📚 Edexcel Physics Topic 2 Revision Essentials | Edexcel 物理 Topic 2 复习要点
Topic 2 Mechanics forms the foundation for understanding motion, forces and energy in Edexcel A Level Physics. Mastering the SUVAT equations, Newton’s laws, momentum, moments and energy principles is essential for success in both the AS and A2 examinations. This article condenses the key concepts, graphs and calculations you need to revise.
Topic 2 力学是 Edexcel A Level 物理中理解运动、力和能量的基础。掌握 SUVAT 方程、牛顿定律、动量、力矩和能量原理对于在 AS 和 A2 考试中取得成功至关重要。本文浓缩了你需要复习的关键概念、图像和计算。
1. Equations of Motion (SUVAT) | 运动学方程（SUVAT）
The SUVAT equations are used to describe uniform acceleration in a straight line. The five variables are displacement s, initial velocity u, final velocity v, acceleration a and time t. When an object moves with constant acceleration, any one of the four equations can be selected based on the known quantities.
SUVAT 方程用于描述匀加速直线运动。五个变量分别是位移 s、初速度 u、末速度 v、加速度 a 和时间 t。当物体以恒定加速度运动时，可以根据已知量从四个方程中任选一个。
v = u + at
s = ut + ½ at²
v² = u² + 2as
s = (u+v)t / 2
Always choose a positive direction before substituting values. Quantities acting in the opposite direction must carry a minus sign. If an object decelerates, the acceleration a is negative. It is good practice to list the knowns, identify the missing variable, select the equation that contains that missing variable and then solve.
代入数值前务必选定正方向。与正方向相反的物理量必须带上负号。如果物体减速，加速度 a 为负。良好的习惯是列出已知量，确定缺失变量，选择包含该缺失变量的方程，然后求解。
2. Motion Graphs | 运动图像
Graphs of displacement, velocity and acceleration against time provide a visual way to analyse motion. For a displacement–time graph, the gradient gives the velocity. A straight line indicates constant velocity; a horizontal line means the object is at rest. A curved line signals changing velocity, i.e. acceleration.
位移、速度和加速度随时间变化的图像提供了分析运动的可视化方法。对于位移–时间图，斜率表示速度。直线表示匀速运动；水平线表示物体静止。曲线则表示速度在变化，即存在加速度。
On a velocity–time graph, the gradient is the acceleration and the area under the graph equals the displacement. Constant acceleration appears as a straight, sloping line; constant velocity appears as a horizontal line. An acceleration–time graph shows the variation of acceleration; the area under it gives the change in velocity.
在速度–时间图上，斜率是加速度，图线下的面积等于位移。匀加速表现为一条倾斜的直线；匀速则表现为水平线。加速度–时间图显示加速度的变化；其下面积表示速度的变化量。
- Displacement–time: gradient = velocity
- Velocity–time: gradient = acceleration; area = displacement
- Acceleration–time: area = change in velocity
- 位移–时间：斜率 = 速度
- 速度–时间：斜率 = 加速度；面积 = 位移
- 加速度–时间：面积 = 速度变化量
3. Free Fall and Acceleration due to Gravity | 自由落体和重力加速度
In the absence of air resistance, all objects falling freely near the Earth’s surface experience the same uniform acceleration due to gravity, g = 9.81 m s⁻². Motion is vertical, so the SUVAT equations apply directly with a = g (taking downwards as positive) or a = -g (taking upwards as positive).
在没有空气阻力的情况下，所有在地球表面附近自由下落的物体都受到相同的重力加速度 g = 9.81 m s⁻²。运动是竖直方向的，因此可以直接应用 SUVAT 方程，取向下为正值时 a = g，取向上为正值时 a = -g。
A classic experiment to determine g uses a light gate and a card of known length dropped through the beam. The acceleration is calculated from the two velocities measured at different points and the time interval. Alternatively, a trap door and electromagnet arrangement can be used to measure the time of fall over a known drop height, then s = ½ gt² gives g.
测定 g 的经典实验是用光门和一张已知长度的挡光卡片，让其通过光束自由下落。通过测量不同位置的两个速度和相应时间间隔，即可算出加速度。另一种方法是使用电磁铁和撞击开关，测量物体通过已知高度下落的时间，然后由 s = ½ gt² 求出 g。
4. Projectile Motion | 抛体运动
Projectile motion can be analysed by treating the horizontal and vertical components independently. The horizontal velocity remains constant (assuming negligible air resistance), while the vertical motion is uniformly accelerated with a = g downwards.
抛体运动可以通过分别处理水平分量和竖直分量来分析。水平速度保持不变（假设空气阻力可忽略），而竖直方向做向下的匀加速运动，加速度为 g。
Resolve the initial velocity u at an angle θ relative to the horizontal:
uₓ = u cos θ , uᵧ = u sin θ
将初速度 u 按与水平方向夹角 θ 分解：水平分量 uₓ = u cos θ，竖直分量 uᵧ = u sin θ。
For the vertical motion, apply SUVAT with a = -g if upwards is positive. The time of flight, maximum height and range can all be derived. Remember that at the highest point the vertical velocity is zero, but the horizontal velocity is still u cos θ.
竖直方向上，若取向上为正向，应用 SUVAT 时 a = -g。飞行时间、最大高度和射程都可以由此导出。记住，在最高点处竖直速度为零，但水平速度仍然是 u cos θ。
5. Forces and Free-body Diagrams | 力与受力分析图
Forces are vector quantities with both magnitude and direction. Common forces in mechanics include weight (W = mg), normal reaction, friction, tension, and applied forces. A free-body diagram isolates a single object and shows all the forces acting upon it using arrows pointing in the direction of each force.
力是具有大小和方向的矢量。力学中常见的力包括重力（W = mg）、法向反作用力、摩擦力、张力和施加力。受力分析图将单个物体隔离出来，并用箭头标出所有作用在该物体上的力，箭头的方向即力的方向。
The resultant force is the vector sum of all forces. If an object is in equilibrium, the resultant force is zero and the forces form a closed vector polygon. For an object on an inclined plane, the weight must be resolved into components parallel and perpendicular to the slope.
合力是所有力的矢量和。如果物体处于平衡状态，合力为零，且各力矢量构成闭合多边形。对于斜面上的物体，必须将重力分解为平行和垂直于斜面的分力。
- Weight = mg (always vertically downwards)
- Normal reaction (perpendicular to the contact surface)
- Friction (opposing motion or tendency of motion)
- 重力 = mg（总是竖直向下）
- 法向反作用力（垂直于接触面）
- 摩擦力（与运动或运动趋势方向相反）
6. Newton’s Laws of Motion | 牛顿运动定律
Newton’s first law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by a resultant external force. This introduces the concept of inertia.
牛顿第一定律指出，任何物体都将保持静止或匀速直线运动状态，直到有外合力迫使它改变这种状态。这引入了惯性的概念。
Newton’s second law links resultant force, mass and acceleration: F = ma. The net force is in the same direction as the acceleration. This vector equation can be applied to each perpendicular axis separately. For systems with connected bodies, treat the whole system first to find the common acceleration, then isolate individual parts to find tensions.
牛顿第二定律将合力、质量和加速度联系起来：F = ma。合力的方向与加速度的方向相同。这个矢量方程可以分别应用于相互垂直的各个轴。对于连接体系统，可先对整个系统分析求出共同加速度，再隔离单个物体求出张力等力。
Newton’s third law states that if body A exerts a force on body B, then body B exerts an equal and opposite force on body A. These paired forces act on different objects and are of the same type.
牛顿第三定律指出，若物体 A 对物体 B 施加一个力，那么物体 B 会同时对物体 A 施加一个大小相等、方向相反的力。这对力作用在不同物体上，且属于同种性质的力。
7. Momentum and Impulse | 动量与冲量
Linear momentum is defined as p = mv and is a vector quantity with the same direction as the velocity. Impulse is the product of force and the time for which it acts: Impulse = F t. The impulse–momentum theorem states that impulse equals the change in momentum: F t = Δ(mv).
线动量定义为 p = mv，它是矢量，方向与速度方向相同。冲量是力与力作用时间的乘积：冲量 = F t。冲量–动量定理指出，冲量等于动量的变化量：F t = Δ(mv)。
The principle of conservation of momentum states that in the absence of external forces, the total momentum of a system remains constant. This applies to both collisions and explosions. In a collision, distinguish between elastic collisions (kinetic energy conserved) and inelastic collisions (kinetic energy is not conserved, but momentum is always conserved).
动量守恒定律指出，在没有外力作用时，系统的总动量保持不变。这适用于碰撞和爆炸。在碰撞中，要区分弹性碰撞（动能守恒）和非弹性碰撞（动能不守恒，但动量总是守恒的）。
8. Moments and Equilibrium | 力矩与平衡
The moment of a force about a point is the product of the force and the perpendicular distance from the point to the line of action of the force: Moment = F × d. The unit is newton metre (N m). A moment can cause rotation either clockwise or anticlockwise.
力对某点的力矩是力与该点到力的作用线的垂直距离的乘积：力矩 = F × d。单位是牛顿米（N m）。力矩可以引起顺时针或逆时针转动。
An object is in static equilibrium when the resultant force and the resultant moment about any point are both zero. The principle of moments states that for an object in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about any pivot. When solving problems, choose a pivot where an unknown force acts to simplify calculations.
当合力和关于任意点的合力矩都为零时，物体处于静力平衡。力矩原理表明，对于处于平衡状态的物体，对于任意转轴，顺时针力矩之和等于逆时针力矩之和。解题时可选择未知力作用点作为转轴以简化计算。
9. Work and Energy | 功与能
Work is done when a force moves its point of application in the direction of the force. W = F x cos θ, where θ is the angle between the force and the displacement. Work is a scalar quantity measured in joules (J).
当力的作用点沿力的方向发生位移时，该力做了功。W = F x cos θ，其中 θ 为力与位移之间的夹角。功是标量，单位为焦耳（J）。
Kinetic energy is the energy due to motion: Ek = ½ m v². Gravitational potential energy near the Earth’s surface is Ep = m g h, where h is the height above a chosen reference level. The work–energy principle states that the net work done on an object equals its change in kinetic energy.
动能是由于运动而具有的能量：Eₖ = ½ m v²。地球表面附近的重力势能为 Eₚ = m g h，其中 h 是相对于选定参考平面的高度。功能原理指出，对物体做的净功等于其动能的变化量。
10. Power and Efficiency | 功率与效率
Power is the rate of doing work: P = W / t or P = ΔE / t. It is measured in watts (W), where 1 W = 1 J s⁻¹. For a constant force moving an object at constant speed v in the direction of the force, the power can be expressed as P = F v.
功率是做功的快慢程度：P = W / t 或 P = ΔE / t。单位是瓦特（W），1 W = 1 J s⁻¹。当恒力作用于物体且物体沿力的方向以恒定速度 v 运动时，功率可表示为 P = F v。
Efficiency measures how much of the input energy or power is converted into useful output. It is calculated as Efficiency = (useful output energy / total input energy) × 100% or Efficiency = useful power output / total power input. In any real process, efficiency is always less than 1 (or 100%) due to energy dissipated as heat, sound, etc., in line with the principle of conservation of energy.
效率衡量输入能量或功率有多少转化为有用输出。计算公式为 效率 = (有用输出能量 / 总输入能量) × 100% 或 效率 = 有用输出功率 / 总输入功率。在任何实际过程中，由于能量会以热、声等形式耗散，根据能量守恒定律，效率总是小于 1（或 100%）。
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