Edexcel A-Level Physics Topic 6: Further Mechanics | 爱德思 A-Level 物理第6单元：进阶力学

📚 Edexcel A-Level Physics Topic 6: Further Mechanics | 爱德思 A-Level 物理第6单元：进阶力学

This revision guide covers the core ideas in Edexcel A-Level Physics Topic 6, Further Mechanics. You will meet momentum, impulse, conservation laws, collisions, and circular motion. These concepts build on GCSE forces and motion and appear frequently in both AS and A2 exams.

本复习指南涵盖爱德思 A-Level 物理第 6 单元“进阶力学”的核心内容。你将学习动量、冲量、动量守恒、碰撞以及圆周运动。这些概念建立在 GCSE 力与运动的基础上，在 AS 和 A2 考试中都经常出现。

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1. Momentum and Impulse | 动量与冲量

Momentum p is the product of an object’s mass and velocity: p = mv. Since velocity is a vector, momentum is also a vector pointing in the same direction as velocity. Its SI unit is kg m s⁻¹.

动量 p 是物体质量与速度的乘积：p = mv。由于速度是矢量，动量也是矢量，方向与速度方向相同。动量的国际单位是 kg m s⁻¹。

p = mv

Impulse is the change in momentum caused by a resultant force acting over a time interval. The impulse-momentum equation is FΔt = Δp = mΔv, where F is constant force and Δt is contact time.

冲量是由合力在一段时间内作用引起的动量变化。冲量-动量方程为 FΔt = Δp = mΔv，其中 F 为恒力，Δt 为作用时间。

FΔt = Δp = m(v – u)

The area under a force-time graph equals the impulse delivered to an object. This is useful when the force is not constant, such as during a kick or a collision.

力-时间图下的面积等于施加给物体的冲量。当力不恒定时（例如踢球或碰撞过程中），这一关系非常有用。

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2. Conservation of Momentum | 动量守恒

In a closed system with no external resultant force, total momentum before a collision or explosion equals total momentum after. This is a direct consequence of Newton’s third law.

在没有外部合力的封闭系统中，碰撞或爆炸前的总动量等于碰撞或爆炸后的总动量。这是牛顿第三定律的直接结果。

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Here m₁ and m₂ are the masses, u₁ and u₂ are the initial velocities, and v₁ and v₂ are the final velocities of the two objects. You must choose a positive direction before substituting values.

其中 m₁ 和 m₂ 是两物体的质量，u₁ 和 u₂ 是初速度，v₁ 和 v₂ 是末速度。代入数值前必须先规定正方向。

Momentum is especially useful for analysing collisions because it is conserved even when kinetic energy is not. This makes momentum calculations more powerful than energy calculations in many impact problems.

动量在分析碰撞时特别有用，因为即使动能不守恒，动量仍然守恒。在许多撞击问题中，动量计算比能量计算更有效。

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3. Elastic and Inelastic Collisions | 弹性碰撞与非弹性碰撞

In an elastic collision both momentum and kinetic energy are conserved. In an inelastic collision momentum is conserved but kinetic energy is not, usually because some energy is transferred to heat, sound or deformation.

在弹性碰撞中，动量和动能都守恒。在非弹性碰撞中，动量守恒但动能不守恒，通常因为部分能量转化为热能、声能或形变能。

A perfectly inelastic collision is one where the two bodies stick together after impact. The combined mass moves with a common velocity. Momentum is still conserved, but the loss of kinetic energy is at a maximum.

完全非弹性碰撞是两物体碰撞后粘在一起的情况。合并后的质量以共同速度运动。动量仍然守恒，但动能损失最大。

m₁u₁ + m₂u₂ = (m₁ + m₂)v

Elastic collision | 弹性碰撞	Inelastic collision | 非弹性碰撞
Momentum conserved | 动量守恒	Momentum conserved | 动量守恒
Kinetic energy conserved | 动能守恒	Kinetic energy not conserved | 动能不守恒
Objects rebound separately | 物体分开反弹	Objects may stick together | 物体可能粘在一起

Examples of nearly elastic collisions include gas molecule collisions and Newton’s cradle. Car crashes and clay hitting a wall are inelastic collisions because kinetic energy is dissipated.

接近弹性碰撞的例子包括气体分子碰撞和牛顿摆。汽车碰撞和粘土撞墙是非弹性碰撞，因为动能被耗散。

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4. Explosions and Recoil | 爆炸与反冲

Explosions are the reverse of inelastic collisions: initially the total momentum is zero, so after separation the momenta of fragments must add to zero. This is why a gun recoils when a bullet is fired.

爆炸是非弹性碰撞的逆过程：初始总动量为零，因此分离后各碎块的动量之和必须为零。这就是为什么开枪时枪会反冲。

0 = m₁v₁ + m₂v₂ → m₁v₁ = -m₂v₂

The negative sign shows that the two objects move in opposite directions. The lighter fragment gets a greater speed because it has the same magnitude of momentum.

负号表示两个物体沿相反方向运动。质量较小的碎片获得更大的速度，因为它的动量大小相同。

This principle also explains rocket propulsion: expelled exhaust gases gain backward momentum, so the rocket gains equal forward momentum.

这一原理也解释了火箭推进：喷出的燃气获得向后的动量，因此火箭获得相等的向前动量。

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5. Radians and Angular Velocity | 弧度与角速度

Radians are used to measure angular displacement. One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius.

弧度用于测量角位移。1 弧度是圆心角所对的弧长等于半径时的角度。

θ = s / r and 2π rad = 360°

Angular velocity ω is the rate of change of angular displacement: ω = Δθ / Δt. It is measured in rad s⁻¹. For an object moving in a circle of radius r, its linear speed v is linked to ω by v = ωr.

角速度 ω 是角位移的变化率：ω = Δθ / Δt，单位为 rad s⁻¹。对于在半径为 r 的圆周上运动的物体，其线速度 v 与角速度的关系为 v = ωr。

v = ωr

If an object completes one full revolution in period T, then ω = 2π / T. Since frequency f = 1 / T, we also have ω = 2πf.

如果物体在周期 T 内完成一整圈转动，则 ω = 2π / T。因为频率 f = 1 / T，我们还可以得到 ω = 2πf。

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6. Centripetal Acceleration | 向心加速度

An object moving in a circle at constant speed is still accelerating because its direction is continuously changing. This acceleration is directed towards the centre of the circle and is called centripetal acceleration.

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