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I have shown you yesterday that the speed of the particle as it goes around the circle is this .
我昨天讲过,质点做圆周运动的速率等于这个
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At any instant, your motion, if it follows any curve, locally can be approximated as being part of some circle.
在任何时候,如果做曲线运动,都可以近似地认为是圆周的一部分
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You can take circles of different size and place them against your trajectory and see which one fits.
你可以做不同大小的圆周运动,然后把它们放到你的轨迹上,看哪一个匹配
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You've got to ask yourself, let the time it takes to do a full circle, that's the time period, do a full circle.
你已经问你自己了,留足够的时间让它运动一整圈,那就是运动整个圆周的时间周期
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When a body is going around a circle, they say that's some centrifugal force acting.
如果一个物体做圆周运动,他们就说有离心力作用于这个物体
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It's related to the frequency with which you go around the circle Why is that?
它也跟圆周运动的频率有关,为什么呢
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I'm asking what's the tangential speed as it moves along the circle?
它在做圆周运动时,切向速度是多少
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Suppose the particle is not moving in a circle, but does this.
假设这个质点不是做圆周运动,而是这样
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This describes a particle that's going around in a circle.
这个式子描述了质点的圆周运动
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We're describing the motion of a particle in a circle.
我们描述了圆周上一个点的运动
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It's going around a circle.
它沿着圆周运动
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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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When a particle moves in a circle, it has an acceleration towards the center of this size, v^2 over R.
当一个质点在圆周上运动时,它有一个指向圆心的加速度,v^2 / R
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It tells you when a particle moves in a circle, it has an acceleration in a negative R direction, namely directed towards the center.
它告诉你当一个物体在圆周上运动时,它有一个在 -R 方向的加速度,也就是说是直接指向圆心的
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Whenever you see a particle moving in a circle, even if it's at a constant speed, it has an acceleration, v square over r directed towards the center.
只要看到质点做圆周运动,即使是匀速圆周运动,也存在一个加速度,大小为 v^2 / r,方向指向圆心
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So we know it's moving on a circle of radius r.
因此这个质点始终在做半径为 r 的圆周运动
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If it's going in a circle, you will say from now on, that it, indeed, has an acceleration, even though no one's stepping on the accelerator, of amount v^2 over R.
如果它在一个圆周上运动,你会说从现在起它其实有加速度,即使没有人去踩油门,加速度大小为 v^2 / R
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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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