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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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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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Different understandings of what that piece means gives you different values, and that's a bit of a problem.
应该是半径为1角度为,弧度为2比圆周率的一半，稍微多一点。
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And since we are not expecting the mass of the particle to change, what we really are saying is the uncertainty in its velocity times the uncertainty in its position is greater than the ratio of the Planck constant divided by 2 pi.
因为我们不期望,粒子质量发生变化，我们说的是,它速度的不确定度,乘以它位置的不确定度,比普朗克常量,除以2除以圆周率要大。
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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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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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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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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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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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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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