I write it without an arrow here.

在这里我用不带箭头的 a 写出来
That's equal to ω^2 times a magnitude of this vector,

它就等于 ω^2 乘以这个矢量的模长
which is just R.

也就是 R
But now, I can also write it as v^2 over R.

但现在我也可以写成 v^2 / R
So, here, ready? This is a very important formula.

准备好了吗这是个非常重要的公式
I don't know how many kids, generation after generation,

我不知道有多少孩子一代又一代
get in trouble because they do not remember the following fact.

因为没有记住下面的内容而遇到困难
I'm going to say it once more with feeling.

我要再深情地讲一次
When a particle moves in a circle,

当一个质点在圆周上运动时
it has an acceleration towards the center of this size, v^2 over R.

它有一个指向圆心的加速度 v^2 / R
Very simple.

非常简单
It comes from the fact that velocity is a vector

其原理就是速度是矢量