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When you want a point particle, if you wake up and find a point particle on your bed, what's your reaction?
当你想要一个质点,想当你醒来时发现一个质点在你的床上,你是什么反应
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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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If all you know is the particle is falling under the affect of gravity, that's not enough to say where the particle is, right?
如果你只知道,质点受重力作用下落,那并不足以表明物体的位移,对吧
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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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Because any velocity I ascribe to a particle or an object, you will add a certain constant to it by the law of composition of velocity.
因为我描述的任何一个质点或者物体的速度,你都要根据速度叠加法则,给它加上某个常数
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So we have to ask now, now that my claim is, you can ask me any question you want about this particle and I can answer you.
现在我们要问,我的观点是,你可以问我任何关于,这个质点的问题,我都可以回答你们
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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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For example, let's take the case where the particle is falling under gravity.
比如说,举个例子,一个质点正在重力的作用下下落
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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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At least there, the fact is not a point particle is important.
至少在那个时候,它不是质点才是最重要的
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I cannot make the object simpler than being just a mathematical point.
找不到比质点更简单的模型了
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Here it meant particle that was released from the ground earlier.
这里我说的是先前从地面释放的质点
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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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You want to know how fast the guy is moving.
你们想知道这个质点的速度有多快
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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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Now we know everything about this particle.
现在我们了解了关于这个质点的一切情况
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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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A clock tells you what time it is, but you can also say what time it is by seeing how fast the particle is moving because you know it started with some speed.
时钟能告诉你现在的时间,但你也可以通过测量质点速度,来判断当前的时间,因为你知道它的初速度
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It knows that this particle happened to have a height of 15, at the time of 0, and a velocity of 10, and it is falling under gravity with an acceleration of -10.
这个质点恰好处在高度为15的地方,零时刻,初速为10,并在重力作用下以-10的加速度下坠
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How fast is this particle moving?
那么这个质点的速度是多少
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I want to consider a particle which has definite acceleration a, a constant one, but a is now a vector.
我想考虑一个加速度为 a 的质点,加速度恒定,但 a 是一个矢量
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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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You're only given the particle has acceleration a, and you are asked to find out what is x?
你只知道质点的加速度为a,你需要求出x是多少
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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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The answer was: at any time t, the location of the particle is given by this formula.
答案是,在任意时刻 t,这个质点的位移都由这个式子给出
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So what I'm saying here is we are specializing to a limited class of motion where the particle has a definite acceleration, a.
我在这里想说的是,我们正在专门讨论一类问题,这些问题中,质点都有一个确定的加速度a
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