During this part, when you're doing a quarter of a circle, this is supposed to be a quarter of a circle.

在这部分,当你沿着四分之一圆运动,这就是个一个圆的四分之一

耶鲁公开课 - 基础物理课程节选

improve your range of motion and strengthen those muscles, they get weaker during that process

改善你的运动范围并加强这些肌肉，它们就会在运动过程中变弱，

健康生活 - SpeakingMax英语口语达人

If you give a sign, on top of the number, that takes care of all ambiguity in one dimension.

如果你在数字前加一个符号,就把一维运动的所有的歧义解决了

耶鲁公开课 - 基础物理课程节选

So if you were learning rhetoric, for example, you might practice giving speeches at the gymnasium.

如果你在学习修辞学，就可以在运动场通过演讲来练习。

耶鲁公开课 - 新约课程节选

Or a football player--when you're running down the field, why did you go to this way instead of that way ? when you're running down the field?

或者是问一个橄榄球运动员--当你在操场上奔跑时，你为什么要往这边跑而不是那边呢,当你在操场上跑的时候？

耶鲁公开课 - 金融市场课程节选

as Plato and Socrates clearly understand, a very real tendency within democracy to identify the good human being, you might say, the good sport, the regular guy, the cooperative fellow, you know, someone who goes along and gets along with others.

柏拉图和苏格拉底清楚地明白，那存在着一种很真实的倾向,在民主之中辨识出好的人性，你也许会说喜爱运动的人，好人，乐于合作的人，即可以轻易和众人,打成一片的人。

耶鲁公开课 - 政治哲学导论课程节选

I mean the truth is I'm proud to be part of a movement in which I get to call you a colleague and a friend and a mentor because what you can do here at Princeton with the Faith Council, what college chaplains, what pastors and rabbis what other people in the interfaith organizations we're a movement and we're fighting with each other and we're moving together.

事实上，我很自豪能参与到一项运动中,在这里我能称你为同事或朋友,或导师,因为你在普林斯顿大学,为信仰委员会所做的，大学牧师，基督教及犹太教牧师,以及其他在跨信仰组织中工作的人们,我们在发起运动，我们相互斗争,我们一同前进。

普林斯顿公开课 - 人性课程节选

And so you can imagine that even in its— with all of this activity on your skin, even at its most--least serious level, it's a terrible disease.

你可以想象这些,即使在,伴随着皮肤上的任何运动,即使是最轻微的活动,也会带来严重的问题

耶鲁公开课 - 生物医学工程探索课程节选

So, your tongue is closer to your jaw than it is to your hip in the body; so too in both the motor cortex and the somatosensory cortex.

所以相对于屁股,你的下巴在身体上距离你的舌头更近,而在运动皮层与感觉皮层上的位置,也是这样对应着的

耶鲁公开课 - 心理学导论课程节选

But things which were at rest will move at a constant velocity, opposite of the velocity that you have relative to me.

这些静止的东西都在匀速运动,方向正好跟你相对我运动的速度方向相反

耶鲁公开课 - 基础物理课程节选

In other words, you don't have to be moving actually in a circle to have the acceleration.

也就是说,你不必真的在一个圆上运动以获得相应的加速度

耶鲁公开课 - 基础物理课程节选

You cannot see the horse, but the horse is moving.

你看不到马,但是它在运动

耶鲁公开课 - 基础物理课程节选

When you have a velocity in the moving plane frame and you want to find the velocity on the ground, you should add to every object in the plane the velocity of the plane with respect to the ground.

当你在运动的飞机上运动,然后你想找到相对于地面的速度,你就应该给每个物体加上,飞机相对于地面的速度

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 基础物理课程节选

The way the physics works is you will find some laws of motion in mathematical form, you put in the initial conditions of whatever, you solve the equations, and the answer that comes, you have no choice.

在物理问题中,你可以用数学方法得到运动定律,你代入初始条件,然后解方程,获得答案,你别无选择

耶鲁公开课 - 基础物理课程节选

You see an object in motion, you find a and you give a a certain numerical value, 10 meters per second squared.

你看到一个物体在运动,你会发现它的 a,然后给 a 赋值,10 米每秒平方

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 基础物理课程节选

You see how long you are in the air and the whole time you are in the air, you are traveling horizontally at this speed.

你可以知道在空中停留的时间,当你在空中运动的时候,你一直以这个水平速度在运动

耶鲁公开课 - 基础物理课程节选

What's your plan for measuring acceleration if some little thing is moving?

如果某个小物体在运动,你要如何测量加速度

耶鲁公开课 - 基础物理课程节选

For example, suppose you use vertical motion and you use y instead of x; and a would be g or -g; that's a particle falling down under the affect of gravity.

例如,假设在竖直运动中,你用 y 来代替 x,那么 a 就是 g 或者 -g,这就是一个受重力作用下落的质点

耶鲁公开课 - 基础物理课程节选

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

耶鲁公开课 - 基础物理课程节选

If you want to know how fast it's moving at a given time, if you want to know the velocity, I just take the derivative of this answer, which is 10-10t.

如果你想知道它在给定时刻的运动有多快,如果你想知道它的速度,我只要对这个式子求导,得到10-10t

耶鲁公开课 - 基础物理课程节选