IB物理Core 运动学 牛顿定律 动量 圆周运动 | IB Physics Core Kinematics Newtons Laws Momentum Circular Motion

IB物理Core 运动学 牛顿定律 动量 圆周运动

IB Core Physics Mechanics is the foundation of the IB Physics syllabus, covering kinematics, Newton's laws, momentum, energy, and circular motion. These topics appear across Paper 1 (MCQ), Paper 2 (short answer + extended response), and the Internal Assessment (IA). Mastering mechanics means understanding both the conceptual framework and the mathematical tools -- SUVAT equations, vector resolution, free-body diagrams, and energy conservation. This guide breaks down each topic with worked examples, exam tips, and common pitfalls.

IB Core物理力学是整个IB物理大纲的基础模块，涵盖运动学、牛顿定律、动量、能量和圆周运动。这些内容在Paper 1选择题、Paper 2简答与扩展题以及IA内部评估中反复出现。掌握力学的关键是理解概念框架并熟练运用数学工具：：SUVAT方程、矢量分解、受力分析和能量守恒。本指南逐项拆解各知识点，配有例题计算、考试技巧和常见陷阱分析。

1. Kinematics 运动学: SUVAT and Graphs

Kinematics describes motion without considering its causes. The five SUVAT equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t) for uniformly accelerated motion. The IB Data Booklet provides all five -- but you must know which one to pick. The key is identifying which three quantities you know and which one you need. Graphs are equally important: slope of s-t gives velocity; slope of v-t gives acceleration; area under v-t gives displacement; area under a-t gives change in velocity. A common Paper 1 trick is asking for the distance traveled from a v-t graph that crosses the time axis -- you need the total area, not the signed displacement.

运动学描述运动本身而不涉及引起运动的原因。五个SUVAT方程连接位移s、初速度u、末速度v、加速度a和时间t，前提是匀加速运动。IB公式表提供了全部五个方程，关键是会选用：确认已知哪三个量、要求哪一个量。图像同样重要：s-t图的斜率是速度；v-t图的斜率是加速度；v-t图下的面积是位移；a-t图下的面积是速度变化量。Paper 1常见陷阱是给出一条穿过时间轴的v-t图求路程：：需要求总面积而非带符号的位移。

Worked Example 例题

A car accelerates from 12 m/s to 28 m/s over 80 m. Find the acceleration and time.

Step 1: List knowns: u = 12, v = 28, s = 80.
Step 2: Need a -- use v^2 = u^2 + 2as.
28^2 = 12^2 + 2a(80) → 784 = 144 + 160a → a = 4.0 m/s^2.
Step 3: Need t -- use v = u + at.
28 = 12 + 4t → t = 4.0 s.

Pitfall 陷阱

Using v = s/t when acceleration is NOT zero. The equation s = (u+v)t/2 works for uniform acceleration, but v_avg = total_s/total_t only works when acceleration is zero. Always check: is "a" explicitly or implicitly zero before using constant-velocity formulas.

2. Forces and Newton's Laws 力与牛顿定律

Newton's three laws are the backbone of IB mechanics. First law: an object maintains constant velocity unless a net external force acts on it (inertia). Second law: F_net = ma -- the vector sum of all forces equals mass times acceleration. Third law: if A exerts a force on B, B exerts an equal and opposite force on A -- these forces act on DIFFERENT bodies. The single most important skill in IB mechanics is drawing a correct free-body diagram (FBD): isolate the body, draw all forces as vectors (weight mg downward, normal reaction N perpendicular to surface, friction f opposing motion, tension T along the string), resolve into components, and apply ΣF = ma in each direction. On inclined planes, break weight into mg sin θ (parallel to slope) and mg cos θ (perpendicular).

牛顿三定律是IB力学的核心框架。第一定律：物体在不受外力或合外力为零时保持静止或匀速直线运动（惯性）。第二定律：F_net = ma，所有力的矢量和等于质量乘加速度。第三定律：A对B施加力，B同时对A施加等大反向的力：：这两个力作用在不同物体上。IB力学最重要的技能是画受力分析图（FBD）：隔离物体，画出所有力的矢量（重力mg向下，法向支持力N垂直于接触面，摩擦力f与运动趋势反向，拉力T沿绳方向），分解为分量，在每个方向上应用ΣF = ma。在斜面上，将重力分解为mg sin θ平行于斜面、mg cos θ垂直于斜面。

Worked Example 例题

A 5.0 kg block on a 30 degree incline (μ = 0.20). Find acceleration.

mg sin θ = 5.0 x 9.81 x sin 30 = 24.5 N
N = mg cos θ = 5.0 x 9.81 x cos 30 = 42.5 N
f = μN = 0.20 x 42.5 = 8.5 N
F_net = 24.5 - 8.5 = 16.0 N
a = F_net / m = 16.0 / 5.0 = 3.2 m/s^2

Pitfall 陷阱

Forgetting N is NOT always mg. On an incline, N = mg cos θ. In an accelerating elevator, N = m(g ± a). In a banked curve, N provides the centripetal force. Always derive N from the force balance in the perpendicular direction -- never assume N = mg blindly.

3. Momentum and Impulse 动量与冲量

Momentum p = mv is a vector quantity. The impulse-momentum theorem states FΔt = Δp: the impulse (force x time) equals the change in momentum. This is why airbags and crumple zones work -- increasing the collision time reduces the average force. Conservation of momentum applies when no external net force acts on a system. For collisions in 2D, resolve momentum into x and y components and conserve each independently. Elastic collisions conserve kinetic energy; inelastic collisions do not (the "lost" energy becomes heat, sound, or deformation). The IB often asks you to determine whether a collision is elastic by comparing total KE before and after.

动量 p = mv 是矢量。冲量-动量定理：FΔt = Δp，即力乘以时间等于动量变化量。这就是安全气囊和溃缩区的工作原理：：延长碰撞时间从而减小平均冲击力。当系统不受外合力时动量守恒。对于二维碰撞，将动量分解为x和y分量，各自独立守恒。弹性碰撞动能守恒；非弹性碰撞动能减少（减少的能量转化为热能、声能或形变能）。IB常考判断碰撞是否为弹性：比较碰撞前后的总动能。

Worked Example 例题

A 2.0 kg cart at 3.0 m/s collides head-on with a 1.0 kg cart at rest. They stick together. Find the final speed and the energy lost.

p_initial = 2.0 x 3.0 + 1.0 x 0 = 6.0 kg m/s
m_total = 3.0 kg, so v_final = 6.0 / 3.0 = 2.0 m/s
KE_initial = 0.5 x 2.0 x 9.0 = 9.0 J
KE_final = 0.5 x 3.0 x 4.0 = 6.0 J
Energy lost = 3.0 J (inelastic collision)

Pitfall 陷阱

Sign errors with velocity direction. Momentum is a vector -- if two objects move in opposite directions, one velocity must be negative. Always define a positive direction at the start and stick to it throughout the calculation.

4. Work, Energy and Power 功、能与功率

Work done W = Fs cos θ measures energy transferred by a force along a displacement. Only the component of force parallel to displacement does work. Kinetic energy KE = 1/2 mv^2; gravitational potential energy GPE = mgh (near Earth's surface). The work-energy theorem states W_net = ΔKE: the net work done equals the change in kinetic energy. Power P = W/t = Fv measures the rate of energy transfer. Efficiency η = useful output / total input. Conservation of mechanical energy (KE + GPE = constant) holds when only conservative forces (gravity, spring) do work; dissipative forces (friction, air resistance) cause mechanical energy to decrease. The IB expects you to use energy methods as an alternative to Newton's laws -- often much simpler for problems involving changes in height and speed.

功 W = Fs cos θ，衡量力沿位移方向转移的能量。只有与位移平行的分力才做功。动能 KE = 1/2 mv^2；重力势能 GPE = mgh（近地表面）。功能原理：合外力做功等于动能变化量 W_net = ΔKE。功率 P = W/t = Fv，衡量能量转移速率。效率 η = 有用输出 / 总输入。当只有保守力（重力、弹力）做功时，机械能守恒 KE + GPE = 常数；耗散力（摩擦力、空气阻力）使机械能减少。IB期望你用能量方法替代牛顿定律：：对于涉及高度和速度变化的题目通常更简单。

Worked Example 例题

A 0.50 kg ball is dropped from 20 m. Find its speed just before hitting the ground (ignore air resistance).

Using energy: GPE_top = mgh = 0.50 x 9.81 x 20 = 98.1 J
At ground: KE = 98.1 J = 1/2 mv^2
v = sqrt(2 x 98.1 / 0.50) = sqrt(392.4) = 19.8 m/s

Using SUVAT: v^2 = 0 + 2 x 9.81 x 20 → same result. Energy is faster for pure height-drop problems.

Pitfall 陷阱

Using KE = 1/2 mv^2 for non-rigid bodies. This formula is for translational KE of a point mass. Rolling objects also have rotational KE = 1/2 Iω^2. If the problem mentions a "rolling ball" or "rotating wheel," include rotational terms in your energy balance.

5. Circular Motion 圆周运动

Uniform circular motion is motion at constant speed along a circular path. Even though speed is constant, velocity is changing (direction changes), so there IS acceleration -- centripetal acceleration a_c = v^2/r = ω^2 r, directed toward the center. Centripetal force F_c = mv^2/r = mω^2 r is NOT a new type of force -- it is the net force pointing toward the center, provided by tension, gravity, normal reaction, or friction. Key scenarios: (a) car rounding a flat curve -- friction provides F_c; (b) car on a banked curve -- horizontal component of N provides F_c; (c) ball on a string in a vertical circle -- tension varies, minimum at top = mv^2/r - mg, maximum at bottom = mv^2/r + mg; (d) satellite in orbit -- gravity provides F_c, GMm/r^2 = mv^2/r. The IB often asks: "What provides the centripetal force in this situation?" -- always name the physical force, not "centripetal force" as a separate category.

匀速圆周运动是沿圆形轨道以恒定速率运动。尽管速率恒定，但速度方向不断改变，因此存在加速度：：向心加速度 a_c = v^2/r = ω^2 r，方向指向圆心。向心力 F_c = mv^2/r = mω^2 r 不是一种新的力，而是指向圆心的合外力，由拉力、重力、支持力或摩擦力提供。关键场景：(a) 汽车在水平弯道：：摩擦力提供向心力；(b) 汽车在倾斜弯道：：支持力的水平分量提供向心力；(c) 绳系小球在竖直平面做圆周：：拉力变化，顶点最小 T = mv^2/r - mg，底端最大 T = mv^2/r + mg；(d) 卫星轨道：：万有引力提供向心力，GMm/r^2 = mv^2/r。IB常问："在这个情境中谁提供了向心力？"：：答案必须是具体的物理力名称，而非"向心力"这个笼统说法。

Worked Example 例题

A 1200 kg car takes a flat curve of radius 50 m at 15 m/s. What is the minimum coefficient of static friction?

f_s = μ_s N = μ_s mg provides F_c
μ_s mg = mv^2 / r
μ_s = v^2 / (rg) = 225 / (50 x 9.81) = 0.46

Pitfall 陷阱

Confusing angular velocity ω (rad/s) with linear speed v. They are related by v = ωr. IB problems may give you ω and ask for F_c -- convert to v first: F_c = m(ωr)^2/r = mω^2 r. Also remember that 1 revolution = 2π radians, and period T = 2π/ω = 2πr/v.

6. IB Exam Strategy IB应试策略

Paper 1 (MCQ) 选择题

30 questions in 45 minutes for SL, 40 in 60 min for HL. No calculator for SL Paper 1. For mechanics MCQs: (1) Draw a quick FBD -- 40% of errors come from missing a force. (2) Cross out obviously wrong answers -- usually 2 are absurd. (3) Watch for unit traps -- the answer might be in cm when the question used m. (4) On graph questions, check axes labels carefully -- a v-t graph misread as s-t is the most common Paper 1 mistake.

Paper 2 简答与扩展题

Short answer + extended response. For mechanics: (1) Always show your FBD even when not explicitly asked -- it is evidence of correct reasoning and earns partial credit. (2) State assumptions clearly: "assume no air resistance," "assume string is light and inextensible." (3) Use vector notation (arrows or bold) for forces and velocities. (4) For "explain" questions, use cause-and-effect chains: "As the angle increases, mg sin θ increases, therefore the acceleration increases." (5) Check units in final answers.

7. Common Mistakes Checklist 常见错误清单

1

Sign conventions: Define positive direction once at the start. If upward is positive, g = -9.81 m/s^2. Many students use g = +9.81 in SUVAT when motion includes both upward and downward phases. 符号约定：一开始就确定正方向，全程保持一致。

2

Mass vs. weight: Mass (kg) is scalar, weight (N) is mg downward. In FBD, always use weight = mg, not "mass = 5.0 N." 质量与重力混淆：质量单位是kg，重力是mg，方向向下。

3

Third law pair identification: If Earth pulls the book down (weight), the third-law pair is "the book pulls Earth up with equal force." It is NOT the normal force from the table. 第三定律作用力与反作用力：必须作用在不同物体上。

4

Forgetting to square v in centripetal force: F_c = mv^2/r, not mv/r. The v^2 makes high-speed curves dramatically more dangerous -- doubling the speed requires quadruple the centripetal force. 向心力公式：别忘了v的平方。

5

Energy conservation without checking for non-conservative forces: If friction is present, GPE_loss ≠ KE_gain. Use work-energy theorem instead: W_net = ΔKE. 能量守恒前先检查是否有摩擦力等耗散力。

6

Unit conversion: IB often gives data in km/h, cm, g, or minutes. Convert to SI (m/s, m, kg, s) before plugging into equations. 1 km/h = 1000/3600 = 0.278 m/s. 单位转换：IB常给非国际单位，代入公式前必须统一到SI单位。

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