题型概述：能量、转动与引力Question types: energy, rotation & gravitation
SPC 常把熟悉的力学规律放进日常或天文情境：Part I 要快速识别数量级、分量和守恒量，Part II 要把几何约束与物理规律联立。本组含 3 道选择题和 2 道书面题；常见失分点是漏掉平方、混淆角度基准，以及把不同到达时刻当成同一时刻。SPC uses everyday and astronomical settings for familiar mechanics: Part I rewards rapid recognition of scales, components and conservation laws; Part II combines geometry with physics. This set contains three multiple-choice and two written questions. Common errors include missing squares, measuring angles from the wrong line and confusing separate arrival times with the same instant.
1用能量比较状态Compare states with energy
只受重力时，始末高度与初速决定末速。先选势能零点，再统一单位；eV 是能量单位，不是只适用于粒子的公式。Under gravity alone, endpoint heights and initial speed determine final speed. Choose a potential-energy zero and use consistent units; eV is an energy unit, not a particle-only formula.
½mu² + mgh = ½mv²; 1 eV = 1.602176634 × 10⁻¹⁹ J方向写在速度中，动能只取速率平方。Velocity carries direction; kinetic energy uses speed squared.
2力矩与轨道几何Moments and orbital geometry
先找支点和垂直力臂，再列力矩平衡。轨道题则先画观测点、太阳与轨道；最大离角由切线条件确定。Identify the pivot and perpendicular lever arm before balancing moments. For orbital geometry locate observer, Sun and orbit; maximum elongation follows from tangency.
τ = Fd⊥; sin εmax = rinner/robserver角度相对哪条线测量，是这两类题的共同关键。In both types, identify the line from which the angle is measured.
3连续性与重力加速Continuity and gravitational acceleration
稳定的不可压缩水流每秒通过各截面的体积相同。流速变快时面积变小；再用重力加速关系确定绝对速率。In steady incompressible flow the same volume passes every section each second. Faster flow requires smaller area; gravitational acceleration then fixes the actual speed.
A₁v₁ = A₂v₂; A = πd²/4; v₂² − v₁² = 2gH直径、面积和速率之间的平方关系要逐层保留。Keep the square relationships between diameter, area and speed.
小练习：速率加倍，动能如何变化？Quick experiment: double the speed
| 子题型Subtype | 识别特征Recognise | 核心步骤Core step | 真题Question |
|---|---|---|---|
| 动能数量级Kinetic-energy scale | 宏观能量用 eV 表示Macroscopic energy in eV | SI 单位 → ½mv² → eVSI units → ½mv² → eV | 2022 I-3 |
| 力矩平衡Moment balance | 铰链、均匀杆、斜向拉力Hinge, uniform rod, oblique force | 选支点 → 垂直分力Pivot → perpendicular component | 2020 I-5 |
| 重力与能量Gravitational energy | 同速反向抛出Equal-speed opposite throws | 比较始末状态Compare initial and final states | 2023 I-4 |
| 轨道几何Orbital geometry | 内行星、最大角距Inner planet, greatest separation | 切线 → 反正弦 → 时间Tangent → inverse sine → time | 2016 II-8 |
| 水流连续性Flow continuity | 下落、缩径、装满时间Falling, narrowing, filling | d²v 不变 → v² 关系Constant d²v → v² relation | 2025 II-13 |