Now, I will not derive it here but what comes out of it, that it is the torque which is the one that we have here in this case, divided by the spin angular momentum.

As the wheel spins, it has spin angular momentum, but as it precesses around like this, there will also be angular momentum in this direction because it's rotating like this.

只要车轮旋转，就会有旋转的角动量，但是当它像这样运动时，就会有一个这个方向的角动量，因为它是像这样转动的。

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So this only holds in situations where the spin angular momentum is way, way larger than the angular momentum that you get due to the precession.

所以成立的情况是，旋转的角动量，比旋进的角动量要，大很多很多才行。

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So the torque will also change direction and so this angular momentum, spin angular momentum will keep chasing the torque and start to rotate freely.

所以力也会改变方向，这个角动量，角动量会保持追着力，并开始自由地转动。

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And as long as I torque it like this, that spin angular momentum wants to go around in the horizontal plane.

只要我这样使力，旋转的角动量就是想要，水平的转动。

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The spin angular momentum is now in this direction, so I'm going to give it a torque like so.

旋转的角动量现在是这个，方向的，我给它一个这样的力。

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It has spin angular momentum.

有了旋转的角动量。

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I am the spin angular momentum.

我就是旋转的角动量。

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What will the spin angular momentum vector then do if the torque is in this direction?

，旋转的角动量矢量会怎样，如果力是这个方向。

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The spin angular momentum is chasing the torque.

旋转的角动量在，追随着力。

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And what does the spin angular momentum do?

旋转的角动量怎么了呢？

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Look at that spin angular momentum.

观察那个旋转角动量。

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Angular momentum has two key components: spin angular momentum and orbital angular momentum.

角动量有两个分量：自旋角动量和轨道角动量。

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So this was originally the spin angular momentum of the wheel.

所以，这是原本的旋转的，角动量。

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So the torque is persuading the spin angular momentum to change.

所以力是使得旋转的角动量，改变的理由。

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Spin angular momentum will start to chase the torque.

旋转的角动量会开始，跟随那个力。

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Matrix Representation about Spin Angular Momentum Operator and Eigenvector on System of Double Electrons

双电子体系自旋算符及其本征矢的矩阵表示

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We have here the spin angular momentum that you saw.

这有一个旋转的角动量，如你们所见。

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So spin angular momentum has the property of stabilizing things.

旋转的角动量有，稳定事物的性质。

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I've changed the direction of the spin angular momentum.

我改变了旋转角动量，的方向。

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You give it spin angular momentum, it becomes stable.

有了一个旋转的角动量，就变得稳定。

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