IB Physics: Core Mechanics Concepts | IB物理：力学核心知识点梳理

📚 IB Physics: Core Mechanics Concepts | IB物理：力学核心知识点梳理

Mechanics is often the first and most important topic in IB Physics. It builds the physical intuition and mathematical language needed for electricity, waves, and fields. This guide covers the core mechanics concepts you must master for both SL and HL.

力学通常是IB物理中第一个也是最重要的主题。它为你学习电学、波动和场打下了物理直觉和数学语言基础。本指南涵盖SL和HL都必须掌握的力学核心知识点。

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1. Kinematics Quantities | 运动学基本量

Kinematics describes motion without considering its cause. The three fundamental quantities are displacement, velocity, and acceleration. Displacement is a vector: it has both magnitude and direction. Distance, by contrast, is scalar.

运动学描述运动而不考虑其产生原因。三个基本物理量是位移、速度和加速度。位移是矢量：既有大小也有方向。相比之下，距离是标量。

• Displacement s is measured in metres (m).
• 位移 s 的单位是米（m）。
• Velocity v = Δs/Δt is measured in m s⁻¹.
• 速度 v = Δs/Δt 的单位是 m s⁻¹。
• Acceleration a = Δv/Δt is measured in m s⁻².
• 加速度 a = Δv/Δt 的单位是 m s⁻²。

Instantaneous velocity is the gradient of the displacement-time graph at a particular instant, while average velocity is total displacement divided by total time. Remember that speed is the magnitude of velocity.

瞬时速度是位移-时间图像在某一点的切线斜率，而平均速度是总位移除以总时间。请记住：速率是速度的大小。

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2. Equations of Motion | 运动学方程

For motion with constant acceleration, the SUVAT equations apply. These connect displacement s, initial velocity u, final velocity v, acceleration a, and time t.

对于匀加速运动，可以使用SUVAT方程。这些方程把位移s、初速度u、末速度v、加速度a和时间t联系起来。

v = u + at

s = ut + ½at²

v² = u² + 2as

When using these equations, choose a positive direction and keep each quantity consistent. For vertical motion under gravity alone, a = g = 9.8 m s⁻² on Earth, with direction downward.

使用这些方程时，选择一个正方向并保持各物理量一致。对于仅在重力作用下的竖直运动，地球表面 a = g = 9.8 m s⁻²，方向向下。

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3. Motion Graphs | 运动图像

Graphical analysis is heavily tested in IB Physics. You should be able to interpret and sketch displacement-time, velocity-time, and acceleration-time graphs.

图像分析是IB物理的考察重点。你应该会解读和绘制位移-时间、速度-时间和加速度-时间图像。

• Gradient of s-t graph = instantaneous velocity.
• s-t 图像的斜率 = 瞬时速度。
• Gradient of v-t graph = acceleration.
• v-t 图像的斜率 = 加速度。
• Area under v-t graph = displacement.
• v-t 图像下方的面积 = 位移。
• Area under a-t graph = change in velocity.
• a-t 图像下方的面积 = 速度变化量。

When acceleration is constant, the v-t graph is a straight line. If the line is horizontal, acceleration is zero. A curved s-t graph means velocity is changing.

当加速度恒定时，v-t 图像是一条直线。如果图像水平，则加速度为零。s-t 图像弯曲表示速度在变化。

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4. Forces and Newton’s Laws | 力与牛顿定律

Dynamics connects force and motion. A force is any push or pull that can change the motion of an object. The net force is the vector sum of all forces acting on an object.

动力学将力与运动联系起来。力是任何能改变物体运动状态的推或拉。合力是作用在物体上的所有力的矢量和。

Newton’s three laws are central to the IB Physics mechanics syllabus.

牛顿三大定律是IB物理力学大纲的核心。

First law: an object stays at rest or continues at constant velocity unless acted on by a net external force.

第一定律：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。

Second law: the net force on an object equals the rate of change of momentum. For constant mass, this gives F = ma.

第二定律：物体所受合力等于其动量的变化率。当质量恒定时，可写为 F = ma。

Third law: if object A exerts a force on object B, then object B exerts an equal and opposite force on object A.

第三定律：如果物体A对物体B施力，那么物体B对物体A也施加大小相等、方向相反的力。

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5. Free-Body Diagrams | 受力分析图

To solve mechanics problems, you must draw a free-body diagram. This shows only the object of interest and all forces acting on it, represented as labelled arrows.

解决力学问题时，你必须画出受力分析图。该图只画出关注对象以及作用在它身上的所有力，用带标签的箭头表示。

• Weight W = mg always acts downward.
• 重力 W = mg 始终竖直向下。
• Normal reaction N acts perpendicular to the surface.
• 支持力 N 垂直于接触面。
• Friction f acts parallel to the surface, opposing motion or attempted motion.
• 摩擦力 f 平行于接触面，阻碍运动或运动趋势。
• Tension T in a string or rope pulls along the string.
• 绳子中的张力 T 沿绳子方向拉动。

On an inclined plane, resolve weight into components: mg sinθ parallel to the slope and mg cosθ perpendicular to the slope. This decomposition is essential for nearly every incline problem.

在斜面上，把重力分解为：沿斜面方向 mg sinθ 和垂直斜面方向 mg cosθ。这种分解几乎对每个斜面问题都至关重要。

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6. Momentum and Impulse | 动量与冲量

Momentum p is a vector quantity defined as the product of mass and velocity.

动量 p 是矢量，定义为单位质量和速度的乘积。

p = mv

Impulse is the product of force and time, and it equals the change in momentum. This is known as the impulse-momentum theorem.

冲量是力和时间的乘积，它等于动量的变化量。这就是动量定理。

J = FΔt = Δp

The unit of momentum is kg m s⁻¹, and the unit of impulse is N s. These are equivalent because 1 N s = 1 kg m s⁻¹. When force is not constant, the impulse is the area under a force-time graph.

动量的单位是 kg m s⁻¹，冲量的单位是 N s。两者等价，因为 1 N s = 1 kg m s⁻¹。当力不恒定时，冲量等于力-时间图像下方的面积。

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7. Conservation of Momentum | 动量守恒

In any closed system with no net external force, total momentum remains constant. This principle is used to analyse collisions and explosions.

在任何没有合外力的封闭系统中，总动量保持不变。这一原理用于分析碰撞和爆炸问题。

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

In an elastic collision both momentum and kinetic energy are conserved. In an inelastic collision momentum is conserved but some kinetic energy is converted into heat, sound, or deformation. In a completely inelastic collision the objects stick together.

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，但部分动能转化为热能、声能或形变能。在完全非弹性碰撞中，碰撞后物体粘在一起运动。

For explosions, the total initial momentum is zero, so the fragments fly apart with equal and opposite momenta. Rocket propulsion and recoil of a gun are classic applications.

对于爆炸过程，初始总动量为零，因此各碎片以大小相等、方向相反的动量飞开。火箭推进和枪的后坐力是经典应用。

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8. Work and Kinetic Energy | 功与动能

Work W is done when a force moves an object through a displacement. The general formula includes the angle θ between force and displacement.

当力使物体发生位移时，力就做了功 W。一般公式包含力与位移之间的夹角 θ。

W = Fs cosθ

• If θ = 0°, work is positive.
• 如果 θ = 0°，做正功。
• If θ = 90°, work is zero.
• 如果 θ = 90°，做功为零。
• If θ = 180°, work is negative.
• 如果 θ = 180°，做负功。

Kinetic energy of a moving object is given by ½mv². The work-energy theorem states that the net work done on an object equals its change in kinetic energy.

运动物体的动能为 ½mv²。动能定理表明：合外力对物体做的净功等于物体动能的变化。

W_net = ΔE_k = ½mv² – ½mu²

Work and energy are measured in joules (J), where 1 J = 1 N m = 1 kg m² s⁻².

功和能量的单位是焦耳（J），其中 1 J = 1 N m = 1 kg m² s⁻²。

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9. Potential Energy and Conservation of Energy | 势能与能量守恒

Gravitational potential energy is the energy stored due to height in a gravitational field.

重力势能是由于物体在重力场中处于一定高度而储存的能量。

E_p = mgh

For an ideal spring, elastic potential energy is stored according to Hooke’s law, F = kx, and is given by:

对于理想弹簧，弹性势能根据胡克定律 F = kx 储存，其大小为：

E_elas = ½kx²

When only conservative forces do work, total mechanical energy is conserved. For example, a ball thrown upward converts kinetic energy into gravitational potential energy and back again with no loss.

当只有保守力做功时，机械能守恒。例如，竖直上抛的小球把动能转化为重力势能，再转化回来，没有能量损失。

If friction is present, mechanical energy is not conserved. The lost energy appears as thermal energy, and you must account for it using the work done against friction.

如果存在摩擦力，机械能不守恒。损失的能量以热能形式出现，你必须用克服摩擦力所做的功来计算这部分损失。

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10. Power and Efficiency | 功率与效率

Power is the rate at which work is done or energy is transformed. Its SI unit is the watt (W), where 1 W = 1 J s⁻¹.

功率是做功或能量转化的快慢。其国际单位是瓦特（W），其中 1 W = 1 J s⁻¹。

P = W/t

For an object moving at constant velocity under a constant force, power can also be written as P = Fv. This is useful for vehicles: to maintain a high speed, an engine must provide enough power to overcome air resistance and friction.

对于在恒定力作用下匀速运动的物体，功率也可写为 P = Fv。这对车辆问题很有用：为保持高速，发动机必须提供足够功率以克服空气阻力和摩擦。

Efficiency compares useful output energy to total input energy.

效率是比较有用输出能量与总输入能量。

Efficiency = (useful output energy / total input energy) × 100%

No real machine is 100% efficient. In IB questions, always identify which energy is useful and which is wasted as heat or sound.

任何真实机器都不可能100%高效。在IB题目中，务必判断哪些能量是有用的，哪些以热能或声能形式被浪费。

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11. Uniform Circular Motion | 匀速圆周运动

Uniform circular motion appears under mechanics in IB Physics. When an object moves in a circle at constant speed, its direction changes continuously, so it is accelerating.

匀速圆周运动在IB物理中属于力学部分。当物体以恒定速率做圆周运动时，其方向不断改变，因此存在加速度。

Angular speed ω is the angle swept out per unit time.

角速度 ω 是单位时间内扫过的角度。

ω = 2π/T = 2πf

where T is the period and f is the frequency. Linear speed is related by v = ωr.

其中 T 是周期，f 是频率。线速度与角速度的关系为 v = ωr。

Centripetal acceleration points toward the centre of the circle and is given by:

向心加速度指向圆心，其大小为：

a_c = v²/r = ω²r

Therefore the net force toward the centre, centripetal force, is:

因此指向圆心的合力，即向心力，为：

F_c = mv²/r = mω²r

Remember that centripetal force is not a new type of force. It must be provided by tension, gravity, friction, a normal reaction, or a combination of these. For a satellite in orbit, gravity provides the centripetal force.

记住：向心力并不是一种新类型的力。它必须由张力、重力、摩擦力、支持力或这些力的组合来提供。对于轨道上的卫星，重力提供向心力。

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These core mechanics concepts form the foundation for the rest of IB Physics. Master the vector nature of forces and momentum, practise free-body diagrams, and always check whether energy is conserved. With consistent problem-solving practice, you will turn these ideas into exam success.

以上力学核心概念构成了IB物理其余部分的基础。掌握力和动量的矢量性，勤练受力分析图，并始终检查能量是否守恒。通过持续的问题解决训练，你一定能将这些知识转化为考试中的出色表现。

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