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If you can see it, it's wrong, because it's not supposed to have any length.
只要你们能看到它,那就是错的,因为它不该有模长
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It's good to have a vector pointing in the radial direction of length one.
所以引入这么一个模长为 1,方向沿圆心向外辐射的矢量作用很大
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When I draw something without an arrow, I'm talking about the magnitude.
如果我写下的字母没有箭头,那就说明我在讨论模长
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I have to be really careful when I said, "Add the lengths."
当我说"模长相加"的时候需要非常小心
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The length of the vector is the length of the vector.
这个矢量的模长是保持不变的
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The fact that when you go in a circle, you accelerate is what we're learning here, coming from the fact that velocity is a vector and its change can be due to change in the magnitude or change in direction.
而当你做圆周运动时你也在加速,这是我们在这里所学到的,原因就在于,速度是一个矢量,其变化可以通过改变模长,或者方向来实现
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If you drop the arrow, it's the usual convention, if you're talking about the length of the vector A.
如果你把箭头去掉,就表示矢量 A 的模长,这是约定俗成的
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But then, I combine i times Ax with i times Bx, because that's the vector parallel to i, with the length Ax.
然后我把 i ? Ax 和 i ? Bx 加起来,因为这是平行于 i,模长为 Ax 的矢量
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But since sine square plus cosine square is 1, you'll find this vector has a fixed length R.
但是由于正弦和余弦的平方和为1,你会发现这个矢量模长恒等于 R
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That's clear. If I add them, I'll get a vector parallel to i with lengths Ax + Bx.
这很明显 如果把他们加起来,就得到一个平行于 i,模长为 Ax + Bx 的矢量
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That means the acceleration is pointing towards the center of the circle and it has a magnitude a.
也就是说加速度,始终指向圆心,其模长为 a
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You can see from trigonometry and the length of the vector I'm going to call by A.
可以用三角的知识,然后我把矢量的模长记为 A
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At each point, er is a different vector pointing in the radial direction of length one.
矢量 er 在每一点处都不同,方向都从圆心指向该点,模长为1
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er is a vector at each point of length one pointing radially away from the center.
r 是一个模长恒为 1 的矢量,方向沿半径向外
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So i and j are vectors of length one, pointing along x and y.
和 j 是模长为1的矢量,分别指向 x 轴和 y 轴方向
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First thing you can tell is that if you find the length of this vector, you'll find the square of the x and the square of the y.
首先你可以知道的是,如果你已有了这个矢量的模长,你就可以得到 x 和 y 分量的平方
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If you give me a pair of numbers, Ax and Ay, that's as good as giving me this arrow, because I can find the length of the arrow by Pythagoras' theorem.
如果给我一组数字,Ax 和 Ay,就相当于给了我这个箭头示意图,因为我可以利用毕达哥拉斯定理定理求出模长
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That's the vector parallel to i, with length Bx.
这个是平行于 i,模长为 Bx 的矢量
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take the derivative of this, get the velocity vector and you notice his magnitude is a constant Whichever way you do it, you can then rewrite this as v square over r.
对这个式子求一次导,就能得到速度矢量,你会发现其模长是常数,不管用什么方法,加速度也可以写成 v^2 / r
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Then j with Ay + By.
同样有平行于 j,模长为 Ay + By 的矢量
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The magnitude is v square over r.
模长为 v^2 / r
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A is the length of A.
表示矢量 A 的模长
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We know it's going around in a circle because if I find the length of this vector, which is the x-square part, plus the y-square part, I just get r square at all times, because sine square plus cosine square is one.
我们之所以知道它做圆周运动,是因为我求出了这个矢量的模长,也就是 x 的平方加上 y 的平方,我就得到了它在任意时刻的模长平方,因为正弦平方加余弦平方始终等于1
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