📚 Physics Bowl Core Concepts, Essential Formulas, and Past Paper Compilation | 物理碗竞赛核心知识点、必背公式与真题整理
The Physics Bowl is a challenging 40-question, 45-minute contest that tests a vast range of high school physics topics, from mechanics to modern physics. Success demands not only a deep conceptual understanding but also rapid recall of key formulas and the ability to apply them under time pressure. This guide compiles the must-know concepts, essential equations, and a selection of authentic past-paper problems with clear solutions to help you prepare effectively.
物理碗竞赛是一项极具挑战性的赛事，需在45分钟内完成40道选择题，覆盖从力学到近代物理的宽广知识面。要想脱颖而出，不仅需要深刻理解概念，还要能快速调用核心公式并灵活运用。本文梳理了必考知识点、必背公式，并精选真题附上详细解析，助你高效备考。
1. Kinematics and Dynamics | 运动学与动力学
Kinematics describes motion without considering its causes. The four constant-acceleration equations link displacement (Δx), initial velocity (v₀), final velocity (v), acceleration (a), and time (t). They are the go‑to tool for any linear motion problem.
运动学研究物体的运动而不涉及引起运动的原因。四个匀加速运动方程将位移(Δx)、初速度(v₀)、末速度(v)、加速度(a)和时间(t)联系起来，是解决直线运动问题的基本工具。
| Equation | Missing Variable |
| v = v₀ + a t | Δx |
| Δx = v₀ t + ½ a t² | v |
| v² = v₀² + 2 a Δx | t |
| Δx = ½ (v₀ + v) t | a |
For two‑dimensional projectile motion, separate the velocity into horizontal and vertical components. Horizontally, velocity is constant (ignoring drag); vertically, acceleration is -g. The range formula R = (v₀² sin 2θ)/g applies when launch and landing are at the same height.
处理二维抛体运动时，将速度分解为水平与竖直分量。水平方向速度不变（忽略空气阻力），竖直方向做加速度为 -g 的匀变速运动。若发射点与落地点等高，射程公式为 R = (v₀² sin 2θ)/g。
Newton’s second law is the core of dynamics: net force = mass × acceleration. On an inclined plane without friction, the component of weight along the slope is m g sin θ, giving acceleration a = g sin θ. Friction introduces static (f_s ≤ μ_s N) and kinetic (f_k = μ_k N) forces.
牛顿第二定律是动力学的核心：合外力 = 质量 × 加速度。在无摩擦的斜面上，重力沿斜面的分量为 m g sin θ，因此加速度 a = g sin θ。存在摩擦时，需考虑静摩擦力 (f_s ≤ μ_s N) 和动摩擦力 (f_k = μ_k N)。
F_net = m a
2. Energy, Work, and Momentum | 能量、功与动量
Work done by a constant force is W = F d cosθ. Kinetic energy KE = ½ m v², gravitational potential energy near Earth is PE = m g h, and spring potential energy is U_s = ½ k x².
恒力做的功为 W = F d cosθ。动能 KE = ½ m v²，地面附近的重力势能 PE = m g h，弹簧的弹性势能 U_s = ½ k x²。
The work‑energy theorem, W_net =
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