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First, the electron isn't actually spinning. Physical objects made up of collections of electrons and protons (and neutrons) can have angular momentum because they rotate; the electron does not get its angular momentum for the same reason. Second, the magnetic moment of an object with angular momentum L is proportional to $$ \mu \propto \frac{qL}{M} $$ ...


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You seem to be saying that friction couldn't speed it up, because nothing else is moving that fast. Well, how fast is it moving? We can imagine the gyroscope axis parallel to the z axis, and the casing to be aligned such that the x axis goes through it. If the casing is tipped slightly, the gyroscope resists that turning and one side of the shaft has firm ...


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Not all galaxies are disk-shaped, but some certainly are. (Some others are spiral, etc.) For one thing, we see a lot of galaxies, and several of them look exactly like they would if they were disk-shaped and we were just seeing them from different angles. Some seem circular because we are seeing them head-on, while others seem more linear or elliptical ...


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1) I don't understand your questions really well. Consider rephrasing it to make it a bit clearer. What I can tell you is the following: The mathematical definition of the principal axes of inertia is that they are the eigenvectors of the inertia tensor. The physical interpretation of the principal axes of inertia is that they represent the directions ...


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For the relation between the abstract position basis and the $L^2$ spaces, I refer you to my answer here (read the other answers too, they're good ;) ) You are quite close with your understanding of the representations, but not quite there: First of all, for the 2-dim spin-$\frac{1}{2}$ Hilbert space $\mathcal{H}_{\uparrow\downarrow}$, the set of ...


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There seems to be no way to proceed unless more information is given. In fact, from what you have above (correcting the typo pointed out by Bernhard and ticster): $$ \vec{j}=\vec{l}+\vec{s} \quad \Rightarrow \quad \vec{j}^2=\big(\vec{l}+\vec{s}\big)^2 = \vec{l}^2+\vec{s}^2 + 2\, \vec{l}\cdot\vec{s}\,, $$ meaning that knowledge of the eigenvalues of ...


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$$D(\hat{X}_i):= \left\{ \psi \in L^2(K, d^nx)\:\left|\: \int_K x_i^2|\psi(x)|^2 d^nx< \right.+\infty \right\} = L^2(K, d^nx)$$ where the last identity holds true if $K$ is bounded (in particular compact) because $x_i^2$ is bounded as well thereon (in this case the operator is bounded, too). Moreover $$D(\hat{J}^2):= \left\{\psi \in L^2(\mathbb S^2, ...


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As the previous post mentioned, forget about the concept that the electron is actually spinning. Spin, like rest mass and electric charge, is an intrinsic property of subatomic particles. Yes, it's angular momentum. No, nothing is spinning. Although many physicists today do not like this explanation, special relativity introduces a useful analogy with mass. ...


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Regarding the second question: The parallel axis theorem states, that if you have rotation around another axis than a body's center of mass, you only have to add the inertia tensor of a point mass at the location of the body's center of mass. And because of your setup, you will probably not be able to measure more than one component of the person's inertia ...



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