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什么是角动量? – 译学馆
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什么是角动量?

What IS Angular Momentum?

物理学 从本质上来讲 是对宇宙中物质的运行规律做出描述
Physics, at its most basic, is just a description of the motion of the stuff in our universe.
“这个行星这样运行 那个火箭那样运行” 除了某些情况
“This planet goes this way, that rocket goes that way” – except that some – in
实际上 许多物体在做不位移地运动 更确切地说
fact, many – objects move without moving. Or, more precisely, they move without going
他们不改变位置地运动着
anywhere.
我接下来将谈论进行各种各样旋转的物体
I’m talking objects that spin, revolve, rotate, pirouette, orbit, circle, gyrate,
类似于行星环绕恒星 电子围绕原子核旋转
whirl, twirl, cartwheel, and so on. Like a planet around a star, an electron in an atom,
还有我们的太阳系围绕着银河系的引力中心旋转
or even our solar system going around the gravitational center of the milky way: from
它们确实在运动 但从宏观意义上讲 这种运动并没有使他们
up close they’re certainly moving, but in the grand scheme of things, that motion doesn’t
发生任何移动
take them anywhere.
我们可以通过以下概念来研究这种运动
We can still talk about it, though: just like “momentum” is a concept that describes
动量可以描述物体做直线运动时所具有的引力
how much oomph an object has when it moves in a straight line, “angular momentum”
而角动量可以准确而形象地描述物体做圆周运动时
is a way to account for how much oomph objects have when they’re going in circles – figuratively,
所具有的引力
or literally.
角动量的定义很简单:选取任意一点
And angular momentum is simple, in theory: pick a point, any point. Pretend your object
假设你的物体正在绕着那个点做圆周运动 弄清楚物体绕点
is moving in a circle around that point. Figure out how fast the object is moving along the
旋转的速度有多快(即便它不是做精确的圆周运动
circle (never mind that it probably isn’t moving exactly along the circle, and that
圆周会随着物体的运动轨迹而改变也无妨)然后
the circle might have to change size over time to follow the object), then multiply
把物体的速度和它的旋转半径以及它的质量相乘你就能得到
that speed times the size of the circle and the object’s mass, and there you have it:
它的角动量了
angular momentum.
举个例子 有一个质量为2kg 直径为60cm的自行车轮 当它的速度为20km/h时
For example, a 2 kilogram 60 cm-diameter bicycle wheel going 20 km per hour would have an angular
它所具有的角动量大约是7千克平方米每秒
momentum of about 7 kilogram meters squared per second.
我们之所以关心角动量是因为如果你把一堆
The reason we care about angular momentum is that if you take a bunch of objects that
通过电磁力或万有引力或其他相互作用的物体的角动量
are interacting electromagnetically or gravitationally or whatever, and add up all of their angular
全部加和 他们的总值不会随着时间改变(除非有
momenta into one number, then that total value won’t change over time (unless some other
外界的物体进来把这个体系打乱)
objects from outside come in and mess things up).
那么地球 距离太阳150,000,000km 转速为30km/s
So earth, which is 150 million kilometers from the sun, orbits at 30 km/s and has a
质量为6*10^24kg 所具有的角动量就是2.7*10^40kg·m²/s
mass of 6*10^24 kilograms, has an angular momentum of 2.7 * 10^40 kilogram meters squared
是自行车轮的四千的千亿的千亿倍!
per second. That’s four thousand quintillion quintillion bicycle wheels! And this angular
并且这个角动量在地球年复一年的绕行中近似守恒
momentum stays roughly constant over the course of the earth’s orbit year in and year out.
然而惊人的是 即便太阳和太阳系中其他的天体
But what’s amazing is that even if the sun and the rest of the solar system were to suddenly
突然消失 地球仍然会保持相同的动量
disappear, the earth would STILL have that same angular momentum about the point where
而一旦失去太阳的引力 地球会自然沿直线运动
the sun.Once without the sun’s gravity, the earth would of course now move in a straight
随着它远离太阳原先的位置 它所在位置的圆轨道也会越来越大
line, requiring an ever-larger imaginary circle as it got farther from the point where the
然而随着地球持续在太空中穿梭 它30km/s的速度也会
sun used to be. But as the earth continued through space, its 30km/s velocity would also
变得越来越小 因此当你计算角动量时 减小的
point less and less along the circle, so when you calculated the angular momentum, the decrease
速度和增加的圆半径恰好抵消 你就总会
in velocity would exactly cancel out the increase in the size of the circle, and you’d always
得到相同的答案——2.7*10^40kg·m²/s
get the same answer. 2.7 * 10^40 kilogram meters squared per second.
因此即使是在没有任何旋转的运动中 角动量依然守恒
So even when nothing is rotating at all, angular momentum is still conserved. And that’s
而这也正是物理学的魅力——你永远无法打破它的规律!
the beauty of a law of physics –It works even when you try to break it!

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让我们一起通过漫画的形式来认识有趣的角动量吧

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