In rotation, force becomes torque, mass becomes moment of inertia, and acceleration becomes angular acceleration.
在旋转时，力变成力矩，质量变成转动惯量，加速度变成角加速度。
And so all we have to do now is to calculate the moment of inertia of the system, and then we can predict what the period — of this pendulum is going to be — which is not my goal.
所以我们现在要做的，是算出这个系统里的转动惯量，然后就可以预测出，这个摆的周期是多少-，这并不是我的目的。
I will ask you for a moment of inertia for some weird line or something like that. OK, but these you should know.
我会让你们求一些，比较奇怪的曲线的转动惯量，这些你们都应该知道。
So we now have a way of calculating the kinetic energy of rotation provided that we know how to calculate the moment of inertia.
现在我们有一个计算，旋转动能的方法，如果我们知道，怎样计算转动惯量。
We have the mass of the sun, we have the radius of the sun so you can calculate the moment of inertia of the sun.
我们知道太阳的质量，太阳的半径,所以可以计算出,太阳的惯性是多少。
Torque divided by moment of inertia is what will cause the angular acceleration, namely the derivative of angular velocity.
扭矩除以转动惯量,就会引起角加速度，也就是角速度的导数。
For the moment of inertia, we want the square of a distance to the axis of rotation.
至于转动惯量，要求的其实是到旋转轴距离的平方。
It has to do, of course, with the moment of inertia, but again, it's independent of mass, radius and length.
肯定是，与时间惯量有关，再次，它与材料无关，还有半径和长度无关。
I mean, there are some spokes here, but let's assume that everything is here, so then the moment of inertia is MR squared.
我是说，有一些偏差，但是假设每件事都在这，所以时间惯量是MR的平方。
I am using fancy words today. And the moment of inertia — the difference with a mass is that the moment of inertia is defined about some axis.You choose an axis.
我今天措辞别致，转动惯量就是——，与质量不同，转动惯量的定义跟旋转轴有关，选定一个旋转轴。
But it's completely different, the moment of inertia, if you rotated it about this axis.
但它完全不同，转动惯量，如果将其绕这轴旋转。
What is the moment of inertia for rotation of a rod about this axis?
关于这个轴的,旋转动动量是多少？
How hard it is to spin something, on the other hand, is given by its moment of inertia.
旋转东西有多难，换着来讲的话，是跟转动惯量有关的。
So, of course, the moment of inertia is extremely modest compared to the sun, because the radius is so small and the moment of inertia goes with the radius squared.
当然，转动惯量是,怎么也比不上太阳的，因为半径太小,而转动惯量,与半径的平方有关。
If I know the moment of inertia, then I know how much rotational kinetic energy there is.
若知道转动惯量我就能知道，转动动能是多少。
Needless to say, that the moment of inertia depends on what kind of object you have.
不用说，转动惯量取决于，你选择的物体。
And that's a very easy thing to apply, and that allows you now in many cases, to find the moment of inertia in situations which are not very symmetric.
它很容易运用，可以运用于很多例子，为了得到，非完全对称情况下的，转动惯量。
If we have a solid cylinder, then the moment of inertia about this axis Q through the center of mass, which I've called Q, equals 1/2 MR squared.
假如有一个实心圆柱体，轴心的时间惯量,通过这个物质的中心，等于1/2，MR的平方。
While gyro and trail effects can contribute to stability, other factors such as the distribution of mass and the bike's moment of inertia can play a role as well.
Ruina说，虽然陀螺效应和轨道效应都有助于稳定性的提高，但是还有其他因素诸如质量的分布，车子当时的惯性。
1/2I So this can also be written as one-half I, C I put a C there you will see shortly why, because the moment of inertia depends upon which axis of rotation I choose times omega squared.
它也可以被写成，这里我写上,你们马上会发现原因，那就是转动惯量,取决于我选择，哪一个转动轴,乘以ω的平方。
OK, so moment of inertia about the z axis so, what's the distance to the z axis?
关于绕z轴的转动惯量,到z轴的距离是多少？
So it is bMg divided by the moment of inertia about that point P.
也就是bMg除以,点P的转动惯量。
And so I know now I can substitute that in there rMg so I get an omega precession now equals rMg times the moment of inertia.
我知道我可以替换,得到ω等于,乘以时间惯量。
For example, the moment of inertia about the z-axis is dV the triple integral of x squared plus y squared density dV.
例如，关于z轴的转动惯量,是∫∫∫δ
By optimization design on the configuration and electromagnetism parameters, the output torque can be effectively enhanced with lower moment of inertia and faster response characteristics.
通过合理设计电机的结构参数和电磁参数，可有效提高电机输出转矩，降低转动惯量，提高电机响应特性。
The pan driving motor assembled on the foundation. Thus this can reduce tilt's moment of inertia and increase the platform's agility.
该平台结构相对紧凑、运动范围广；左右旋转电机固定在底座上，减少了俯仰转动惯量，提高了平台的灵活性。
Conservation of angular momentum, moment of inertia, parallel axis theorem.
角动量守恒，惯量，平行轴原理。
It is demonstrated that the influence of fluid resistance can not be neglected and the effect of moment of inertia of plate may be cancelled.
证明了流体阻力的影响是不可忽略的，而圆板转动惯量的影响是较小的。
It is demonstrated that the influence of fluid resistance can not be neglected and the effect of moment of inertia of plate may be cancelled.
证明了流体阻力的影响是不可忽略的，而圆板转动惯量的影响是较小的。
应用推荐