📚 A-Level Edexcel Physics: Key Points of Dynamics | A-Level Edexcel 物理：动力学 考点精讲
Dynamics is the branch of mechanics that deals with the motion of objects and the forces causing that motion. Mastering it is essential for Edexcel A-Level Physics, as it forms the foundation for many advanced topics. This article unpacks the key concepts step by step, with clear explanations and handy summaries.
动力学是力学中研究物体运动及其受力原因的分支。掌握动力学对 Edexcel A-Level 物理至关重要，因为它为许多高级课题奠定了基础。本文逐步拆解核心概念，配以清晰的解释和实用的总结。
1. Kinematics Quantities | 运动学量
Displacement (s) is the straight-line distance in a given direction, a vector quantity measured in metres (m). It differs from distance, which is scalar.
位移 (s) 是给定方向上的直线距离，是矢量，单位为米 (m)。它与标量的路程不同。
Velocity (v) is the rate of change of displacement, also a vector, expressed in m s⁻¹. Speed is the scalar equivalent.
速度 (v) 是位移的变化率，也是矢量，单位为 m s⁻¹。速率为相应的标量。
Acceleration (a) is the rate of change of velocity, a vector quantity, measured in m s⁻². Uniform acceleration means constant acceleration.
加速度 (a) 是速度的变化率，矢量，单位为 m s⁻²。匀加速指加速度恒定。
- Average velocity = Δs / Δt
- Instantaneous velocity = gradient of displacement–time graph
- Acceleration = gradient of velocity–time graph
- 平均速度 = 位移变化量 / 时间间隔
- 瞬时速度 = 位移–时间图线的切线斜率
- 加速度 = 速度–时间图线的切线斜率
2. SUVAT Equations | 匀加速运动方程
The SUVAT equations link five variables for motion in a straight line with constant acceleration. They are indispensable for solving kinematics problems.
匀加速运动方程将直线运动中恒加速度下的五个变量联系起来，是解决运动学问题不可或缺的工具。
| Symbol | Meaning | Unit |
| s | displacement | m |
| u | initial velocity | m s⁻¹ |
| v | final velocity | m s⁻¹ |
| a | acceleration | m s⁻² |
| t | time | s |
v = u + at
s = ut + ½at²
s = ½(u + v)t
v² = u² + 2as
Choose the equation that contains the three known quantities and the one unknown. Always state the positive direction before substituting values.
选择包含三个已知量和一个未知量的方程。代入数值前务必先明确正方向。
3. Free Fall | 自由落体
ty alone, ignoring air resistance. The acceleration is g = 9.81 m s⁻², directed downwards.
自由落体是仅受重力作用、忽略空气阻力的运动。加速度 g = 9.81 m s⁻²，方向向下。
ns apply, with a = ±g depending on the chosen sign convention. If upwards is positive, a = –9.81 m s⁻².
所有匀加速运动方程均适用，加速度 a = ±g 取决于规定的正方向。若取向上为正，则 a = –9.81 m s⁻²。
Symmetry of motion: for an object thrown vertically upwards, the time to rise to the maximum height equals the time to fall back, and the speed at the same level is the same on the way up and down.
运动的对称性：竖直上抛物体，上升到最高点的时间等于落回原处的时间，经过同一高度的速率在上抛和下落到相同位置时相等。
4. Projectile Motion | 抛体运动
A projectile moves under constant velocity horizontally and constant acceleration vertically, with both motions independent.
抛体水平方向做匀速直线运动，竖直方向做匀加速运动，两个方向相互独立。
ts separately: uₓ = u cosθ, uᵧ = u sinθ. Horizontally aₓ = 0, vertically aᵧ = g downwards.
将初速度分解为水平分量 uₓ = u cosθ 和竖直分量 uᵧ = u sinθ。水平方向 aₓ = 0，竖直方向 aᵧ = g 向下。
time T = (2 u sinθ) / g, maximum height H = (u² sin²θ) / (2g), range R = (u² sin 2θ) / g.
飞行时间、最大高度和射程通过竖直运动计算。对于对称抛物线轨迹，总时间 T = (2 u sinθ) / g，最大高度 H = (u² sin²θ) / (2g)，射程 R = (u² sin 2θ) / g。
5. Newton’s First Law | 牛顿第一定律
by a resultant external force. This defines inertia and the equilibrium condition: ΣF = 0.
物体保持静止或匀速直线运动状态，除非受到合外力的作用。这定义了惯性及平衡条件：合力 ΣF = 0。
If the resultant force is zero, the velocity is constant (this includes zero velocity). It does not mean no forces act; they simply cancel.
若合力为零，速度恒定（包括零速度）。这并不意味着没有力作用，而是力相互抵消了。
6. Newton’s Second Law | 牛顿第二定律
The resultant force acting on an object is proportional to the rate of change of its momentum. For constant mass, this simplifies to
F = m a
where F is resultant force in newtons (N), m is mass in kg, and a is acceleration in m s⁻².
物体受到的合外力与其动量的变化率成正比。当质量恒定时，简化为 F = m a，其中 F 为合外力 (N)，m 为质量 (kg)，a 为加速度 (m s⁻²)。
This is a vector equation: the acceleration is in the same direction as the resultant force. Always draw a free-body diagram before applying the law.
这是一个矢量方程：加速度方向与合外力方向相同。应用定律前务必画受力分析图。
7. Newton’s Third Law | 牛顿第三定律
If body A exerts a force on body B, then body B exerts an equal and opposite force on body A. These forces are of the same type and act on different bodies.
若物体 A 对 B 施加力，则 B 同时对 A 施加等大反向的力。这对力属于同一类型，作用在不同物体上。
Common mistake: equating the normal reaction and weight as an action–reaction pair. They act on the same body; the correct pair is the force the block exerts on the table and the table’s normal force on the block.
常见错误：把支持力与重力当成一对作用力与反作用力。它们作用在同一物体上；正确的反作用力是物块对桌面的压力与桌面对物块的支持力。
8. Friction and Resistive Forces | 摩擦与阻力
is Fₛ = μₛ R, where R is the normal reaction. Kinetic friction when sliding is Fₖ = μₖ R.
静摩擦力在无相对运动时作用，最大静摩擦 Fₛ = μₛ R，R 为支持力。滑动时的动摩擦 Fₖ = μₖ R。
Drag forces (air resistance) increase with speed and oppose motion. Terminal velocity is reached when drag equals driving force, giving zero net force.
阻力（空气阻力）随速度增大而增大，方向与运动方向相反。当阻力等于驱动力时，合力为零，物体达到终极速度。
9. Connected Particles | 连接体问题
For objects connected by a light inextensible string over a smooth pulley, the tension is the same throughout, and the accelerations have the same magnitude.
对于通过轻绳跨过光滑滑轮的连接体，绳中张力处处相等，且两物体的加速度大小相同。
ately, writing equations of motion. Solve simultaneously to find acceleration and tension.
分别对每个质点应用 F = ma，列出动力学方程。联立求解得到加速度和张力。
Example: for masses m₁ and m₂ with m₁ > m₂, a = (m₁ – m₂)g / (m₁ + m₂) and T = (2m₁m₂)g / (m₁ + m₂).
示例：质量 m₁ 和 m₂ (m₁ > m₂)，加速度 a = (m₁ – m₂)g / (m₁ + m₂)，张力 T = (2m₁m₂)g / (m₁ + m₂)。
10. Momentum and Impulse | 动量与冲量
s⁻¹. Impulse is the change in momentum: Impulse = Δp = F Δt, where F is the average force.
线动量 p = mv，矢量，单位 kg m s⁻¹。冲量是动量的变化量：冲量 = Δp = F Δt，F 为平均作用力。
The area under a force–time graph gives the impulse. In collisions, the contact time is short, so forces are large but the impulse is finite.
力–时间图线下方的面积表示冲量。碰撞中作用时间极短，因此力很大，但冲量是有限的。
11. Conservation of Momentum | 动量守恒
For any system with no external resultant force, total momentum remains constant:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
This principle is essential for collision and explosion problems.
对于不受合外力的系统，总动量保持不变：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。这是解决碰撞和爆炸问题的关键原理。
Remember to assign a positive direction and substitute velocities with correct signs. Momentum is a vector.
务必规定正方向，代入速度时带上正确的符号。动量是矢量。
12. Elastic and Inelastic Collisions | 弹性与非弹性碰撞
In a perfectly elastic collision, kinetic energy is conserved as well as momentum. In an inelastic collision, momentum is conserved but kinetic energy is not; some is converted to heat or deformation.
完全弹性碰撞中，动能与动量均守恒。非弹性碰撞中，动量守恒但动能不守恒，部分动能转化为热能或形变能。
the objects stick together and move with a common velocity v = (m₁u₁ + m₂u₂) / (m₁ + m₂).
对于两等质量物体的弹性正碰，速度交换。对于完全非弹性碰撞，物体粘在一起以共同速度 v = (m₁u₁ + m₂u₂) / (m₁ + m₂) 运动。
Check whether a collision is elastic by comparing total kinetic energy before and after. If equal, it is elastic; if not, inelastic.
通过比较碰撞前后总动能来判断碰撞类型。若相等则为弹性碰撞，否则为非弹性碰撞。
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