That's like -1 times a vector.

那相当于-1乘以一个矢量

耶鲁公开课 - 基础物理课程节选

That's -Pi times a vector.

就等于用 -π 乘以那个矢量

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You go back to the same x-y plane; here is some vector A.

回到刚才的 x-y 平面上,这是某个矢量 A

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Then, I want to think of a vector that I can call -A.

现在我有一个矢量,我将其称为 -A

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I expect that if I add -A to A, I should get the guy who plays the role of 0 in this world, which is the vector of no length.

我希望如果用 -A 加上 A,应该得到一个零矢量,也就是一个没有模长的矢量

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If you want to write it as a vector equation, you want to write it as v square over r minus-- I want to say that it's pointing in the direction toward the center.

如果要写出矢量方程,就应该写成 -v^2 / r,也就是说,方向就向圆心

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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

耶鲁公开课 - 基础物理课程节选