# Will macroscopic object change its angular velocity after absorbing electron?

Consider macroscopic object (a ball for instance) which has angular momentum equals 0. Now single electron hits the ball and is absorbed by it. Let's assume it hits in direction perpendicular to tanget plane to the point of hit.

As an electron is quantum of angular momentum, the total angular momentum of composite system (ball and electron) must change due to conservation of angular momentum.

As angular velocity of macroscpic object is proportional to its angular momentum the ball should start rotating (although very slowly due to small amount of momentum carried by electron and large moment of inertia of ball).

Is this true? And if so, how is it possible to rotate an object using non-rotating particle (electron)?

This question is perhaps naive and maybe I miss something, but I would be grateful for explaining this.

• Are you still interested in an answer? Did I answer your question? Oct 6 '13 at 21:23
• Yes, thanks for the answer. I'm sorry for no feedback. My question is of course not well formulated, but I cannot do it better for now. What I'm trying to understand is the connection between quantum (no rotation) and macroscopic angular momentum. How concept of the former is connected to the concept of rotation of large object. Oct 8 '13 at 14:24

If you hit the ball “in direction perpendicular to tanget plane to the point of hit”, you mean radially? That way, the impact would not exert any torque onto the ball. So if the electron has a significant mass, you would not see the ball rotating.

I think you are refereing to the spin of the electron. The electron has a spin of $\hbar/2$, which is nothing compared to a macroscopic object.

The important thing is, that although it has the same dimension as angular momentum, spin is something from quantum mechanics and has no classical analogue. One of my professors said that “Nobody has ever seen anything spinning there. It just behaves like angular momentum, mathematically.”

On the other hand, black holes are described by only a handful parameters. Two are spin and mass. And there are rotating black holes, so spin should be able to make those spin.

I assume that your problem is different, because the electron has its spin, but it has to keep it, because of quantum mechanics. Therefore, it cannot give the spin to the ball. Additionally, just because there is a spinning object on the ball, the ball does not have to spin.

If you hold a spinning object, like a bicycle wheel, above your head, you do not start spinning, although the total angular momentum of you and the wheel is not zero any more.

So I would say that the total angular momentum, that consists of classical and spin, is not zero. The ball does not rotate, though.