📚 IB AQA Physics: Key Concepts in Dynamics | IB AQA 物理：动力学 考点精讲
Dynamics is the branch of mechanics that studies the motion of objects and the forces causing that motion. In the IB Physics curriculum (aligned with AQA standards), mastering dynamics is essential for understanding how the world moves — from falling apples to orbiting planets. This article distills the key concepts, equations, and problem-solving strategies that every student needs to know.
动力学是力学的一个分支，研究物体的运动以及引起该运动的力。在 IB 物理课程（对标 AQA 标准）中，掌握动力学对于理解从落下的苹果到沿轨道运行的行星等一切运动方式至关重要。本文提炼了每位学生都需要掌握的核心概念、方程及解题策略。
1. Displacement, Velocity & Acceleration | 位移、速度与加速度
Displacement is a vector quantity representing the change in position of an object. It must include both magnitude and direction, unlike scalar distance.
位移是表示物体位置变化的矢量，必须同时包含大小和方向，与标量路程不同。
Velocity is the rate of change of displacement: v = Δs / Δt. Acceleration is the rate of change of velocity: a = Δv / Δt. Both are vectors.
速度是位移的变化率：v = Δs / Δt。加速度是速度的变化率：a = Δv / Δt。两者都是矢量。
On an s–t graph, velocity is found from the gradient; on a v–t graph, acceleration is given by the gradient and displacement by the area under the curve.
在位移–时间图上，速度从斜率得出；在速度–时间图上，加速度由斜率给出，位移由图下面积表示。
2. Uniformly Accelerated Motion (SUVAT) | 匀加速运动（SUVAT 方程）
For constant acceleration, four kinematic equations (SUVAT) relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).
在加速度恒定的情况下，四个运动学方程（SUVAT）描述了位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t) 之间的关系。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
These equations are valid only when acceleration is uniform. Choose the appropriate equation based on the known and unknown quantities.
这些方程仅在加速度恒定时才有效。根据已知量和未知量选择合适的方程。
3. Free Fall & Vertical Motion | 自由落体与竖直运动
Free fall occurs when the only force acting on an object is gravity. Near Earth’s surface, the acceleration due to gravity is g = 9.81 m s⁻² downwards.
自由落体发生在物体仅受重力作用时。在地表附近，重力加速度为 g = 9.81 m s⁻²，方向向下。
In vertical motion problems, take one direction as positive (usually upwards). Then acceleration a = −g if upward is positive.
在竖直运动问题中，指定一个方向为正（通常向上）。若向上为正，则加速度 a = −g。
Symmetry of free fall: time up equals time down for an object returning to the same level, and launch speed equals impact speed (ignoring air resistance).
自由落体的对称性：对于回到同一高度的物体，上升时间等于下落时间，发射速率等于落地速率（忽略空气阻力）。
4. Projectile Motion | 抛体运动
Projectile motion results from an initial velocity at an angle to the horizontal, with constant horizontal velocity and constant vertical acceleration due to gravity.
抛体运动由与水平方向成一定角度的初速度引起，水平速度恒定，竖直方向加速度恒为重力加速度。
Resolve the initial velocity into horizontal and vertical components: uₓ = u cosθ, uᵧ = u sinθ.
将初速度分解为水平和竖直分量：uₓ = u cosθ，uᵧ = u sinθ。
Apply SUVAT equations independently in the x‑direction (aₓ = 0) and y‑direction (aᵧ = −g). The trajectory is parabolic.
分别在 x 方向（aₓ = 0）和 y 方向（aᵧ = −g）独立应用 SUVAT 方程。轨迹为抛物线。
5. Newton’s Laws of Motion | 牛顿运动定律
First Law: An object remains at rest or in uniform straight‑line motion unless acted upon by a net external force.
第一定律：除非受到净外力作用，物体将保持静止或匀速直线运动状态。
Second Law: The net force on an object is directly proportional to the rate of change of its momentum. For constant mass, F = ma.
第二定律：物体所受合外力与其动量的变化率成正比。当质量恒定时，F = ma。
Third Law: If body A exerts a force on body B, then body B exerts an equal and opposite force on body A.
第三定律：若物体 A 对物体 B 施加一个力，则物体 B 同时对物体 A 施加一个大小相等、方向相反的力。
6. Free‑Body Diagrams & Resultant Force | 受力分析图与合力
A free‑body diagram shows all forces acting on a single object: weight (mg), normal contact force, tension, friction, applied forces. Use arrows to represent vectors.
受力分析图显示作用在单个物体上的所有力：重力 (mg)、法向接触力、张力、摩擦力、外加力。用箭头表示矢量。
The resultant force is the vector sum of all these forces. Apply Fnet = ma in each direction separately.
合力是所有这些力的矢量和。分别在各个方向应用 Fnet = ma。
7. Friction & Air Resistance | 摩擦力与空气阻力
Static friction prevents motion up to a maximum value fs ≤ μsN. Kinetic friction opposes motion: fk = μkN, where N is the normal force.
静摩擦力阻止运动，最大值为 fs ≤ μsN。动摩擦力阻碍运动：fk = μkN，其中 N 为法向力。
Air resistance (drag) increases with speed and depends on the shape and size of the object. At terminal velocity, drag equals weight and net force is zero.
空气阻力（拖曳力）随速度增加而增大，并与物体的形状和大小有关。达到终极速度时，阻力等于重力，合力为零。
8. Work, Energy & Power | 功、能量与功率
Work done by a constant force: W = F s cosθ, where θ is the angle between the force and the displacement. Work is measured in joules (J).
恒力做功：W = F s cosθ，θ 为力与位移之间的夹角。功的单位是焦耳 (J)。
Kinetic energy: Ek = ½mv². Gravitational potential energy: Ep = mgΔh. Elastic potential energy for a spring: Eel = ½kx².
动能：Ek = ½mv²。重力势能：Ep = mgΔh。弹簧的弹性势能：Eel = ½kx²。
Power is the rate of doing work: P = W / t = F v cosθ (for constant force and velocity).
功率是做功的速率：P = W / t = F v cosθ（适用于力和速度恒定的情况）。
9. Conservation of Energy | 能量守恒
Energy cannot be created or destroyed, only transferred or transformed. In a closed system without external work, the total mechanical energy (Ek + Ep) remains constant if only conservative forces act.
能量既不能创造也不能消灭，只能转移或转化。在无外力做功的封闭系统中，若只有保守力作用，总机械能 (Ek + Ep) 保持恒定。
Apply the principle: Total initial energy = Total final energy, including work done against non‑conservative forces (e.g., friction).
应用原理：初始总能量 = 最终总能量，包括克服非保守力（如摩擦力）所做的功。
10. Momentum & Impulse | 动量与冲量
Momentum is a vector: p = mv. Impulse is the change in momentum: J = Δp = F Δt. The area under a force–time graph gives impulse.
动量是矢量：p = mv。冲量是动量的变化量：J = Δp = F Δt。力–时间图下的面积即为冲量。
Newton’s second law in terms of momentum: F = Δp / Δt. This form is valid even when mass changes (e.g., rocket).
牛顿第二定律的动量表述：F = Δp / Δt。该形式在质量变化（如火箭）时仍然有效。
11. Conservation of Momentum | 动量守恒
In a closed system with no external forces, total momentum is conserved: Σpinitial = Σpfinal.
在无外力的封闭系统中，总动量守恒：Σp初始 = Σp最终。
Apply this principle to collisions and explosions. Distinguish between elastic collisions (kinetic energy conserved) and inelastic collisions (some kinetic energy lost).
将该原理应用于碰撞和爆炸。区分弹性碰撞（动能守恒）和非弹性碰撞（部分动能损失）。
12. Common Pitfalls & Exam Tips | 常见误区与应试技巧
Always assign a consistent sign convention for direction, especially in SUVAT and Newton’s law problems.
始终为方向指定一致的符号约定，尤其在 SUVAT 和牛顿定律问题中。
Check that units are consistent (e.g., convert g to kg, cm to m). Draw clear free‑body diagrams before writing equations.
确保单位一致（例如将 g 转换为 kg，cm 转换为 m）。先画出清晰受力分析图再写方程。
In projectile motion, remember horizontal velocity is constant; work with components separately. In energy problems, include work done against friction if present.
在抛体运动中，记住水平速度恒定；对各分量分别处理。在能量问题中，若存在摩擦，应包含克服摩擦力所做的功。
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