题型概述：Physics Bowl 力学Question types: Physics Bowl mechanics
Top在我们整理的 15 套真题（2010–2025）里，743 道题中有 324 道属于力学（运动学、力与运动、圆周运动、动量与能量、转动、引力、流体），约占 44%，是分量最重的一块。每题 1 分、约 67 秒，不倒扣分，所以关键是快速认出题型，再用最短的路径排除干扰项。本模块选 5 道 2024–2025 年的高频题型。Across the 15 papers in our bank (2010–2025), 324 of 743 questions are mechanics (kinematics, force and motion, circular motion, momentum and energy, rotation, gravitation, fluids): about 44%, the largest block by far. Every question is worth 1 point and gets about 67 seconds, with no penalty for a wrong answer, so the skill is to recognise the type fast and take the shortest route through the distractors. This module works five high-frequency types from 2024–2025.
1考场约定：g = 10.0 m/s²Contest convention: g = 10.0 m/s²
2013、2024、2025 年的试卷封面都写明"所有题目取 g = 10.0 m/s²"。选项是按 g = 10 算出来的；用 9.8 算偶尔会落在两个选项之间。计算器可以用，但只能用试卷提供的公式和常数。The 2013, 2024 and 2025 papers all say "treat g = 10.0 m/s² for all questions". The options are computed with g = 10; using 9.8 can occasionally land you between two options. A calculator is allowed, but only the formulas and constants printed with the contest may be used.
2运动学：斜率与面积Kinematics: slopes and areas
x–t 图的斜率是速度；v–t 图的斜率是加速度、面积是位移（t 轴下方的面积为负）。路程把所有面积都按正的加起来，位移要带符号。平抛/斜抛：水平和竖直方向独立，竖直方向只由 g 决定。The slope of an x–t graph is velocity; on a v–t graph the slope is acceleration and the area is displacement (area below the t-axis counts negative). Distance adds every area as positive, displacement keeps the sign. Projectiles: horizontal and vertical motions are independent, and the vertical one depends on g alone.
平均速率 = 路程 / 时间 平均速度 = 位移 / 时间average speed = distance / time average velocity = displacement / time3力、摩擦与圆周运动Forces, friction and circular motion
圆周运动不是一种新的力，而是对合力的要求：指向圆心的合力必须等于 mv²/r。在水平弯道上这个力只能由静摩擦提供，最大为 μsmg，于是 vmax = √(μsgr)，与质量无关。牛顿第三定律的一对力总是等大反向，所以"轮胎对路面的力大于路面对轮胎的力"这类说法一律是错的。Circular motion is not a new force but a requirement on the net force: the inward net force must equal mv²/r. On a flat curve only static friction can supply it, at most μsmg, so vmax = √(μsgr), independent of mass. Newton's third-law pairs are always equal and opposite, so any option saying "the tyres push on the road harder than the road pushes on the tyres" is wrong.
4动量、能量与滚动Momentum, energy and rolling
碰撞、弹开、爆炸：系统动量守恒总是成立（无外力时）；动能守恒只在弹性碰撞时成立，弹簧释放能量时动能会增加。滚动不打滑的物体把一部分势能分给转动：mgh = ½mv²(1 + k)，其中 k = I/(mR²)。Collisions, spring pushes and explosions: total momentum is conserved whenever there is no external force; kinetic energy is conserved only in an elastic collision, and a released spring adds kinetic energy. An object rolling without slipping shares its potential energy with rotation: mgh = ½mv²(1 + k), where k = I/(mR²).
| 物体Object | k = I/(mR²) | 底端速度Speed at the bottom |
|---|---|---|
| 无摩擦滑块Frictionless sliding block | 0 | √(2gh) |
| 实心球Solid sphere | 2/5 | √(10gh/7) |
| 实心圆盘 / 圆柱Solid disk / cylinder | 1/2 | √(4gh/3) |
| 圆环 / 薄壁圆筒Hoop / thin ring | 1 | √(gh) |
5本模块的 5 道题The five questions in this module
| 题型Type | 识别特征How to spot it | 核心一步Core step | 真题Paper |
|---|---|---|---|
| 平抛相遇Projectiles meeting | 两物同时同高水平抛出Two objects launched level at the same time and height | 竖直运动相同 ⇒ 永远同高Same vertical motion ⇒ always level | 2025 Q2 |
| v–t 图v–t graph | 问平均速率 / 平均速度Asks average speed or average velocity | 面积：路程取绝对值，位移带符号Areas: distance unsigned, displacement signed | 2024 Q1–2 |
| 弯道打滑Skidding on a curve | 半径、速度、μsRadius, speed and μs given | vmax = √(μgr) | 2025 Q20 |
| 弹簧碰撞Spring-loaded collision | "碰后 A 静止""after the collision A is at rest" | 先动量，再能量Momentum first, then energy | 2025 Q29 |
| 斜面滚动Rolling down a slope | "rolls without slipping""rolls without slipping" | mgh = ½mv²(1 + k) | 2025 Q11 |