Dynamics
A-Level Physics Topic 3 20:03 English narration · English + 中文 subtitles burned in
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In the empty vacuum of space, there is nothing to push against — no ground, no air, nothing at all.
在太空的真空里，没有任何可以推的东西——没有地面，没有空气，什么都没有。
And yet a rocket can still speed up.
可是火箭仍然能够加速。
How?
怎么做到的？
It throws mass out behind it.
它把质量向后抛出。
The rocket pushes the hot gas backward, and by Newton's third law, the gas pushes the rocket forward.
火箭把炽热的气体向后推， 根据牛顿第三定律，气体把火箭向前推。
The momentum lost by the gas is gained by the rocket.
气体失去的动量，正是火箭得到的动量。
Nothing to push against — and it still flies.
没有可推之物——它依然飞了起来。
This is dynamics: why things speed up, slow down, and push on one another.
这就是动力学：为什么物体会加速、减速，并彼此推挤。
Today, mass and momentum, Newton's three laws, drag and terminal velocity, and the great rule of collisions.
今天我们学习质量与动量、 牛顿三大定律、阻力与收尾速度，以及那条伟大的碰撞法则。
Let's begin.
让我们开始吧。
First, two words people mix up: mass and weight.
首先，两个常被混淆的词：质量和重力。
Mass measures how strongly an object resists a change in its motion — its inertia.
质量衡量一个物体多强烈地抵抗其运动的变化—— 也就是它的惯性。
A heavier object needs a bigger force for the same acceleration.
更重的物体，要产生相同的加速度就需要更大的力。
Weight is different: weight is the pull of gravity on that mass, equal to the mass times the gravitational field strength.
重力不同： 重力是引力对这个质量的拉力，等于质量乘以重力场强度。
Mass never changes.
质量永远不变。
But weight does — on the Moon, your weight drops, while your mass stays the same.
但重力会变——在月球上，你的重力减小，而你的质量保持不变。
Near the Earth's surface, weight equals mass times g.
在地球表面附近，重力等于质量乘以 g。
Here g is the acceleration of free fall, about nine point eight one metres per second squared.
这里的 g 是自由落体加速度，大约是每秒平方九点八一米。
Weight is a vector: it always points towards the centre of the Earth.
重力是矢量：它总是指向地心。
Mass is a scalar, measured in kilograms.
质量是标量，单位是千克。
Keep them separate in your head: mass is how much stuff you have; weight is how hard gravity pulls on that stuff right where you stand.
在脑子里把它们分开： 质量是你有多少物质；重力是引力在你所在之处对那物质拉得多用力。
Linear momentum captures how hard something is to stop.
动量刻画了一个东西有多难停下来。
It is simply mass times velocity.
它就是质量乘以速度。
A heavy truck rolling slowly and a light bullet flying fast can carry the same momentum.
一辆缓慢滚动的重卡车， 和一颗高速飞行的轻子弹，可以带有相同的动量。
Because velocity has a direction, momentum is a vector — it points the same way the object moves.
因为速度有方向，动量是一个矢量—— 它指向物体运动的方向。
Its unit is the kilogram metre per second, which is the same as the newton second.
它的单位是千克米每秒，也就等于牛顿秒。
Newton's second law, in full, says that force is the rate of change of momentum.
牛顿第二定律的完整表述是：力等于动量的变化率。
Push for longer, or change the momentum by more, and the force is larger.
推得越久，或动量改变得越多，力就越大。
When the mass is constant, this becomes the familiar force equals mass times acceleration.
当质量恒定时，它就变成我们熟悉的：力等于质量乘以加速度。
Take a ball hitting a wall.
看一个撞墙的球。
It arrives at eight metres per second and bounces back at six.
它以每秒八米飞来，又以每秒六米弹回。
Its momentum changes a lot, because the direction flips.
它的动量变化很大，因为方向反了过来。
Divide that change by the short contact time, and the average force is about fifty-six newtons.
把这个变化除以短暂的接触时间，平均力约为五十六牛顿。
That change in momentum has another name: impulse.
动量的这个变化还有另一个名字：冲量。
On a force–time graph, the impulse is the area under the curve.
在力–时间图上，冲量就是曲线下方的面积。
A tall thin spike and a lower longer hump can deliver the same impulse — the same change in momentum — if their areas match.
一个又高又窄的尖峰，和一个又矮又长的鼓包，只要面积一样，就能给出相同的冲量—— 也就是相同的动量变化。
So average force times contact time equals delta p.
所以平均力乘以接触时间等于动量变化。
Cambridge questions love collisions and short contact times: they want you to write force equals delta p over delta t, not just force equals m a.
剑桥考题特别喜欢碰撞和 极短的接触时间：他们要你写出力等于动量变化除以时间变化，而不只是力等于质量乘加速度。
Work the ball carefully, with signs.
仔细做这个撞墙的球，并带上符号。
A zero point two zero kilogram ball hits a wall at eight point zero metres per second and bounces straight back at six point zero.
一个零点二零千克的球以每秒八点零米撞墙， 又以每秒六点零米径直弹回。
Contact lasts zero point zero five zero seconds.
接触持续零点零五零秒。
Choose the rebound direction as positive, so the approach velocity is negative eight, and the leave velocity is positive six.
取弹回方向为正， 所以接近速度是负八，离开速度是正六。
Then delta p is mass times final minus initial: zero point two zero times fourteen, which is two point eight kilogram metres per second.
于是动量变化是质量乘以末速度减初速度： 零点二零乘以十四，等于两点八千克米每秒。
Divide by the contact time: fifty-six newtons.
再除以接触时间：五十六牛顿。
Without the sign flip you would under-count the change.
如果没有符号翻转，你就会把变化量算少。
Sometimes you know the momenta but not the speeds.
有时你知道动量，却不知道速率。
Remember that kinetic energy equals p squared over two m, because half m v squared is the same as p squared over two m.
记住动能等于 p 的平方除以二 m， 因为二分之一 m v 的平方就等于 p 的平方除以二 m。
So the change in kinetic energy between two states is p two squared minus p one squared, all over two m.
所以两个状态之间动能的变化， 是 p 二的平方减去 p 一的平方，再除以二 m。
Use this when you know the momenta — for example after reading them from a force–time impulse — and you need the energy change without first finding each speed.
当你知道动量时——例如从力–时间冲量读出之后—— 又需要能量变化而不想先求每个速率，就用这个式子。
Newton gave us three laws.
牛顿给了我们三条定律。
The first: with no resultant external force, an object keeps still, or keeps moving at a steady velocity.
第一条：没有合力时，物体保持静止，或保持匀速运动。
The second: a resultant force changes the momentum, at a rate equal to that force.
第二条：合力改变动量，其变化率等于这个力。
The third: every force comes in a pair — if A pushes B, then B pushes back on A, equally and oppositely.
第三条：每个力都成对出现—— 如果甲推乙，那么乙也会以相等而相反的力推回甲。
To apply those laws you draw a free-body diagram.
要应用这些定律，你得画受力图。
Isolate one object and draw every force that acts on it — and only those forces.
单独取出一个物体，画出作用在它上面的每一个力—— 而且只画那些力。
Here a block is pulled at an angle: pull P at twenty degrees above the horizontal, weight W straight down, normal contact force R straight up, and friction F along the surface opposing the slide.
这里一个物块被斜向拉：拉力 P 与水平成二十度，重力 W 竖直向下， 支持力 R 竖直向上，摩擦力 F 沿表面阻碍滑动。
Resolve P into horizontal and vertical parts, then apply Newton's second law along each direction.
把 P 分解成水平和竖直分量， 再沿每个方向应用牛顿第二定律。
Miss a force, or put a force on the wrong body, and the answer is wrong.
漏掉一个力，或把力画到错误的物体上，答案就错了。
A book resting on a table is a quiet case of the first law.
放在桌上的书，是第一定律的安静例子。
Weight pulls down; the normal contact force from the table pushes up.
重力向下拉；桌子的支持力向上推。
The two arrows are equal in length, so the resultant is zero and the book stays at rest.
两支箭头长度相等，所以合力为零，书保持静止。
Equal and opposite on the same object means equilibrium — that is Newton's first law, not the third.
同一物体上大小相等、方向相反， 意味着平衡——那是牛顿第一定律，不是第三定律。
The third law pairs live elsewhere, as we will check next.
第三定律的力对在别处，我们接下来核对。
The third law hides a classic trap.
第三定律藏着一个经典陷阱。
A book rests on a table.
一本书放在桌上。
Its weight pulls down; the table pushes up.
它的重力向下拉，桌子向上推。
These look like a pair — but they are not.
它们看起来像一对——但其实不是。
A third-law pair must act on two different objects, and be the same type of force.
一对作用力与反作用力必须作用在两个不同的物体上， 而且是同一种类型的力。
The true partner of the book's weight is the pull of the book on the whole Earth.
书的重力真正的搭档，是书对整个地球的拉力。
And the partner of the table's push is the book pushing down on the table.
而桌子推力的搭档，是书向下压桌子的力。
Here is the true contact pair drawn clearly.
这里清楚地画出了真正的接触力对。
R acts upward on the book — the table pushing the book up.
R 向上作用在书上——桌子把书往上推。
R prime acts downward on the table — the book pushing the table down.
R 撇向下作用在桌子上——书把桌子往下压。
Same size, opposite direction, same type of force, two different objects.
大小相同，方向相反，同一种力，两个不同物体。
That is a third-law pair.
这才是第三定律力对。
Weight and the normal force on the book fail two of those tests at once: same object, and different force types — gravity versus contact. The pair must be the same type: both gravitational, both contact, both electrostatic.
书上的重力和支持力一下子就不符合其中两条：同一物体， 而且力的类型不同——引力对接触力。
Back to the rocket.
再回到火箭。
The thrust on the rocket and the force on the exhaust gases are a third-law pair: the engine pushes the gas down, the gas pushes the engine up.
火箭上的推力和排出气体上的力是一对第三定律力对： 发动机把气体往下推，气体把发动机往上推。
Weight of the rocket and air resistance are other forces on the rocket — they are not part of that pair.
火箭的重力和空气阻力是作用在火箭上的其他力—— 它们不属于这一对。
In empty space, weight and drag may be tiny, but the gas pair still works.
在真空里，重力和阻力可能很小，但气体这对力仍然成立。
That is why thrust does not need air to push against.
这就是为什么推力不需要空气来顶着推。
Real objects meet resistance.
真实的物体会遇到阻力。
Friction acts between solid surfaces.
摩擦力作用在固体表面之间。
Drag acts in air or water, and it grows as the speed grows.
阻力作用在空气或水中， 并且随速度增大而增大。
Drop an object, and at first only its weight acts, so it speeds up.
放开一个物体，起初只有重力作用，所以它加速。
But as it gets faster, the drag grows, until the drag balances the weight.
但随着速度变快，阻力增大，直到阻力与重力平衡。
Then the resultant force is zero, and the speed stops rising.
这时合力为零，速度不再上升。
This steady speed is the terminal velocity.
这个稳定的速度就是收尾速度。
Two more things the examiner wants named here.
这里还有两件考官要你点名的事。
The shape — a straight start of gradient g, then a bend, then a constant speed — is how falling with air resistance differs from free fall in a uniform gravitational field.
那个形状——起初是斜率为 g 的直线，然后弯曲，再变成恒定速度—— 正是「有空气阻力的下落」区别于「匀强重力场中的自由落体」的地方。
And for an object falling through a liquid there are three forces, not two: weight down, viscous drag up, and upthrust up.
而对于在液体中下落的物体，受力是三个而不是两个： 向下的重力，向上的黏滞阻力，还有向上的浮力。
The upthrust comes from hydrostatic pressure — pressure in a liquid increases with depth, so the liquid pushes harder on the bottom of the object than on the top.
浮力来自流体静压强——液体中的压强随深度增大， 所以液体对物体底部的推力比对顶部的更大。
Friction is the force between two solid surfaces that opposes sliding along the surface.
摩擦力是两个固体表面之间、阻碍沿表面滑动的力。
Drag, or a viscous force, is the resistive force from a fluid — a liquid or a gas — on an object moving through it.
阻力，或黏性力，是流体——液体或气体—— 对在其中运动的物体的阻力。
Air resistance is the air case.
空气阻力就是空气的情形。
You do not need coefficients of friction or viscosity in this topic.
本主题不需要摩擦系数或黏度。
A simple model is enough: at zero speed, drag is zero; as speed rises, drag rises.
一个简单模型就够了：速度为零时，阻力为零；速度上升时，阻力上升。
On this free-body diagram the pull P is opposed by friction F, while weight and the normal force balance vertically.
在这张受力图上，拉力 P 被摩擦力 F 所对抗，而重力和支持力在竖直方向平衡。
Drag also grows with the cross-sectional area of the object and with the density of the fluid — which is exactly how a parachute works, by making the area, and so the drag, much larger, so the falling object decelerates sharply to a new, much lower terminal velocity.
阻力还随物体的横截面积和流体的密度增大—— 降落伞正是靠这一点工作的：把面积、从而把阻力变得大得多， 于是下落的物体急剧减速，降到一个新的、低得多的收尾速度。
For an object dropped from rest through air, three stages matter.
对一个从静止开始在空气中下落的物体，有三个阶段很重要。
At first only weight acts downward, so it accelerates at g.
起初只有重力向下，所以它以 g 加速。
As speed grows, upward drag grows; the resultant shrinks, so the acceleration shrinks too.
随着速度增大，向上的阻力增大；合力变小，加速度也变小。
In the end drag equals weight: resultant force zero, acceleration zero, constant speed — terminal velocity.
最后阻力等于重力： 合力为零，加速度为零，速度恒定——收尾速度。
In a fluid you may also see upthrust upward; the same story holds with the upward forces added.
在流体中你还可能看到向上的浮力； 把向上的力加在一起，故事一样。
This is how falling with air resistance differs from free fall in a vacuum.
这就是带空气阻力的下落与真空自由落体的不同。
On a velocity–time graph the story is visual.
在速度–时间图上，这个故事一目了然。
The line starts with gradient g — that is the initial free-fall stretch.
曲线开始时斜率是 g——那是起初的自由落体段。
Then it bends as drag grows and acceleration falls.
然后随着阻力增大、加速度减小而弯曲。
Finally it flattens at the terminal velocity: a horizontal asymptote.
最后在收尾速度处变平：一条水平渐近线。
A dashed tangent at the origin reminds you of the initial gradient g; a dashed line at the top marks the terminal speed.
原点处的虚线切线提醒你初始斜率是 g；顶部的虚线标出收尾速率。
Fast start, slowing acceleration, then constant speed — that shape is the signature of falling with air resistance.
起步快，加速度逐渐减小，然后匀速——这个形状就是带空气阻力下落的标志。
Why the spread-eagle pose?
为什么要张开大字形？
Spreading arms and legs gives the largest area facing the air, so the most drag at a given speed.
张开手臂和腿，迎风面积最大，所以在给定速度下阻力最大。
Bigger drag means drag balances weight sooner — and at a lower steady speed.
阻力更大，就意味着阻力更早与重力平衡——而且稳定速度更低。
Curl up into a dive and the area shrinks, drag drops, and the terminal velocity rises.
缩成俯冲姿势， 面积减小，阻力下降，收尾速度升高。
Shape and orientation change terminal velocity without changing mass.
形状和姿态能改变收尾速度，而不改变质量。
That is a favourite exam story.
这是一道很受青睐的考试故事。
At terminal velocity a parachutist's kinetic energy stays constant — speed is steady.
在收尾速度时，跳伞者的动能是恒定的——速率稳定。
But gravitational potential energy keeps falling as they go down.
但重力势能随着下降不断减少。
Where does that energy go?
那些能量去了哪里？
Almost all of it becomes thermal energy of the air around them.
几乎全部变成了周围空气的热能。
It does not become extra kinetic energy of the parachutist; that stays constant.
它不会变成跳伞者额外的动能； 那部分保持不变。
Drag does negative work on the jumper and positive heating on the air.
阻力对跳伞者做负功，对空气做正加热。
A cyclist or car at constant speed on a flat road has zero resultant force.
自行车或汽车在平路上以恒定速度行驶时，合力为零。
The forward driving force is equal and opposite to the total resistive force — friction, air resistance, rolling resistance.
向前的驱动力与总阻力大小相等、方向相反—— 摩擦力、空气阻力、滚动阻力。
At higher speed the drag is larger, so the driving force must be larger too.
速度更高时阻力更大，所以驱动力也必须更大。
Power is force times speed, so the power must be larger as well.
功率是力乘以速度，所以功率也必须更大。
That is why holding a high steady speed costs so much more fuel or effort than a gentle cruise.
这就是为什么保持高速匀速比缓缓巡航 耗费多得多的燃料或体力。
Here is one of the deepest rules in physics.
这是物理学中最深刻的法则之一。
In any system with no outside force, the total momentum never changes.
在任何没有外力的系统中，总动量永远不变。
Watch this collision.
看这次碰撞。
Before, one ball moves and one is still.
碰撞前，一个球在动，一个球静止。
After, the momentum is shared between them — but add it all up, and the total is exactly the same as before.
碰撞后，动量在两者之间分配—— 但把它们全部加起来，总量与之前完全相同。
This is the conservation of momentum.
这就是动量守恒。
It holds in every collision, every explosion, and every recoil.
它在每一次碰撞、每一次爆炸、每一次反冲中都成立。
State it the way the scheme does: the total momentum of a system of objects remains constant provided no resultant external force acts on the system.
要照评分标准的说法陈述： 只要没有合外力作用于系统，系统内所有物体的总动量保持不变。
The proviso is half the mark — without it the statement is simply false.
那个附加条件占了一半的分——去掉它，这句话就是错的。
In a crash, a large force acts over a very short time to change the momentum.
在碰撞事故中，一个很大的力在极短时间内作用，以改变动量。
Crumple zones and airbags stretch that time so the same delta p needs a smaller average force — safer for the people inside.
溃缩区和安全气囊拉长那个时间， 使同样的动量变化只需要更小的平均力——对车内的人更安全。
The principle is the same impulse idea: force times time equals change in momentum.
原理就是同一个冲量概念： 力乘以时间等于动量变化。
Make the time longer, and the peak force falls.
把时间拉长，峰值力就下降。
Why does conservation work?
守恒为什么成立？
In an isolated two-particle system the only forces between them are a third-law pair: equal and opposite.
在一个孤立的双粒子系统中，它们之间的力只是一对第三定律力对： 大小相等、方向相反。
So the rate of change of momentum of A is minus the rate of change for B.
所以甲的动量变化率是乙的负值。
Their total momentum's rate of change is zero.
它们总动量的变化率为零。
No outside resultant force means total momentum stays constant — in one dimension or in two.
没有外部合力，就意味着总动量保持恒定——一维或二维都一样。
Momentum conservation even works from rest.
动量守恒甚至在从静止出发时也成立。
Two trolleys sit still, pressed against a squeezed spring, with a total momentum of zero.
两辆小车静止不动，压着一根被压缩的弹簧， 总动量为零。
Release them, and they fly apart.
松开它们，它们就飞散开来。
Because the total must stay zero, their momenta are equal and opposite.
因为总量必须保持为零， 它们的动量大小相等、方向相反。
A two-kilogram trolley leaving at six metres per second pushes a three-kilogram trolley the other way at four.
一辆两千克的小车以每秒六米离开， 就把一辆三千克的小车以每秒四米推向相反方向。
The standard version is a decay.
标准版本是一次衰变。
A stationary nucleus of mass two hundred and twenty-two u emits an alpha particle of mass four u at one point six times ten to the seventh metres per second.
一个静止的、质量为二百二十二 u 的原子核， 放出一个质量为四 u 的 α 粒子，速度是一点六乘以十的七次方米每秒。
Before the decay the total momentum is zero, so afterwards the two momenta are equal and opposite: two hundred and eighteen u times v equals four u times that speed, giving about two point nine times ten to the fifth metres per second, in the opposite direction.
衰变前总动量是零，所以衰变后两个动量大小相等、方向相反： 二百一十八 u 乘以 v，等于四 u 乘以那个速度， 得到大约二点九乘以十的五次方米每秒，方向相反。
Notice the u cancels, so its value is never needed.
注意 u 被约掉了，所以它的具体数值从来不需要。
Momentum is always conserved — but kinetic energy is not.
动量总是守恒——但动能不一定。
In an elastic collision, the kinetic energy is also conserved: the objects bounce cleanly, and the speed at which they approach equals the speed at which they separate.
在弹性碰撞中，动能也守恒：物体干净地弹开， 它们相互接近的速率等于分开的速率。
In an inelastic collision, some kinetic energy is lost — to heat, to sound, to deformation.
在非弹性碰撞中，一部分动能损失掉—— 变成热、声音和形变。
If they stick together, like two cars locking in a crash, the collision is as inelastic as it gets.
如果它们粘在一起，就像两辆车在碰撞中锁在一起， 这种碰撞就是最彻底的非弹性碰撞。
Solving collision problems in one dimension: for two objects that hit head-on, write mass one times u one plus mass two times u two equals mass one times v one plus mass two times v two.
对两个正面相撞的物体，写下质量一乘以 u 一加质量二乘以 u 二， 等于质量一乘以 v 一加质量二乘以 v 二。
Use signed velocities: pick one direction as positive and stick to it.
使用带符号的速度：选定一个方向为正并坚持下去。
If the collision is elastic, add the relative-speed equation: the relative speed of approach equals the relative speed of separation — or equate total kinetic energy before and after.
如果碰撞是弹性的，再加相对速率方程：接近的相对速率等于分离的相对速率—— 或者让碰撞前后总动能相等。
That gives two equations for two unknowns.
这样就有了两个方程对应两个未知量。
A fifteen hundred kilogram car moving at twelve metres per second runs into a stationary one thousand kilogram car, and they lock together.
一辆一千五百千克的汽车以每秒十二米撞上一辆静止的一千千克汽车，并且锁在一起。
Momentum is conserved, and because they stick, they share one common velocity v.
动量守恒，又因为它们粘住，所以共用一个共同速度 v。
So fifteen hundred times twelve, plus one thousand times zero, equals twenty-five hundred times v.
于是一千五百乘以十二， 加一千乘以零，等于两千五百乘以 v。
That gives v equals eighteen thousand over twenty-five hundred, which is seven point two metres per second.
得到 v 等于一万八千除以两千五百， 也就是每秒七点二米。
Perfectly inelastic — kinetic energy is not conserved, but momentum is.
完全非弹性——动能不守恒，但动量守恒。
A useful special case: a head-on elastic collision of mass m with a stationary mass M.
一个有用的特例：质量 m 与静止质量 M 的正面弹性碰撞。
The incoming mass leaves with velocity m minus M over m plus M, times u.
入射质量离开时的速度是 m 减 M 除以 m 加 M，再乘以 u。
The target leaves with two m over m plus M, times u.
靶质量离开时的速度是二 m 除以 m 加 M，再乘以 u。
If m is much smaller than M, the lighter mass bounces back at nearly u and the heavier target barely moves.
如果 m 远小于 M，较轻的质量几乎以 u 弹回，较重的靶几乎不动。
If the masses are equal, equal masses simply swap: the first stops and the second takes speed u.
如果质量相等， 它们只是交换：第一个停下，第二个带上速率 u。
Memorise the pattern for quick checks.
记住这个模式便于快速检查。
What if the objects do not move in a straight line?
如果物体不沿直线运动怎么办？
The rule still holds — you just apply it twice.
这条法则依然成立——你只需应用它两次。
Split every velocity into two directions at right angles.
把每个速度分解成两个互相垂直的方向。
Momentum is conserved along each direction on its own: across, and along.
动量沿每个方向各自守恒：横向，和纵向。
Solve the two directions separately, and you have the full answer.
分别求解这两个方向，你就得到了完整的答案。
In a glancing collision an incoming particle strikes a stationary one and both move off at angles.
在斜碰中，一个入射粒子撞上一个静止粒子，两者以一定角度飞开。
Choose one axis along the first object's original motion and one across it.
选一个轴沿第一个物体 原来的运动方向，另一个轴与之垂直。
Along the line of motion, both outgoing momentum components count; across it, the two side components cancel or balance depending on the angles.
沿运动方向，两个出射动量分量都要计入； 横向，两个侧向分量按角度抵消或平衡。
Write conservation of momentum along each axis separately, with perpendicular components.
沿每个轴分别写下动量守恒，使用垂直分量。
That is the whole method.
这就是全部方法。
A rocket pushes out gas at exhaust speed u relative to itself, at a mass-flow rate m-dot in kilograms per second.
火箭以相对自身的排气速率 u 推出气体，质量流率为 m 点，单位是千克每秒。
The thrust equals m-dot times u.
推力等于 m 点乘以 u。
That formula comes from force equals delta p over delta t: the momentum given to the gas each second is the thrust on the rocket the other way.
这个公式来自力等于动量变化除以时间变化： 每秒给予气体的动量，就是反方向作用在火箭上的推力。
Newton's third law again — the rocket pushes the gas one way, the gas pushes the rocket the other way.
又是牛顿第三定律—— 火箭把气体往一边推，气体把火箭往另一边推。
Bigger exhaust speed or bigger mass flow means bigger thrust.
更大的排气速率或更大的质量流率， 意味着更大的推力。
Three marks to lock in.
三个要拿稳的分。
First, Newton's second law is force equals the rate of change of momentum — the mass-times-acceleration equation is just the constant-mass case.
第一，牛顿第二定律是：力等于动量的变化率—— 质量乘加速度那个式子只是质量恒定的特例。
Second, name third-law pairs correctly: the same type of force, on two different bodies.
第二，正确说出作用力与反作用力对： 同一种类型的力，作用在两个不同的物体上。
Third, momentum is conserved in every collision, but kinetic energy only in an elastic one.
第三，动量在每一次碰撞中都守恒， 但动能只在弹性碰撞中守恒。
Master these, and dynamics is yours.
掌握这些，动力学就是你的了。
The fixed-wording definitions, one answer only.
固定措辞的定义，只给一个答案。
Mass: the property of an object that resists a change in its motion.
质量：物体抵抗其运动状态改变的性质。
Linear momentum: the product of an object's mass and its velocity.
线动量：物体质量与速度的乘积。
Force: the rate of change of momentum.
力：动量的变化率。
Newton's first law: an object remains at rest or moves at constant velocity unless acted on by a resultant force.
牛顿第一定律：除非受到合力作用，物体保持静止或者做匀速直线运动。
Newton's second law: the resultant force is proportional to the rate of change of momentum and acts in the direction of that change.
牛顿第二定律：合力与动量的变化率成正比，并且方向与该变化的方向相同。
Newton's third law: when two bodies interact, the force on one is equal in magnitude and opposite in direction to the force on the other.
牛顿第三定律：两个物体相互作用时， 一个受到的力与另一个受到的力大小相等、方向相反。
Weight: the force on an object due to a gravitational field, equal to mass times the acceleration of free fall.
重量：物体在重力场中受到的力，等于质量乘以自由落体加速度。
Conservation of momentum: the total momentum of a system remains constant provided no resultant external force acts on it.
动量守恒：只要没有合外力作用于系统，系统的总动量保持不变。
An elastic collision is one in which total kinetic energy is conserved.
弹性碰撞：总动能守恒的碰撞。
Two traps.
两个陷阱。
Do not write that the forces are balanced or that they cancel out — say the resultant force on the object is zero.
不要写「力平衡了」或者「力抵消了」——要说「物体所受的合力为零」。
And in a head-on collision do not add both speeds because momentum is "total": choose a positive direction, give the opposing velocity a minus sign, and then add.
另外正碰时不要因为动量是「总的」就把两个速率相加： 先选定一个正方向，给反向的速度加负号，然后再相加。