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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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The answer is that simply knowing the particle has an acceleration is not enough to tell you where the particle will be.
答案是这样的,仅仅知道质点的加速度,是不足以告诉你它接下来的运动的
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The other two you know are stuff you can add, and you know where you're adding those things, because the particle has a head start.
另外两项是可加可不加的,而且你也知道这两项是怎么来的,因为质点运动是有起点的
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This particle is constantly changing its direction, but it therefore has an acceleration and the acceleration, we have shown here, is pointing towards the center.
这个质点恒定地改变它的运动方向,因此它具有加速度,而且这个加速度,我们前面也讲过了,指向圆心
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So, time is measured as a parameter along the motion of the particle.
这样,时间就被记为质点运动的一个参数
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You must remember that this describes a particle going side to side.
务必记住,描述的是一个质点的横向运动
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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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I can also describe a particle going up and down.
我也可以描述一个质点的纵向运动
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If you want to describe this particle, what's the kinematics?
如果你想描述这个质点,如何从运动学角度来描述呢
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We are talking about particles of constant acceleration.
我们目前都是在讨论匀加速运动的质点
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It's the actual motion of the particle.
这是质点的实际运动路线
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What is the fate of this particle?"
质点会怎样运动呢"
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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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I will draw the famous picture of some particle moving and it's here at t of some value of x.
我会画某个质点运动的,经典图像,这是某个x值对应的时间t
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What a particle tries to do generally is some crazy thing which doesn't have a name, but it's a function x of t.
一个质点的运动一般非常混乱,因此对应的函数没有名字,但它还是函数x
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Then, I gave you one other very important example of a particle moving in the x-y plane.
下面我再拿一个重要的例子,质点在 x-y 平面内的运动
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So what I've said so far is, a particle moving in time from point to point can be represented by a graph, x versus t.
到目前为止,我说过,一个质点随时间的连续运动,可以用一幅x-t图来表示
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Our picture now is going to be some particle that's traveling in the x-y plane.
我们现在的情景是在 x-y 平面内,运动的质点
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We said, "Let's take, for the simplest case that we can possibly imagine, namely a particle moving in one dimension along the x-axis with a constant acceleration a.
我们说过,"考虑我们可以想象的最简单的情况,即质点在一维空间运动,沿着 x 轴且保持恒定加速度 a
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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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We're going to take an entity that lives along the x axis.
我们拿一个只能沿着X轴运动的质点
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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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So, this certainly describes a particle whose acceleration is a.
它确实描述了一个加速度为a的质点的运动
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