Why is it that the raising and lowering operators in a spin 1/2 system have a factor of $\hbar ?$
From Sakurai:
$$S_+ \equiv \hbar | + \rangle \langle - |, S_- \equiv \hbar | - \rangle \langle + |$$
"So the physical interpretation of $S_+$ is that it raises the component by one unit of $\hbar...
By dimensional analysis, we have that the wavenumber: $$k = \frac{\text{radians}}{\text{distance}}$$
And the wavelength:
$$\lambda = \frac{\text{distance}}{1 \text{wave}}$$
Then:
$$\lambda k = \frac{\text{radians}}{\text{distance}}\frac{\text{distance}}{1 \text{wave}} = \frac{\text{radians}}{1...
Suppose I wanted to prove the work-kinetic energy theorem. This means that I want to show that
\frac{1}{2}m( \vec {v}^2_f - \vec{v}^2_i)=\int_{x_1}^{x_2} \vec{F} \cdot dx.
So, I go ahead and start on the right side:
\int_{x_1}^{x_2} (m \frac{d\vec{v}}{dt}) \cdot dx = m \int_{x_1}^{x_2}...
Newtonian mechanics is considered an extremely valid "approximation" for large objects whose speed relatively small (compared to the speed of light).
But, we generally acknowledge that they aren't "true," even though they are still useful. My question is are Maxwell's equations similar in this...
Haha yes, I realized as much today, but you beat me to it! I am going to try and not look at the rest of your post because I want to derive it on my own, but it looks like you know what you are doing. Also, what commands do you use on this forum for Latex support?
Can you explain what you mean...
Something like:
-T(x)cos(Θ) +T(x+Δx)cos(Θ+ΔΘ)=0
Where T is a function of x. I am not really committed to an intuition either way as to whether or not the tension force has to be constant throughout the string.
I am not really sure how the midpoint is suspended at all if there is no component...
Thank you for your reply. Unfortunately, I have not taken a course in classical mechanics yet, and so I do not know what a Langrangian/Hamiltonian is. Here is an example of a force analysis of the problem, but I don't quite understand some of the steps they take...
I am not quite sure, I too do not see how the tension can be the same everywhere. Also, as you pointed out, how is it that at the midway point the center is suspended at all if theoretically the slope of the line at that point is zero (and so there can be no vertical component of T)?
Let's say I am trying to derive the equation for the hanging cable. The solution is a catenary curve. My question is:
In the setup for this problem, one would begin by considering some small segment of the string and analyzing the forces on it. Because it is in static equilibrium, the forces...
Imagine I have a rocket with a certain amount of energy stored as chemical energy, lets say its 10Js, that exhausts itself after 5 seconds. If I attach this rocket to a (relative to an observers frame) stationary cart in such a way that it pushes the cart, it will add 10J of kinetic energy to...
I am not saying that the static frictional force is proportional to the coefficient. The coefficient merely gives a maximal static friction force possible, like you said. But this still does not explain why the static frictional force will be different for the two rolling objects.
If we held the surface area to be the same, why would the frictional force be different? Furthermore, if we assume that the frictional force is only the simplified version of the normal force and the coefficient of friction, then with similar materials the frictional force should be the same.
I am having trouble wrapping my head around a physics concept.
If we roll solid sphere down an inclined plane it will reach the bottom at a different time than if we were to say, roll a hoop down the same inclined plane. This is because they have different rotational inertias, and so more of...
For those of you still interested in this thread, here is where I am at so far.
Ignore the OP's original arguments. I don't see how you can escape the following conclusion:
To Oscar, the event of Jim landing on Alkaid had already happened (in his first frame) but upon switching frames hasn't...
Didn't I specify "really simultaneous" within a certain frame?
"But special relativity tells us that things really are simultaneous in a different frame. "