📚 Pre-U CCEA Physics: High-Frequency Topics and Common Pitfalls | Pre-U CCEA 物理：高频考点与易错题分析
This article examines recurring themes in the CCEA Pre-U Physics examinations and highlights errors that even well-prepared candidates often make. By understanding where pitfalls lie, you can refine your problem-solving technique and boost your confidence.
本文将分析 CCEA Pre-U 物理考试中的高频考点，并指出即使是准备充分的考生也常犯的错误。了解这些易错点，有助于优化解题技巧，提升考试信心。
1. Kinematics and Projectile Motion | 运动学与抛体运动
Always define a positive direction before writing any kinematic equation. A very common mistake is to assign signs inconsistently, particularly when the acceleration due to gravity changes direction relative to the chosen coordinate axes. For upward launch, g should be negative if ‘up’ is taken as positive.
在书写运动学方程前，务必规定正方向。最常见的错误是符号不一致，尤其是重力加速度的方向相对于所选坐标轴改变时。若向上为正，抛体运动中 g 应取负值。
The time of flight in projectile motion is determined solely by the vertical component of motion, not the horizontal. Students often erroneously use horizontal displacement to find time, forgetting that the vertical motion governs how long the object stays in the air.
抛体运动的飞行时间仅由竖直分运动决定，而非水平分量。学生常错误地用水平位移求时间，却忘了竖直运动才决定物体在空中的时长。
Decompose the initial velocity correctly: vₓ = u cos θ, v_y = u sin θ. Treat horizontal and vertical motions independently; they share only the same time variable. Avoid mixing component equations prematurely.
正确分解初速度：vₓ = u cos θ, v_y = u sin θ。水平和竖直运动要独立处理，两者仅时间相同。切勿过早混用不同分量的方程。
The formula for maximum height H = u² sin² θ / (2g) applies only when launch and landing heights are identical. If the projectile lands at a different level, this shortcut fails and the full quadratic equation for displacement must be used.
最大高度公式 H = u² sin² θ / (2g) 仅适用于发射与落点等高的情况。若抛体落点高度不同，此公式失效，必须使用位移的完整二次方程。
2. Circular Motion and Gravitation | 圆周运动与万有引力
Centripetal force is the net force directed toward the centre, not a separate force. When drawing free-body diagrams, never label a ‘centripetal force’ arrow alongside tension, weight, or normal reaction. It results from existing forces.
向心力是指向圆心的合力，并非额外的力。画受力分析图时，绝不可在张力、重力、支持力之外单独标出“向心力”箭头。它是已有力的合力。
Convert revolution frequency to angular velocity correctly: ω = (rpm × 2π) / 60. Many errors arise from omitting the factor 2π or using degrees instead of radians. Remember that one revolution equals 2π radians.
正确将转速转换为角速度：ω = (每分钟转数 × 2π) / 60。许多错误源于遗漏 2π 因子或使用角度制。牢记一圈等于 2π 弧度。
For satellites, orbital radius r = Rₑ + h, where Rₑ is the Earth’s radius and h is altitude above the surface. Using only height h in F = GMm / r² yields a smaller radius and an incorrect gravitational force.
对于卫星，轨道半径 r = 地球半径 + 高度。万有引力公式 F = GMm / r² 中若只代入高度 h，会使半径偏小，导致引力计算错误。
Kepler’s third law T² ∝ r³ is valid only for objects orbiting the same central body. When comparing moons of different planets, the constant of proportionality differs, so direct ratio taking can be misleading.
开普勒第三定律 T² ∝ r³ 仅适用于绕同一中心天体的运动。比较不同行星的卫星时，比例常数不同，直接套用比值会出错。
3. Simple Harmonic Motion | 简谐运动
Before using SHM equations, always verify that the restoring force obeys F ∝ −x. A system can be oscillatory without being simple harmonic if the force is not linearly proportional to displacement. Identifying this condition is a key skill.
使用简谐运动公式前，务必验证回复力服从 F ∝ −x。若力与位移不成正比，系统虽能振动，但不是简谐运动。识别这一条件是核心能力。
When expressing displacement as x = A cos(ωt + φ), the phase constant φ depends on the initial conditions. A typical error is choosing t=0 at equilibrium and writing x = A cos ωt, when the correct form is x = A sin ωt.
位移表达式 x = A cos(ωt + φ) 中，相位常数 φ 取决于初始条件。常见错误是在平衡位置选 t=0 却写成 x = A cos ωt，而正确形式应为 x = A sin ωt。
In a mass–spring system, total energy = ½kA². The potential energy at displacement x is ½kx², measured from equilibrium, not from the unstretched length of the spring. Confusing these references leads to wrong energy calculations.
弹簧振子中，总能量 = ½kA²。位移 x 处的势能为 ½kx²，该位移从平衡位置量起，而非从弹簧原长量起。混淆参考点会导致能量计算错误。
The projection of uniform circular motion on a diameter yields SHM, but the angular speed ω in that analogy is constant. Do not confuse this constant ω with a varying angular velocity of a pendulum bob.
匀速圆周运动在直径上的投影是简谐运动，但该类比中的角速度 ω 是常数。不要将此常数 ω 与摆锤变化的角速度混淆。
4. Electric Fields and Potentials | 电场与电势
Electric field strength E is a vector, whereas electric potential V is a scalar. Consequently, when multiple charges are present, potentials add algebraically, but fields must be added vectorially. Mixing these addition rules is a classic error.
电场强度 E 是矢量，电势 V 是标量。因此，多个电荷存在时，电势取代数和，电场则必须进行矢量相加。混淆这两种加法规则是典型错误。
In uniform fields, E = V / d. Ensure the plate separation d is in metres. Substituting centimetres gives a field strength 100 times too weak or too strong, depending on the conversion slip.
匀强电场中 E = V / d。务必确保板间距 d 以米为单位。代入厘米值会使电场强度差 100 倍，极易失分。
For point charges, E = kQ / r² and V = kQ / r. The potential can be positive or negative depending on the sign of Q. Taking absolute values ignores the sign and makes superposition incorrect.
点电荷的电场 E = kQ / r²，电势 V = kQ / r。电势的正负取决于 Q 的正负。取绝对值会忽略符号，导致叠加结果错误。
In electron deflection tubes, horizontal motion remains uniform while vertical motion is uniformly accelerated. The resulting path is a parabola—not an arc of a circle, as some students assume when confusing electric force with centripetal force.
在电子偏转管中，水平运动为匀速，竖直运动为匀加速。其轨迹是抛物线，而非某些学生误认为的圆弧，因为他们混淆了电场力与向心力。
5. Capacitors and RC Circuits | 电容器与 RC 电路
Q = CV gives the charge stored on one plate. In RC circuit analysis, the discharging current flows in the opposite direction to the charging current. Failing to indicate these correctly in diagrams or sign conventions loses marks.
Q = CV 表示单块极板的电荷量。分析 RC 电路时，放电电流与充电电流方向相反。在示意图或符号规则中未正确标明这一点会失分。
The time constant τ =
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