性碰撞中守恒。
In inelastic collisions, momentum is conserved while kinetic energy is partly converted into heat or deformation. A bullet embedding itself in a target is a classic example where momentum conservation allows calculation of final velocity, but kinetic energy decreases significantly.
在非弹性碰撞中，动量守恒，而动能部分转化为热或形变。子弹嵌入靶块就是一个经典例子，利用动量守恒可计算末速度，但动能明显减小。
4. Work and Energy | 功与能
Work is the process of transferring energy via a force causing displacement. It is calculated as W = Fd cosθ, where θ is the angle between force and displacement. Energy is the capacity to do work and exists in various forms (kinetic, potential, thermal). Work done on an object equals its change in energy.
功是通过力产生位移而转移能量的过程，计算公式为 W = Fd cosθ，其中 θ 是力与位移的夹角。能量是做功的本领，存在多种形式（动能、势能、热能）。对物体做的功等于其能量的变化。
A common confusion arises with the sign of work: when friction opposes motion, work is negative, reducing mechanical energy. If a person holds a heavy box stationary, no work is done on the box in the physics sense, despite the feeling of fatigue — because there is no displacement.
常见的混淆在于功的正负号：当摩擦力与运动方向相反时，功为负，减小机械能。如果一个人静止地托着重箱子，尽管感到疲劳，但从物理意义上对箱子没有做功——因为没有位移。
5. Potential Difference and Electromotive Force | 电势差与电动势
Potential difference (p.d.), or voltage, is the energy transferred per unit charge when charge moves between two points in a circuit. Electromotive force (e.m.f.) is the total energy per unit charge supplied by a source (such as a battery) to drive charge around a complete circuit. Both are measured in volts.
电势差（p.d.，电压）是电荷在电路中两点间移动时每单位电荷转移的能量。电动势（e.m.f.）是电源（如电池）驱动电荷绕完整回路一周时每单位电荷所提供的总能量。两者单位均为伏特。
When no current flows, the terminal p.d. of a battery equals its e.m.f. When current flows, internal resistance causes a lost volt (Ir), so terminal p.d. = ε − Ir. IB and WJEC questions frequently test this distinction by asking students to compare the open-circuit and closed-circuit voltages.
当无电流通过时，电池的端电压等于其电动势。当有电流时，内阻引起失落电压（Ir），因此端电压 = ε − Ir。IB与WJEC试题常通过比较开路和闭路电压来检验这一区别。
6. Magnetic Flux and Magnetic Flux Density | 磁通量与磁通密度
Magnetic flux Φ is a measure of the total magnetic field passing perpendicularly through a given area. It is a scalar with unit weber (Wb). Magnetic flux density B, also called magnetic induction, is a vector describing the strength and direction of the field at a point, measured in tesla (T).
磁通量 Φ 是穿过某一给定面积的垂直磁场总量，为标量，单位韦伯（Wb）。磁通密度 B，也称磁感应强度，是矢量，描述某点磁场的强弱和方向，单位特斯拉（T）。
The relationship is Φ = BA cosθ, where θ is the angle between the field and the area’s normal. Faraday’s law states that the induced e.m.f. equals the rate of change of flux linkage (NΦ). Mixing up B and Φ leads to errors in electromagnetic induction problems.
关系式为 Φ = BA cosθ，其中 θ 是磁场与面积法线间的夹角。法拉第定律指出，感应电动势等于磁链（NΦ）的变化率。混淆 B 与 Φ 会导致电磁感应解题错误。
7. Heat Capacity and Specific Heat Capacity | 热容与比热容
Heat capacity C is the amount of energy needed to raise the temperature of an object by 1 K (or 1 °C), irrespective of mass. Specific heat capacity c is the energy per unit mass per kelvin, a property of the material. Thus, C = mc, and the basic heating equation is Q = mcΔT.
热容 C 是物体温度升高 1 K（或1 °C）所需的能量，与质量无关。比热容 c 是每单位质量每升尔文的能量，是材料属性。因此 C = mc，基本加热方程为 Q = mcΔT。
An aluminium kettle has a certain heat capacity; its specific heat capacity depends only on the aluminium alloy. In calorimetry experiments, students often incorrectly use an object’s heat capacity instead of specific heat capacity when calculating energy exchange with water.
一个铝壶具有一定的热容；其比热容仅取决于铝合金。在量热实验中，学生在计算与水的能量交换时，常错误地使用物体的热容而非比热容。
8. Radioactive Decay Constant and Half-life | 衰变常量与半衰期
The decay constant λ is the probability per unit time that a given nucleus will decay, with unit s⁻¹. Half-life T½ is the average time for half the radioactive nuclei in a sample to decay. They are inversely related by T½ = ln 2 / λ. Activity A = λN depends directly on λ.
衰变常量 λ 是单个原子核在单位时间内衰变的概率，单位为 s⁻¹。半衰期 T½ 是样品中放射性核衰变一半所需的平均时间。两者成反比关系：T½ = ln 2 / λ。活度 A = λN 直接取决于 λ。
A large decay constant means rapid decay and a short half-life, while a small λ corresponds to a long half-life. In IB and WJEC, questions may ask to compute one from the other using ln2 ≈ 0.693. Do not confuse half-life with the time constant τ = 1/λ used in exponential decay.
衰变常量大意味着衰变快、半衰期短，而 λ 小对应半衰期长。在IB和WJEC中，题目可能要求用 ln2 ≈ 0.693 相互换算。勿将半衰期与指数衰减中的时间常数 τ = 1/λ 混淆。
9. Resistance and Resistivity | 电阻与电阻率
Resistance R is a measure of opposition to current for a specific component, depending on its geometry. Resistivity ρ is an intrinsic material property. The link is R = ρL/A, where L is length and A is cross-sectional area. Resistance has units of ohm (Ω); resistivity has Ω·m.
电阻 R 是特定元件对电流阻碍作用的量度，取决于几何形状。电阻率 ρ 是材料的本征属性。两者关系为 R = ρL/A，其中 L 是长度，A 是横截面积。电阻单位是欧姆（Ω），电阻率单位是 Ω·m。
In a wire, doubling the length doubles resistance (if ρ and A constant), while doubling the cross-sectional area halves resistance. Temperature affects ρ, not directly R. Data-analysis questions often ask students to find resistivity from a graph of R versus L.
对于一根导线，长度加倍则电阻加倍（ρ 和 A 一定），而横截面积加倍则电阻减半。温度影响 ρ，而非直接改变 R 的定义。数据分析题常要求学生从 R-L 图中求出电阻率。
10. rms and Peak Values for Alternating Current | 交流有效值与峰值
In AC circuits, current and voltage vary sinusoidally. The peak value I₀ or V₀ is the maximum instantaneous value. The root-mean-square (rms) value is the equivalent DC value that dissipates the same power in a resistor. For sinusoidal signals, Vrms = V₀/√2 and Irms = I₀/√2.
在交流电路中，电流和电压呈正弦变化。峰值 I₀ 或 V₀ 是最大瞬时值。有效值（均方根值）是产生相同电阻热功率的等效直流值。对于正弦信号，Vrms = V₀/√2，Irms = I₀/√2。
Mains electricity in the UK is often quoted as 230 V rms, meaning the peak voltage is about 325 V. When using power equations P = IV or P = I²R with AC, always use rms values to find average power, unless a question asks for instantaneous peak power.
英国市电常标称 230 V 有效值，意味着峰值约为 325 V。在使用交流电功率公式 P = IV 或 P = I²R 时，除非问题要求瞬时峰值功率，否则应使用有效值计算平均功率。
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