科里奥利力是什么，它如何让北半球的大尺度气流向右偏？
What is the Coriolis force, and why does it deflect large-scale airflow to the right in the Northern Hemisphere?
科里奥利力是地球自转带来的惯性效应，只在旋转参考系中“显现”。在北半球运动的物体相对地轴向东的分量会被甩向外，表现为向右偏转；南半球则相反。
The Coriolis force is an inertial effect of Earth's rotation, appearing only in the rotating frame. In the Northern Hemisphere, moving objects are deflected to the right; in the Southern Hemisphere, to the left.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
赵凯华 罗蔚茵,《新概念物理教程·力学》(第二版),高等教育出版社,2004
Zhao Kaihua, Luo Weiyin, New Concept Physics: Mechanics, 2nd ed., Higher Education Press, 2004
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040152012（按标识回读: 新概念物理教程 力学(第二版)）
#科里奥利力 #旋转参考系 #地球自转
单簧管和长笛吹出同一个音，为什么音色完全不同？
Why do a clarinet and a flute sound completely different when playing the same note?
音色由泛音的成分决定。管内的驻波可以同时存在多个模式：基频决定音高，而频率为基频整数倍的泛音各不相同。长笛两端开口，能支持全部谐波；单簧管一端封闭一端开口，由于边界条件限制只能保留奇次谐波，而且各泛音的强弱分布也不同。这些谐波按不同比例叠加出各自独特的波形，人耳便听出迥异的音色。
Timbre is set by the mix of overtones. Standing waves in a tube coexist in many modes: the fundamental fixes the pitch while harmonics at integer multiples of it differ between instruments. A flute, open at both ends, supports every harmonic; a clarinet, closed at one end, keeps mainly odd ones because of its boundary conditions, and the harmonic strengths differ too. These distinct harmonic blends shape each instrument's waveform, which the ear hears as different timbre.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第一卷（谐波）
The Feynman Lectures on Physics, Vol. 1 (harmonics)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#泛音 #谐波 #音色
旋转的足球踢出去后，为什么飞行轨迹会拐弯？
Why does a spinning football bend through the air instead of flying straight?
旋转的球会带动紧贴表面的空气一起转。一侧气流与旋转方向相同而加速、压强降低，另一侧被减速、压强升高，两侧的压差产生一个垂直于飞行方向的侧向力，使球弧线飞行，这就是马格努斯效应。更精确的机制是旋转改变了边界层与气流分离点的位置，伯努利关系只能给出直观图像。
A spinning ball drags a thin layer of air with it. On one side the airflow joins the rotation and speeds up, lowering pressure; on the other side it slows and pressure rises, and the net pressure difference makes a sideways force that curves the ball — the Magnus effect. The fuller mechanism involves the spin shifting the boundary layer and the separation point; Bernoulli gives only a handy intuition.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
赵凯华 罗蔚茵,《新概念物理教程·力学》(第二版),高等教育出版社,2004
Zhao Kaihua, Luo Weiyin, New Concept Physics: Mechanics, 2nd ed., Higher Education Press, 2004
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040152012（按标识回读: 新概念物理教程 力学(第二版)）
#马格努斯效应 #流体力学 #旋转
音叉的声音为什么纯净，而钢琴和小提琴弹同一个音却听得出区别？
Why does a tuning fork sound pure while piano and violin playing the same note sound different?
音叉的两个叉臂对称振动，高次谐波被强烈抑制，主要发出一个基频，所以音色纯净。琴弦或共鸣腔则同时振动出基频和许多整数倍频率的泛音，不同乐器泛音的强弱分布不同，构成各自独特的音色。耳朵对频率比例非常敏感，正是泛音比例让我们分清同音高来自哪种乐器。
A tuning fork's symmetric prongs suppress higher harmonics, so it emits almost pure fundamental and sounds clean. Strings and resonating boxes vibrate at the fundamental plus many integer-multiple overtones, and each instrument weights them differently, which is its timbre. Our ears are sensitive to frequency ratios, and those overtone patterns are what let us tell a piano from a violin at the same pitch.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第一卷（声学）
The Feynman Lectures on Physics, Vol. 1 (acoustics)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#音色 #泛音 #谐波
分析力学为什么能用“广义坐标”来描述一个复杂系统的运动，而不必死盯着每个质点的位置？
Why can analytical mechanics describe a complicated system with 'generalized coordinates' instead of tracking every particle's position?
很多约束（如杆长固定、轮子只滚动）会减少系统的真实自由度，用贴合约束的坐标（角度、弧长等）就能完整描述运动。拉格朗日方程正是基于广义坐标和能量，把牛顿力学的繁复约束化简。这样多体问题往往变得清晰许多。
Many constraints—fixed rod length, pure rolling, and so on—reduce a system's true degrees of freedom, and coordinates that fit those constraints (angles, arc lengths) fully describe the motion. Lagrange's equations build on generalized coordinates and energy to remove the messy constraint forces of Newton's approach. Multi-body problems then become far clearer.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
H. Goldstein, C. Poole & J. Safko,《Classical Mechanics》(第3版),第1章(拉格朗日形式)
H. Goldstein, C. Poole & J. Safko, 'Classical Mechanics' (3rd ed.), Ch.1 (Lagrange's formulation)
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL6211080W：Classical mechanics（首版
#广义坐标 #拉格朗日方程 #约束
物理学中的「最小作用量原理」说的是什么？
What does the principle of least action in physics state?
它说一个力学系统从初态到末态的真实路径，是使「作用量」（拉格朗日量对时间的积分）取驻值的那一条。这把牛顿三定律浓缩成一个变分原理，并可推广到电磁场、广义相对论甚至量子力学（路径积分）。哈密顿原理即作用量的一阶变分为零。
It says the actual path a system takes between two states is the one that makes the 'action' (the time integral of the Lagrangian) stationary. This condenses Newton's laws into a single variational principle and extends to fields, general relativity, and quantum mechanics (path integrals). Hamilton's principle states that the first variation of the action vanishes.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：著录仅给书名，无版次与年份；同一书名常对应多个版次，不臆测具体版本。
《力学》（朗道与栗弗席兹）§2–§3 作用量与最小作用量原理
Landau & Lifshitz, 'Mechanics', §2–§3 on action and the principle of least action
#作用量 #哈密顿原理 #变分法
双摆只有两个摆锤，运动为什么却难以预测？
A double pendulum has only two bobs — why is its motion so hard to predict?
双摆的运动方程是非线性的，它是最经典的混沌系统之一：两个初始角度哪怕只差一丝一毫，之后的轨迹也会以指数速度分道扬镳。但每个时刻的受力与运动都严格服从牛顿定律，系统本质上是确定性的——确定性和不可预测并不矛盾，因为结果对初始条件极其敏感。混沌不是无规律，而是初值敏感的有规律。
The double pendulum's equations are nonlinear, making it a classic chaotic system: two starts differing by the tiniest amount diverge exponentially in their trajectories. Yet every instant obeys Newton's laws, so the system is deterministic — determinism and unpredictability coexist because the outcome is hypersensitive to initial values. Chaos is not randomness; it is law-governed motion that is dramatically sensitive to where you start.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
赵凯华 罗蔚茵,《新概念物理教程·力学》(第二版),高等教育出版社,2004
Zhao Kaihua, Luo Weiyin, New Concept Physics: Mechanics, 2nd ed., Higher Education Press, 2004
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040152012（按标识回读: 新概念物理教程 力学(第二版)）
#双摆 #混沌 #非线性
为什么血管只要稍微变窄，血流阻力就会成倍增加？
Why does even a slight narrowing of a blood vessel sharply increase flow resistance?
层流条件下，圆管流动的阻力与管径的四次方成反比（泊肃叶定律）：半径缩小一半，阻力变成原来的16倍。所以动脉粥样硬化造成的轻度狭窄，就可能让供血明显下降。血管通过舒张、收缩来调节阻力，全身血压的调配也依赖这一规律。
For laminar flow, resistance through a tube scales inversely with the fourth power of the radius (Poiseuille's law): halve the radius and resistance jumps 16-fold. That is why even mild narrowing from atherosclerosis can cut blood supply seriously. Vessels regulate flow by dilating and constricting, and the body's blood-pressure control leans on the same law.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
赵凯华 罗蔚茵,《新概念物理教程·力学》(第二版),高等教育出版社,2004
Zhao Kaihua, Luo Weiyin, New Concept Physics: Mechanics, 2nd ed., Higher Education Press, 2004
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040152012（按标识回读: 新概念物理教程 力学(第二版)）
#泊肃叶定律 #血液流动 #流动阻力
刚体旋转的转动惯量如何计算？
How is the moment of inertia of a rigid body calculated?
转动惯量是刚体绕某轴旋转时惯性的度量，定义为各质元质量与其到轴距离平方的乘积之和 I=∫r²dm。它依赖于质量分布和转轴位置，而非只取决于总质量。同一物体对不同轴的转动惯量可以很不相同。
The moment of inertia measures a rigid body's inertia about a rotation axis, defined as the sum of each mass element times the square of its distance to the axis, I=∫r²dm. It depends on mass distribution and the axis location, not merely total mass. The same body can have very different moments about different axes.
难度 专业 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#转动惯量 #刚体 #旋转
陀螺快倒时，为什么转轴不是直接倒下去，而是绕竖直方向打转？
When a top starts to tilt, why does its axis sweep around the vertical instead of simply falling?
重力产生的力矩方向与角动量垂直，而不是与它平行。力矩的作用是改变角动量的方向而非大小，于是角动量矢量不断绕竖直方向转动，这个过程叫进动。自转越快，进动越慢，所以陀螺转得越快、倒下得越慢。同样的物理机制也解释了地球自转轴的岁差：太阳和月球的引力使地轴大约每26000年扫出一个圆锥。
Gravity's torque acts perpendicular to the angular momentum, not along it. Torque changes the direction of angular momentum rather than its magnitude, so the angular momentum vector keeps rotating around the vertical — that is precession. The faster the spin, the slower the precession, which is why a fast top topples slowly. The same physics drives Earth's axial precession: solar and lunar gravity make the pole sweep a cone roughly every 26,000 years.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第一卷（进动）
The Feynman Lectures on Physics, Vol. 1 (precession)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#进动 #力矩 #地球岁差
同样质量的两根杆，为什么长的那根更难转动？
Why is a longer rod of the same mass harder to spin about its center?
因为转动惯量不仅取决于质量大小，还取决于质量相对转轴的分布。转动惯量等于每个质量元乘以它到转轴距离的平方再求和，即I等于Σmr²。质量离轴越远，对转动惯量的贡献按距离平方放大，所以同样质量的长杆转动惯量大得多。要让长杆获得相同的角加速度，就需要更大的力矩，这就是它"转起来费劲"的原因。
Moment of inertia reflects not just how much mass there is but how it is arranged around the axis. It sums each mass element times the square of its distance from the axis, I = Σmr². Mass farther out counts quadratically more, so a longer rod of equal mass has a far larger moment of inertia. Giving it the same angular acceleration then demands more torque, which is why it feels harder to spin.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第一卷（转动惯量）
The Feynman Lectures on Physics, Vol. 1 (moment of inertia)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#转动惯量 #力矩 #角加速度
同样从斜面顶端滚下，为什么实心球总是比相同大小和质量的空心球先到终点？
Rolling down a ramp, why does a solid ball always beat a hollow ball of the same size and mass?
滚下斜面时，重力势能转化为两部分：前进的平动动能和绕轴转动的转动动能。转动动能占的比例由转动惯量决定：空心球的转动惯量大，能量更多地被"扣"在转动里，用来前进的少，于是滚得慢；实心球转动惯量小，更多能量用于前进，速度始终领先。正因为转动惯量只由形状和质量分布决定，比较它就能预言哪种物体滚得最快。
Rolling downhill, gravitational potential energy splits into translational kinetic energy for forward motion and rotational kinetic energy about the axis. The rotational share is set by the moment of inertia: a hollow ball's larger moment of inertia locks more energy into rotation, leaving less for forward motion, so it lags, while a solid ball's smaller one puts more energy into translation and always stays ahead. Since moment of inertia depends only on shape and mass distribution, comparing it predicts which object wins.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
赵凯华 罗蔚茵,《新概念物理教程·力学》(第二版),高等教育出版社,2004
Zhao Kaihua, Luo Weiyin, New Concept Physics: Mechanics, 2nd ed., Higher Education Press, 2004
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040152012（按标识回读: 新概念物理教程 力学(第二版)）
#转动惯量 #滚动 #能量转化
歌剧歌手真能用高音震碎玻璃杯吗？为什么？
Can an opera singer really shatter a wine glass with a high note, and how?
能，但很不容易。每个玻璃杯都有自己的固有频率，当歌声频率恰好等于它时，每一圈振动都在前一圈的基础上叠加，振幅越摆越大，这就是共振。玻璃在大振幅下反复变形，承受不住应力就会碎裂。歌手通常需要声音足够响，还要正对杯口附近空气。
Yes, but it is difficult. Every glass has a natural frequency; when the note matches it, each vibration adds to the previous one and the amplitude builds up — resonance. Sustained large-amplitude flexing finally overstresses the glass and it shatters. The singer must be loud and aim at the air right by the rim.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
赵凯华 罗蔚茵,《新概念物理教程·力学》(第二版),高等教育出版社,2004
Zhao Kaihua, Luo Weiyin, New Concept Physics: Mechanics, 2nd ed., Higher Education Press, 2004
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040152012（按标识回读: 新概念物理教程 力学(第二版)）
#共振 #固有频率 #声学
气垫船为什么能离开水面行驶？
Why can a hovercraft travel above the surface instead of floating on it?
气垫船从船底向下喷出高压空气，在船体和水面之间托起一层薄薄的气垫。高压空气的压强产生向上的力托住船体，同时空气不断从底部边缘泄出，把船与水面隔开。船和水之间几乎只剩空气，摩擦极小，所以它在水面、泥地、沙地甚至平地上都能滑行。
A hovercraft blows high-pressure air downward, trapping a thin cushion between the hull and the surface. The pressure supports the craft while air leaks out around the edges, isolating it from the water. With almost no friction between craft and surface, it can glide over water, mud, sand, and even flat ground.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第二卷（流体力学）
The Feynman Lectures on Physics, Vol. 2 (fluid dynamics)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#气垫 #压强 #摩擦
1940年塔科马海峡大桥为什么会剧烈扭动着塌掉？
Why did the Tacoma Narrows Bridge twist itself apart in 1940?
大桥在中等风速下发生了「气动弹性颤振」：风绕过桥面时产生的周期性涡旋与结构本身的扭转振动耦合，把能量不断喂给振动，振幅越来远大直至断裂。它常被通俗讲成「共振」，但更准确的机制是流体与结构之间的自激振荡，而非简单的外力频率等于固有频率。
At moderate wind the bridge underwent aeroelastic flutter: vortices shed by the wind coupled with the deck's torsional vibration, continuously pumping energy into the motion until the amplitude grew catastrophic. It is often loosely called 'resonance,' but the precise mechanism is self-excited oscillation between fluid and structure, not a simple external-frequency-equals-natural-frequency case.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
美国国家档案馆保存的塔科马海峡大桥倒塌影像（1940）；Blevins《流致振动》(Flow-Induced Vibration)
U.S. National Archives film of the Tacoma Narrows Bridge collapse (1940); Blevins, Flow-Induced Vibration (Krieger)
独立核验依据 · Independent verification: 核验依据 1 ISBN 9787030698100（豆瓣书目条目: 流致振动）；本条出处含多部著作，此标识只担保上面点名的这部
#颤振 #气动弹性 #涡旋脱落
花样滑冰运动员旋转时收拢手臂，为什么转速会突然加快？
Why do figure skaters spin faster when they pull their arms in?
因为角动量守恒。滑冰时几乎没有外力矩作用，运动员身体的总角动量保持不变，而角动量等于转动惯量乘以角速度。收拢手臂使质量靠近转轴、转动惯量变小，角速度就必须相应增大；张开手臂时转动惯量变大，转速又会慢下来。这是角动量守恒最直观的演示。
Conservation of angular momentum is at work. With essentially no external torque, the skater's total angular momentum stays constant, and angular momentum equals moment of inertia times angular velocity. Pulling the arms in brings mass closer to the spin axis, shrinking the moment of inertia, so the angular velocity must rise; spreading the arms raises it again and slows the spin.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第一卷（转动）
The Feynman Lectures on Physics, Vol. 1 (rotation)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#角动量守恒 #转动惯量 #花样滑冰
为什么单摆只有在摆角很小时才近似“等时”，摆角一大周期就明显变长？
Why is a pendulum only approximately 'isochronous' at small angles, and why does the period grow noticeably at large angles?
小角度时正弦函数可近似为角度本身，运动方程退化成简谐振动，周期与振幅无关。摆角变大后这个近似失效，回复力相对变小，需用椭圆积分描述，周期随振幅增加而变长。这正是大钟摆需要补偿的原因。
At small angles the sine can be approximated by the angle itself, reducing the equation to simple harmonic motion whose period is independent of amplitude. At large angles this approximation breaks down, the restoring force is relatively weaker, and the period—given by an elliptic integral—grows with amplitude. That is why large pendulum clocks need compensation.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
S. T. Thornton & J. B. Marion,《Classical Dynamics of Particles and Systems》(第5版,Brooks/Cole,2004),第4章(非线性振动与混沌)
S. T. Thornton & J. B. Marion, 'Classical Dynamics of Particles and Systems' (5th ed., Brooks/Cole, 2004), Ch.4 (Nonlinear Oscillations and Chaos)
独立核验依据 · Independent verification: 核验依据 1 ISBN 9788131518472 (2003)
#单摆 #等时性 #椭圆积分
势能曲线如何决定物体的运动？
How do potential energy curves determine a body's motion?
在一维问题中，物体的总能量固定，动能等于总能量减去势能。势能曲线的谷底对应稳定平衡，顶峰对应不稳定平衡，势垒高度决定能否越过（或隧穿）。借助势能图可以直观判断运动范围与转折点。
In one-dimensional problems the total energy is fixed and kinetic energy equals total minus potential energy. Valleys in the potential curve are stable equilibria, peaks unstable ones, and barrier height decides whether motion can cross (or tunnel). Potential diagrams intuitively show the range and turning points of motion.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#势能 #平衡 #势垒
为什么旋转的陀螺能保持直立不倒？
Why can a spinning top stay upright instead of falling?
高速旋转的陀螺具有很大的角动量，方向趋于稳定。当重力试图让它倾倒时，不会直接倒下，而是产生进动——自转轴缓慢绕竖直方向画圈。这种陀螺稳定性广泛应用于导航陀螺仪。
A fast-spinning top has large angular momentum whose direction tends to stay fixed. When gravity tries to tip it, instead of falling it precesses—the spin axis slowly circles the vertical. This gyroscopic stability is widely used in navigation gyroscopes.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#陀螺 #角动量 #进动
猫从高处落下时，为什么能在空中迅速翻身、四脚着地？
Why can a falling cat twist in midair and land on its feet?
猫利用「非刚体转动」技巧：先让前半身与后半身朝相反方向弯曲，分别绕不同轴转动，使总角动量保持为零（空中无外力矩）。它收缩前腿、伸展后腿来交替改变转动惯量，从而在不违反角动量守恒的前提下翻转身体。落地前再伸直四肢增大转动惯量、降低转速，平稳着地。
A cat uses a 'non-rigid body' trick: it bends its front and rear halves in opposite directions around different axes so the total angular momentum stays essentially zero (no external torque in free fall). By tucking the front legs and extending the rear ones, it changes its moment of inertia alternately to rotate each half. Just before landing it extends all four legs to raise the moment of inertia and slow the spin for a soft touchdown.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-11-02
来源 · Source
《经典力学》（赫伯特·戈德斯坦、普尔、萨夫科，第3版）关于非刚体角动量守恒的论述
Goldstein, Poole & Safko, 'Classical Mechanics' (3rd ed.), on angular momentum conservation of non-rigid bodies
独立核验依据 · Independent verification: 核验依据 1 ISBN 9787030763150（豆瓣书目条目: 经典力学）
#角动量守恒 #猫翻身反射 #转动惯量
救护车从身边驶过时，警笛声为什么由高变低？
Why does an ambulance siren change from high to low as it passes by?
声源向你靠近时，声波被挤在一起，你每秒接到的波峰更多，听到的频率变高、音调尖锐；声源远离时，波被拉长，频率变低。这就是多普勒效应，相对速度越大，音调变化越明显。测速雷达和天文红移用的也是同一个原理。
When the source moves toward you, its waves bunch up so more crests reach you each second and the pitch sounds high; as it moves away the waves stretch and the pitch drops. That is the Doppler effect, stronger the faster the relative motion. Police radar and the redshift of distant galaxies use the same idea.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
赵凯华 罗蔚茵,《新概念物理教程·力学》(第二版),高等教育出版社,2004
Zhao Kaihua, Luo Weiyin, New Concept Physics: Mechanics, 2nd ed., Higher Education Press, 2004
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040152012（按标识回读: 新概念物理教程 力学(第二版)）
#多普勒效应 #声波 #频率
库仑定律与牛顿引力定律有哪些相似与不同？
What are the similarities and differences between Coulomb's law and Newton's law of gravity?
两者都是与距离平方成反比、与荷成正比的中心力。但电力有正负两种电荷、可相吸或相斥，引力只有质量这一种荷且总是相吸；而且电力通常比引力强得多。它们都体现了几何上的平方反比结构。
Both are central forces inversely proportional to the square of distance and proportional to a charge. But electricity has positive and negative charges that attract or repel, while gravity has only mass and always attracts; and electricity is usually far stronger. Both embody the geometric inverse-square structure.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#库仑定律 #万有引力 #平方反比
为什么谐振子几乎无处不在？
Why is the harmonic oscillator found almost everywhere?
任何在稳定平衡位置附近的系统，其势能都可近似为二次函数，运动方程退化为简谐振动。从分子振动、晶格到电路和量子场，谐振子是普遍模型。它也是少数能精确求解的量子系统之一。
Any system near a stable equilibrium has a potential approximately quadratic, reducing its equation to simple harmonic motion. From molecular vibrations and lattices to circuits and quantum fields, the harmonic oscillator is a universal model. It is also among the few quantum systems solved exactly.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#谐振子 #简谐振动 #平衡
以相同初速斜抛，为什么 45° 发射角通常射程最远？
For the same launch speed, why does a 45° launch angle usually give the maximum range?
射程正比于 sin(2θ)，当 2θ=90° 即 θ=45° 时正弦值最大。不过这忽略了空气阻力，实际最远角度会略小于 45°。
The range is proportional to sin(2θ), which peaks when 2θ=90°, i.e. θ=45°. This ignores air resistance; in reality the optimal angle is a bit below 45°.
难度 进阶 · 适合 小学低段(6-8)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
赵凯华 罗蔚茵,《新概念物理教程·力学》(第二版),高等教育出版社,2004
Zhao Kaihua, Luo Weiyin, New Concept Physics: Mechanics, 2nd ed., Higher Education Press, 2004
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040152012（按标识回读: 新概念物理教程 力学(第二版)）
#抛体运动 #射程 #三角函数
为什么角动量会守恒？
Why is angular momentum conserved?
角动量守恒源于空间旋转对称性：物理定律不随方向改变。只要系统不受外力矩，其总角动量就保持不变。花样滑冰运动员收臂转得更快，正是这一守恒的直观体现。
Angular momentum conservation follows from the rotational symmetry of space: the laws do not depend on direction. As long as no external torque acts, total angular momentum stays constant. A skater spinning faster when pulling in their arms is an intuitive demonstration.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#角动量守恒 #旋转对称 #力矩
傅科摆是怎样证明地球在自转的？
How does a Foucault pendulum demonstrate that the Earth rotates?
傅科摆在巴黎先贤祠于1851年首次展出：由于地球自转，在惯性系看来摆动平面保持固定，而地面随地球转走，于是摆的摆动方向相对地面缓缓转动。转动的角速度随纬度变化，在两极一天转一圈、在赤道不转。它无需仰望星空，就在室内证明了地球自转。
First shown at the Panthéon in Paris in 1851, the Foucault pendulum swings in a fixed plane in an inertial frame while the ground rotates beneath it, so the swing direction appears to rotate relative to the floor. The rotation rate depends on latitude—a full turn per day at the poles, none at the equator—proving Earth's rotation without looking at the sky.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：著录仅给书名，无版次与年份；同一书名常对应多个版次，不臆测具体版本。
法国巴黎先贤祠傅科摆演示（L. 傅科，1851）；《力学》（朗道）§3 非惯性系
Foucault pendulum demonstration at the Panthéon, Paris (L. Foucault, 1851); Landau 'Mechanics' §3 on non-inertial frames
#傅科摆 #地球自转 #科里奥利力
为什么下落物体最终会达到一个不变的终端速度？
Why does a falling object eventually reach a constant terminal velocity?
物体下落时空气阻力随速度增大，当阻力与重力平衡时合外力为零，加速度消失，速度便稳定在某个终值。终端速度正比于重力与阻力系数之比的平方根，因此重的或流线型的物体通常更快。
As an object falls, air drag grows with speed until it balances the weight, leaving zero net force and zero acceleration, so the speed settles at a fixed value. Terminal velocity scales with the square root of weight over the drag coefficient, so denser or more streamlined bodies fall faster.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
Kleppner 与 Kolenkow《力学导论》
Kleppner & Kolenkow, An Introduction to Mechanics
独立核验依据 · Independent verification: 核验依据 1 ISBN 9780070854239 (2018)
#终端速度 #空气阻力 #牛顿力学
为什么挂在弹簧下的小球会一直以同一个周期上下振动？
Why does a mass on a spring keep oscillating with the same period?
弹簧被拉长时，弹力指向平衡位置且大小与位移成正比。小球离平衡位置越远，被拉回的力越大；冲过平衡点后又被反向拉回，于是形成往复运动。因为弹力随位移线性变化，这种振动的周期固定在T等于2π乘以根号下m比k，与振幅无关，这个"等时性"被广泛用在钟表和精密仪器里。
When the spring stretches, the restoring force points back to equilibrium and grows with displacement. The farther the mass is displaced, the harder it is pulled back, and after overshooting it is dragged the other way, giving oscillation. Because the force scales linearly with displacement, the period is fixed at T = 2π√(m/k), independent of amplitude — an "isochronism" exploited in clocks and precision instruments.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第一卷（谐振子）
The Feynman Lectures on Physics, Vol. 1 (the harmonic oscillator)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#谐振子 #周期 #弹力
伯努利原理如何解释飞机机翼产生升力？
How does Bernoulli's principle help explain lift on an airplane wing?
机翼上表面比下表面弯曲更长，气流流过上表面速度更快、压强更低，上下压强差便产生向上的升力。需要补充的是，升力更完整来自机翼偏转气流（牛顿第三定律）与压强分布的共同作用，伯努利关系只是描述流速与压强此消彼长的一部分。
A wing's upper surface is more curved and longer than the lower one, so air moves faster over the top and the pressure drops; the pressure difference produces upward lift. More completely, lift arises from both the wing deflecting air downward (Newton's third law) and the pressure distribution, with Bernoulli's relation describing the speed–pressure trade-off.
难度 进阶 · 适合 小学低段(6-8)
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#伯努利原理 #升力 #流体力学
什么是相空间？
What is phase space?
相空间用位置和动量共同描述一个系统的状态：一个质点由(q,p)一个点表示，n个自由度系统则处在2n维空间。它让我们能整体地看待演化，是统计力学和哈密顿力学的核心语言。
Phase space describes a system's state by both position and momentum: one point (q,p) represents a single particle, and an n-degree-of-freedom system lives in 2n dimensions. It lets us see evolution as a whole and is the core language of statistical and Hamiltonian mechanics.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#相空间 #状态 #哈密顿
单摆的周期主要由什么决定，和摆球重量有关吗？
What mainly determines a pendulum's period, and does it depend on the bob's mass?
在小幅摆动下，单摆周期只取决于摆长和重力加速度，与摆球质量无关。公式 T=2π√(L/g) 表明周期随摆长平方根增大而变长。
For small swings, a pendulum's period depends only on its length and gravity, not on the bob's mass. The formula T=2π√(L/g) shows the period grows with the square root of the length.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》
The Feynman Lectures on Physics
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#单摆 #周期 #简谐运动
风琴管为什么能发出一个固定的音高？
Why does an organ pipe sound a fixed pitch?
风琴管内的空气被气流激发振动，而管口两端的边界条件只允许特定波长的波在管内稳定存在，形成驻波。这些驻波中频率最低的一个决定基音，频率由管长和声速决定：管子越长，驻波的波长越长、音调越低。长笛等管乐器都用同样的驻波机制来定音。
Air blown into an organ pipe excites vibrations, and the boundary conditions at the ends allow only certain wavelengths to persist as standing waves. The lowest-frequency mode sets the fundamental, whose pitch follows from the pipe length and the speed of sound: longer pipes hold longer-wavelength waves and sound lower. Flutes and other wind instruments use this same standing-wave mechanism for pitch.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第一卷（驻波）
The Feynman Lectures on Physics, Vol. 1 (standing waves)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#驻波 #管乐器 #音高
抖动的绳子把波传出去时，绳上的每一小段到底在做什么运动？
When a pulse travels along a rope, what exactly does each small piece of the rope do?
波传播的是能量和扰动，而不是物质本身。抖一下绳子，被拉动的绳段通过张力去拉动相邻的绳段，扰动像多米诺骨牌一样依次传递；每个质点只在平衡位置附近上下振动，并不跟着波一起前进。波速由绳子的张力和线密度共同决定：张力越大、绳子越轻，波传得越快。
A wave transfers energy and disturbance, not matter. When you flick a rope, the pulled segment drags its neighbor through tension, so the disturbance passes down the line like dominoes; each particle merely oscillates about its own equilibrium and does not travel with the wave. The speed is set by the tension and linear density — higher tension and a lighter rope make it faster.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第一卷（波动）
The Feynman Lectures on Physics, Vol. 1 (waves)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#机械波 #传播 #波速
闪电只是一瞬间，为什么雷声却轰隆隆持续好几秒？
Lightning is over in an instant, so why does thunder rumble for several seconds?
闪电通道有数公里长，各段放电发出声音的时间略有先后，不同位置传来的声音到达耳朵的时间也不同；加上声音在云层和山体间来回反射，许多迟到的回声叠加在一起，就汇成了持续的隆隆声。另外光速远大于声速，所以我们总是先看到闪电、过一会儿才听到雷声。
A lightning channel is kilometers long, so its parts produce sound at slightly different moments, and those sounds arrive over a spread of delays; reflections off clouds and hills add late echoes, all blending into a long rumble. And because light far outruns sound, we always see the flash well before we hear the thunder.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#声速 #回声 #雷声
为什么吉他弦有粗有细、有松有紧，弹出的音调就不一样？
Why do guitar strings of different thickness and tension produce different notes?
拨动琴弦后，弦上会形成驻波，但只有弦长为半波长整数倍的振动方式能稳定存在（两端固定，λ=2L/n），其中频率最低的基频决定音调。弦越短、越细、绷得越紧，振动越快，频率越高、声音越尖；又粗又松的长弦振动慢，声音低沉。
A plucked string vibrates in standing-wave patterns; with both ends fixed, only modes whose wavelength satisfies λ = 2L/n can persist (the string length holds a whole number of half-wavelengths), and the lowest one, the fundamental, sets the pitch. A shorter, thinner, or tighter string vibrates faster and sounds higher; a long, thick, loose string vibrates slowly and sounds low.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第一卷（波动）
The Feynman Lectures on Physics, Vol. 1 (waves)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#驻波 #基频 #弦振动
地震时，为什么远处的高楼会比矮房子摆得更厉害？
Why do tall buildings sway more than low ones in a distant earthquake?
每个建筑都有自己的固有频率，地震波抵达时，如果它的主要频率和建筑固有频率接近，就会发生共振，摆动幅度不断累积。高层建筑自振频率低、周期长，对来自远方的低频长周期地震波往往更敏感，所以可能摆得很厉害。工程设计正是靠避开共振频率、加装隔震装置来保护建筑。
Every building has a natural frequency. When seismic waves arrive near that frequency, resonance sets in and sway builds up. Tall buildings have low natural frequencies and long periods, so distant low-frequency waves can hit them harder than squat buildings. Engineers avoid resonant frequency ranges and add base isolators precisely to protect structures.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
赵凯华 罗蔚茵,《新概念物理教程·力学》(第二版),高等教育出版社,2004
Zhao Kaihua, Luo Weiyin, New Concept Physics: Mechanics, 2nd ed., Higher Education Press, 2004
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040152012（按标识回读: 新概念物理教程 力学(第二版)）
#共振 #固有频率 #隔震
为什么香烟冒出的烟一开始笔直上升，到高处就变得弯弯曲曲？
Why does smoke rise in a smooth straight column and then break into twisting swirls?
这由雷诺数决定——它综合了流速、尺寸和流体黏性。雷诺数小时，扰动会被黏性压制，流动平稳有序（层流）；雷诺数超过临界值，微小扰动被放大，流动变成混乱的涡旋（湍流）。烟柱先直后乱，就是层流向湍流的转变。飞机机翼、管道里的水流也都受这条规律支配。
The Reynolds number decides it — a single dimensionless value combining flow speed, size, and viscosity. At small values, viscosity damps disturbances and the flow stays smooth (laminar); beyond a critical value, tiny jitters amplify into chaotic eddies (turbulence). A smoke plume going straight then messy is that very transition, and it rules airplane wings and pipe flow too.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第二卷（湍流）
The Feynman Lectures on Physics, Vol. 2 (turbulence)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#湍流 #雷诺数 #层流
为什么同样质量下，质量离转轴越远转起来越费劲？
Why is it harder to spin an object when its mass is farther from the axis?
转动惯量衡量物体抵抗转动变化的程度，等于各质量元乘其到转轴距离平方的求和。质量分布越靠外，转动惯量越大，加速转动所需力矩也越大。
The moment of inertia measures resistance to changes in spin and equals the sum of each mass element times the square of its distance to the axis. The farther the mass sits from the axis, the larger this is, needing more torque to spin up.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》
The Feynman Lectures on Physics
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#转动惯量 #力矩 #刚体
火箭在真空中没有空气可推，为什么还能前进？
How can a rocket move forward in a vacuum where there is nothing to push against?
火箭依靠动量守恒推进：燃料以高速向后喷出，获得向后的动量，火箭主体便得到大小相等、方向相反的向前动量。它从头到尾不需要空气来反推，这正是火箭能在太空飞行而飞机发动机不能的原因。火箭每次喷出燃气的速度和质量决定了它速度的变化量。
Rockets work by momentum conservation: fuel is expelled backward at high speed, giving the rocket body an equal and opposite forward momentum. No air is ever needed to push against — that is why rockets fly in space while air-breathing engines cannot. Each burst's exhaust speed and mass set how much the rocket's velocity changes.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#动量守恒 #火箭 #反作用力
两颗台球碰撞时，为什么动量一定守恒，而动能却不一定守恒？
When billiard balls collide, why is momentum always conserved but kinetic energy often is not?
碰撞时如果外力可以忽略，总动量必然守恒，因为动量守恒是牛顿第三定律的直接推论：两球之间的力大小相等、方向相反，作用时间相同，动量变化正好抵消。而动能的一部分会在碰撞中转化为热和声音，所以只有完全弹性碰撞才动能守恒。计算碰撞后速度时，通常要用动量守恒加能量守恒两个方程一起解。
During a collision with negligible external forces, total momentum must be conserved because it follows directly from Newton's third law: the forces the balls exert on each other are equal, opposite and last equally long, so their momentum changes cancel. Kinetic energy, though, partly turns into heat and sound, so it is conserved only in perfectly elastic collisions. Solving for the post-collision speeds usually needs the momentum and energy equations together.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
赵凯华 罗蔚茵,《新概念物理教程·力学》(第二版),高等教育出版社,2004
Zhao Kaihua, Luo Weiyin, New Concept Physics: Mechanics, 2nd ed., Higher Education Press, 2004
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040152012（按标识回读: 新概念物理教程 力学(第二版)）
#动量守恒 #碰撞 #动能
为什么对着瓶口吹气会发出嗡嗡声，水越满声音越高？
Why does blowing across a bottle top make a hum, and why does filling it raise the pitch?
气流掠过瓶口产生不稳定，瓶内的空气像弹簧一样被反复压缩、回弹，形成空气柱振动，这叫亥姆霍兹共振。瓶内空气越少（水越多），这根空气弹簧越硬，振动越快，音调越高。往瓶里倒水时声音越变越高，正是这个原因。
The blown air disturbs the mouth of the bottle, and the air inside compresses and rebounds like a spring, setting up a vibration — Helmholtz resonance. The less air remains (the more water), the stiffer the air spring and the higher the pitch. That is why the note climbs as you fill the bottle.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第一卷（声学）
The Feynman Lectures on Physics, Vol. 1 (acoustics)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#亥姆霍兹共振 #空气柱 #音调
蝙蝠在漆黑的洞里为什么不会撞墙？
How do bats fly through pitch-dark caves without crashing?
蝙蝠发出人类听不见的高频超声波，声波撞到物体反射回来，蝙蝠根据回声到达的方向和时间，判断出物体的方位与距离，这叫声呐（回声定位）。超声波的频率越高，能分辨的物体就越小。海豚在水中也用同样的方式看周围世界。
Bats emit high-frequency ultrasonic calls inaudible to us; the echoes bouncing off objects return, and the bat reads their direction and delay to map position and distance — echolocation. Higher frequencies resolve smaller objects. Dolphins use the same trick to see underwater.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
赵凯华 罗蔚茵,《新概念物理教程·力学》(第二版),高等教育出版社,2004
Zhao Kaihua, Luo Weiyin, New Concept Physics: Mechanics, 2nd ed., Higher Education Press, 2004
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040152012（按标识回读: 新概念物理教程 力学(第二版)）
#超声波 #回声定位 #声呐
为什么轻轻推秋千，只要时机对，就能越荡越高？
Why does a gentle push at the right moment make a swing go higher and higher?
每个系统都有自己的固有频率，秋千的固有频率由摆长决定。当你推它的节奏恰好等于这个频率时，每次推力都顺着运动方向给秋千补充能量，振幅不断增大，这就是共振。如果乱推一气，推力时而助力时而抵消，秋千就荡不起来。同样的道理，强烈的风或地震也可以让大桥和楼房剧烈晃动甚至毁坏。
Every system has its own natural frequency, and a swing's is set by its length. When your pushes match that frequency, each push adds energy in the direction of motion and the amplitude grows — that is resonance. Pushing at random times helps and hinders in turn, so the swing never builds up. For the same reason, strong winds or earthquakes can make bridges and buildings shake violently or fail.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#共振 #固有频率 #振幅
水龙头流出的水柱为什么越往下越细？
Why does a stream of water from a tap get thinner the farther it falls?
水下落时被重力不断加速，速度越来越快；而单位时间流过任一截面的水量必须相同（连续性方程），速度与截面积成反比，所以水流越往下越细。河水在峡谷变窄处流得更急，也是同一道理。
Falling water accelerates under gravity, but the same volume must cross every cross-section each second (the continuity equation); since speed and area are inversely related, the faster stream gets thinner. Rivers running faster through a narrow gorge work the same way.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
赵凯华 罗蔚茵,《新概念物理教程·力学》(第二版),高等教育出版社,2004
Zhao Kaihua, Luo Weiyin, New Concept Physics: Mechanics, 2nd ed., Higher Education Press, 2004
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040152012（按标识回读: 新概念物理教程 力学(第二版)）
#连续性方程 #流速 #重力
弹性碰撞与非弹性碰撞的根本区别是什么？
What is the essential difference between elastic and inelastic collisions?
弹性碰撞中动能与动量都守恒，碰撞前后物体总动能不变；非弹性碰撞里动量仍守恒但部分动能转化为内能、声或形变能。完全非弹性碰撞指两物体碰后粘在一起，动能损失最大。
In an elastic collision both momentum and kinetic energy are conserved, so the total kinetic energy is unchanged. In an inelastic collision momentum is still conserved but some kinetic energy converts to internal energy, sound, or deformation; the perfectly inelastic case (objects stick together) loses the most.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
Feynman《物理学讲义》第一卷；Taylor《经典力学》
Feynman, The Feynman Lectures on Physics (Vol. I); Taylor, Classical Mechanics
独立核验依据 · Independent verification: 核验依据 1 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#弹性碰撞 #非弹性碰撞 #动量守恒
为什么自行车在前进时比静止时更稳？
Why is a moving bicycle more stable than a stationary one?
自行车的稳定来自前轮叉的几何“轨迹”（caster）效应与轮子的陀螺进动，二者在车轮转动时共同产生回正力矩，把车身拉回竖直。Jones 在 1970 年的实验表明，即便去掉陀螺效应，前叉几何本身已足以提供大部分稳定性。
Bicycle stability comes from the caster geometry of the front fork plus the gyroscopic precession of the wheels, which together generate a restoring torque that returns the frame toward upright when moving. Jones showed in 1970 that the fork geometry alone provides most of the stability even without gyroscopic effects.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：著录含书名，但缺版次 / 出版社 / 年份中的一部分，需编辑补全后才能做独立比对。
Jones《今日物理》1970 年《自行车的稳定性》
Jones, 'The stability of the bicycle', Physics Today (1970)
#自行车稳定性 #陀螺效应 #轨迹几何
为什么对着两张平行悬挂的纸片中间吹气，纸片反而会靠拢？
Why do two hanging sheets of paper move toward each other when you blow between them?
吹气让两纸之间的空气流速加快，压强随之降低；纸片外侧的空气流速慢、压强大，于是大气压把纸片推向中间。这就是伯努利原理：流体速度越快，压强越低。火车站的黄色安全线、飞机机翼升力都与它有关。
Blowing speeds up the air between the sheets and lowers its pressure, while the slower air outside stays at higher pressure, so atmospheric pressure pushes the sheets together. This is Bernoulli's principle: faster flow, lower pressure. The yellow safety line at train platforms and aircraft lift both rely on it.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第二卷（流体力学）
The Feynman Lectures on Physics, Vol. 2 (fluid dynamics)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#伯努利原理 #流体 #压强
飞机翅膀为什么能产生向上的升力？
How does an airplane wing generate the upward force that lifts it?
机翼以一定迎角切开空气，把气流向下偏折，根据牛顿第三定律，空气反过来把机翼向上推；同时气流流过弯曲的上表面时加速、压强降低，上下表面形成压强差，也贡献向上的力。两者加起来足以抵消重力，飞机就能飞起来。
At a small angle of attack the wing deflects air downward, and by Newton's third law the air pushes the wing upward; meanwhile flow over the curved top surface speeds up and drops in pressure, so the pressure difference across the wing also pushes up. Together they beat gravity and the plane flies.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#机翼升力 #伯努利原理 #牛顿第三定律
打台球时，为什么母球能把几乎全部速度传给静止的球？
In billiards, why can the cue ball pass almost all its speed to a stationary ball?
两球质量相近、正碰且近似弹性时，动量和动能都守恒，于是母球停下、目标球以原速前进。斜碰则会按动量方向分配速度。
When two equal-mass balls collide head-on nearly elastically, both momentum and kinetic energy are conserved, so the cue ball stops and the target moves off at the original speed. Glancing hits split the velocity by direction.
难度 进阶 · 适合 小学低段(6-8)
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#弹性碰撞 #动量守恒 #台球
质心是什么，为什么研究多体系统时常围绕它来分析运动？
What is the center of mass, and why do we often analyze motion around it for many-body systems?
质心是系统质量的加权平均位置，外力只决定质心的加速度（等于总外力除以总质量）。无论系统内部怎样翻滚碰撞，质心都沿简单的抛物线或直线轨道运动。
The center of mass is the mass-weighted average position of a system; only external forces change its acceleration (total force over total mass). No matter how the parts tumble, the center of mass follows a simple parabola or straight line.
难度 进阶 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#质心 #动量 #多体系统
安全气囊是怎么把撞车时的冲击力大大减小的？
How do airbags reduce the enormous force of a car crash?
撞击时人的动量变化量是固定的，而冲量等于力乘以作用时间。气囊在碰撞瞬间迅速充气，让人的头部和胸口在更长的距离和更长的时间内逐渐减速，作用时间被拉长，平均冲击力就大大降低。这和从高处跳下时弯曲膝盖、落在软垫上是同一个道理。
A passenger's change in momentum during a crash is fixed, and impulse equals force times time. An airbag inflates instantly so the head and chest decelerate gradually over a longer distance and time; stretching the interaction time shrinks the average force dramatically. It is the same principle as bending your knees or landing on a cushion after a high jump.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
赵凯华 罗蔚茵,《新概念物理教程·力学》(第二版),高等教育出版社,2004
Zhao Kaihua, Luo Weiyin, New Concept Physics: Mechanics, 2nd ed., Higher Education Press, 2004
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787040152012（按标识回读: 新概念物理教程 力学(第二版)）
#冲量 #缓冲 #安全气囊
为什么弹簧振子的往复运动被称为"简谐运动"？
Why is the back-and-forth motion of a mass on a spring called simple harmonic motion?
弹簧对物体的弹力与它偏离平衡位置的距离成正比，方向总是指向平衡位置，即F等于-kx。在这样的线性回复力作用下，物体的位移随时间按正弦规律变化，整个运动只由单一频率决定，因此称为"简谐"。它的周期只取决于质量和弹簧的劲度系数，与振幅无关，这正是机械钟表能稳定走时的基础。
The spring's force is proportional to the displacement and always points back to equilibrium: F = −kx. Under such a linear restoring force the displacement follows a sine wave at a single frequency, which is why the motion is called "simple harmonic." Its period depends only on the mass and spring constant, never the amplitude, which is the basis for stable mechanical timekeeping.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第一卷（谐振子）
The Feynman Lectures on Physics, Vol. 1 (the harmonic oscillator)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#简谐运动 #弹簧振子 #周期
坐着不动秋千会慢慢停下来，可小孩是怎么让秋千越荡越高的？
A swing slows and stops if you sit still — how do children pump it ever higher?
秋千有自己的固有周期，小孩在荡到合适位置时站起、蹲下，改变重心与有效摆长，等于每个周期都在恰到好处的时机给秋千输入能量，这称为参数共振。时机对了振幅越荡越大，时机错了（乱晃）反而耗能。任何振荡系统都有这个规律：顺着节奏推，振幅就放大。
A swing has its own natural period, and by standing and squatting at the right moments a child shifts the center of mass and the effective length, feeding energy into the motion each cycle — parametric resonance. Well-timed pumping makes the amplitude grow; badly timed wiggling drains it. Every oscillating system obeys this rule: push in rhythm and the swing builds up.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第一卷（共振）
The Feynman Lectures on Physics, Vol. 1 (resonance)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#参数共振 #固有周期 #能量输入
玉米淀粉加水调成的「欧不裂」为什么一打就硬、慢慢放却像液体？
Why does a cornstarch–water 'oobleck' stiffen when struck but flows when handled gently?
它是剪切增稠的非牛顿流体：静止或慢速移动时颗粒间有润滑的液态空隙，表现得像水；快速冲击时颗粒来不及重新排列，相互挤压形成瞬时「固体」网络。这类流体的黏度随剪切速率变化，不遵守牛顿黏性定律，所以能让人跑过表面、一停就陷下去。
It is a shear-thickening non-Newtonian fluid: at rest or slow motion the starch grains are separated by lubricating fluid and it behaves like a liquid, but a fast impact crowds the grains before they can rearrange, forming a momentary solid-like network. Its viscosity changes with shear rate, breaking Newton's law of viscosity—so you can run across it yet sink if you stop.
难度 入门 · 适合 大众
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：著录仅给书名，无版次与年份；同一书名常对应多个版次，不臆测具体版本。
美国物理联合会（AIP）《流变学杂志》关于剪切增稠悬浮液的实验研究
American Institute of Physics (AIP), Journal of Rheology, experimental studies on shear-thickening suspensions
#非牛顿流体 #剪切增稠 #黏度
摩擦力来自哪里？
Where does friction come from?
摩擦力主要来源于接触面微观凹凸的相互咬合，以及表面分子间的电磁吸引。它总是阻碍相对运动或相对运动趋势，并把机械能转化为热。虽然常被近似为常数，实际摩擦与材料、粗糙度和速度都有关。
Friction mainly comes from the interlocking of microscopic surface roughness and from electromagnetic attractions between surface molecules. It always opposes relative motion or its tendency and converts mechanical energy into heat. Though often approximated as constant, real friction depends on material, roughness, and speed.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#摩擦力 #接触面 #热
为什么不同质量的物体自由下落加速度几乎相同？
Why do falling objects of different mass accelerate almost identically?
在忽略空气阻力时，重力与惯性质量成正比，二者抵消使所有物体的加速度都等于当地重力加速度 g。这一“等效原理”最早由伽利略用斜面实验揭示，后来成为爱因斯坦广义相对论的出发点。
Ignoring air resistance, gravitational and inertial mass are proportional, so they cancel and every body accelerates at the same local value g. This equivalence principle, illustrated by Galileo's inclined-plane studies, became the foundation of Einstein's general relativity.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-10-04
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伽利略《两种新科学》1638；爱因斯坦 1907 年等效原理论文
Galileo, Two New Sciences (1638); Einstein, equivalence principle (1907)
独立核验依据 · Independent verification: 核验依据 1 ISBN 9780921332213 (2000)
#自由落体 #等效原理 #重力加速度
能量守恒定律为什么如此可靠？
Why is the law of energy conservation so reliable?
根据诺特定理，能量守恒源于物理定律在时间上的平移对称性——今天和明天规律相同。它在宏观和微观、经典和量子中都被反复验证，至今没有例外。因此能量既不会凭空产生，也不会消失，只会转化形式。
By Noether's theorem, energy conservation follows from the time-translation symmetry of physical laws—the rules are the same today and tomorrow. It has been verified across macroscopic and microscopic, classical and quantum regimes with no known exception. Energy is never created or destroyed, only transformed.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23结论有争议 · Contested
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#能量守恒 #诺特定理 #对称性
摩擦力总是阻碍运动吗，为什么我们走路反而靠它？
Does friction always oppose motion, and why do we actually need it to walk?
摩擦力阻碍的是接触面之间的相对滑动，并不总阻碍整体运动。走路时脚向后蹬，地面给脚向前的静摩擦力，正是这个力推着我们前进。
Friction opposes relative sliding between surfaces, not always the overall motion. When you push your foot backward, the ground pushes your foot forward with static friction, and that is what propels you.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#静摩擦 #行走 #相对滑动
在匀速行驶的高铁上向上跳起，为什么落地时还站在原地，不会落到车尾？
If you jump straight up inside a smoothly moving train, why do you land in the same spot instead of drifting to the back?
因为你和火车一起向前运动，跳起后仍然保持这个向前的速度（惯性）。在火车参考系里你只是上下跳，在地面看来你一边向前飞一边跳。只要火车匀速、不加速，你落地时仍和车厢同步。
You are already moving forward with the train, and when you jump you keep that forward speed (inertia). In the train's frame you only go up and down; from the ground you're moving forward while hopping. As long as the train moves at constant speed, you land exactly where you took off.
难度 入门 · 适合 幼儿(3-6)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
伽利略《关于两门新科学的对话》（1638）关于惯性运动的论述；亦见《费曼物理学讲义》第一卷
Galileo, 'Discourses and Mathematical Demonstrations Relating to Two New Sciences' (1638), on inertial motion; also Feynman Lectures Vol. I
独立核验依据 · Independent verification: 核验依据 1 ISBN 9780921332213 (2000)
#惯性 #参考系 #伽利略相对性
什么是惯性？
What is inertia?
惯性是物体保持原有运动状态（静止或匀速直线运动）的性质，质量越大惯性越强。牛顿第一定律正是对惯性的描述：不受外力时物体运动状态不变。它是我们理解运动和力的起点。
Inertia is an object's tendency to keep its state of motion (rest or uniform straight-line motion); the larger the mass, the stronger the inertia. Newton's first law describes inertia: with no external force, motion stays unchanged. It is the starting point for understanding motion and force.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#惯性 #牛顿第一定律 #质量
火箭在没空气的太空里，靠什么往后推自己往前飞？
In empty space with no air, what pushes a rocket forward?
火箭向后喷出高温气体，气体给火箭一个反方向的反冲力。这就是作用力与反作用力：你推开别人，别人也推开你。
A rocket shoots hot gas backward, and that gas pushes the rocket forward in return. It's action and reaction: when you push something away, it pushes back on you.
难度 入门 · 适合 幼儿(3-6)
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#反作用力 #火箭 #推进
什么是动量？
What is momentum?
动量等于物体的质量乘以速度，是描述运动多少的物理量。它比速度更能反映碰撞中的传递效果，且在不受外力时总量守恒。火箭、撞球等都遵循动量守恒。
Momentum equals an object's mass times its velocity, a quantity describing how much motion there is. It captures collision transfer better than speed alone, and its total is conserved when no external force acts. Rockets and billiard balls both obey momentum conservation.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#动量 #质量 #速度
为什么抛出的物体轨迹是抛物线？
Why is the trajectory of a thrown object a parabola?
在忽略空气阻力、重力近似恒定的情况下，物体在水平方向匀速、竖直方向匀加速，两者合成得到二次曲线即抛物线。这是运动叠加原理的直接结果。真实轨迹会因空气阻力而略有偏离。
Ignoring air resistance with approximately constant gravity, an object moves uniformly horizontally and accelerates vertically, and their combination yields a quadratic curve, the parabola. This is a direct result of the superposition of motions. Real trajectories deviate slightly due to air resistance.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23
来源 · Source
舒幼生,《力学》,北京大学出版社,2005
Shu Yousheng, Mechanics, Peking University Press, 2005
#抛体 #抛物线 #运动叠加
单摆为什么能左右来回摆，而且摆得小的时候周期几乎不变？
Why does a pendulum swing back and forth, and why is its period nearly constant for small swings?
摆球偏离最低点后，重力沿切线方向把它拉回，形成回复力，于是做简谐运动般的往复摆动。当摆角很小时，回复力近似与位移成正比（正弦近似为角度本身），周期只取决于摆长和重力加速度，与幅度无关——这正是伽利略发现钟摆等时性的原因。
Once displaced, gravity pulls the bob back along the tangent, providing a restoring force that drives the back-and-forth swing. For small angles the restoring force is nearly proportional to displacement (sin θ ≈ θ), so the period depends only on length and gravity, not amplitude—the isochronism Galileo noticed in pendulum clocks.
难度 入门 · 适合 小学低段(6-8)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：著录仅给书名，无版次与年份；同一书名常对应多个版次，不臆测具体版本。
《力学》（朗道与栗弗席兹）§1 关于小振动与单摆周期的推导
Landau & Lifshitz, 'Mechanics', §1 on small oscillations and the pendulum period
#简谐运动 #回复力 #等时性
不倒翁为什么不倒?它的秘密全部藏在重心和支点的关系里吗?
Why cant a roly-poly toy fall over — is the whole secret in the center of gravity and pivot?
是的,而且还有一位配角。不倒翁上轻下重,重心被压到接近底部;被推歪时,重力作用线偏离支点,产生一个把它推回正立的恢复力矩,晃几圈便静止在重心最低的平衡位。但若把同样配重装进方形盒,它照样能被推倒——奥妙在于大曲率的球形底:倾斜时支点沿弧面滚动,重心升高的幅度有限,力矩始终指向回正。工程里吊车的配重、赛车的低重心布置、甚至走钢丝者手里的长杆(增大转动惯量延缓倾倒)都是同一套静力学。
Yes — with a co-conspirator. Bottom-weighted, the toys center of gravity sits near its base; tilt it and gravitys line of action leaves the pivot, generating a restoring torque that rocks it upright to rest at minimum height. But put the same weight in a square box and it topples — the spherical bottom matters: as it tilts the contact point rolls along the arc, raising the center only slightly while torque keeps pointing home. Crane counterweights, low-slung race cars and tightrope walkers long poles (boosting rotational inertia) all share this statics.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
Feynman、Leighton 与 Sands,《The Feynman Lectures on Physics》第一卷,Addison-Wesley,1963
R. P. Feynman et al., The Feynman Lectures on Physics Vol. I, Addison-Wesley, 1963
独立核验依据 · Independent verification: 核验依据 1 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#重心 #恢复力矩 #转动惯量
圆圆的罐子放在斜坡上,为什么会自己滚下去?
Why does a round jar roll down a slope by itself?
把圆圆的罐子放在斜坡上,它不用人推就往下滚,这是因为重力在拉它。重力是地球吸引东西的力,方向一直指向地面。斜坡越陡,罐子滚得越快;斜坡越平,滚得越慢。方方的盒子没有圆面不能打转,只会慢慢滑下去,不会滚。
Put a round jar on a slope and it rolls down without a push, because gravity is pulling it. Gravity is the force that draws everything toward the ground, always pointing down. The steeper the slope, the faster the jar rolls; the gentler the slope, the slower it goes. A square box cannot spin like a wheel, so it only slides slowly instead of rolling.
难度 入门 · 适合 小学低段(6-8)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《十万个为什么》第六版物理分册,少年儿童出版社,2013
Ten Thousand Whys: Physics volume, 6th ed., Juvenile and Children Publishing House, 2013
独立核验依据 · Independent verification: 核验依据 1 ISBN 978-7-5324-9328-9 · 核验依据 2 ISBN 9787532493289
#斜坡 #重力 #滚动