I was trying to derive the determinant itself, I know that is the correct form. I was using the definition of a cross product to do the curl; however, the curl is not really a cross product of vectors in an orthonormal basis.
I have a vector in cylindrical Coordinates:
$$\vec{V} = \left < 0 ,V_{\theta},0 \right> $$
where ##V_\theta = V(r,t)##.
The Del operator in ##\{r,\theta,z\}$ is: $\vec{\nabla} = \left< \frac{\partial}{\partial r}, \frac{1}{r}\frac{\partial}{\partial \theta}, \frac{\partial}{\partial z}...
I see, that makes sense. Would you say du/dy is the usual slope V/h ? While ##\partial u / \partial y ## accounts for the velocity V affected by slip and the "new" height, such that ## (V - 2\delta u)/(h + 2b) ## ?
That is for no-slip condition, this is Slip condition. The velocity at the top is not V, because there is slip. Same at the bottom, the fluid is not attached to the plate, as there is slip.
The problem states:
Two parallel plates separated by distance h, the plate at the top moves with velocity V, while the one at the bottom remains stationary.
My initial approach was:
I considered, ##du/dy = V/h## and for the shear stress ##\tau = \mu \frac{\partial u}{\partial y}##
For...
We looked at linear deformations in the x,y and z direction, as infinitesimal displacement, then by rearranging terms we got
$$\frac{1}{V} \frac{dV}{dt} = \nabla \cdot \vec{v}$$
We talked about infinitesimal displacements and we rearranged them (by treating them like ##\Delta x_i##), so we ended...
in class we derived the following relationship:
$$\frac{1}{V}\frac{dV}{dt}= \nabla \cdot \vec{v}$$
This was derived though the analysis of linear deformation for a fluid-volume, where:
$$dV = dV_x +dV_y + dV_z$$
I understood the derived relation as: 1/V * (derivative wrt time) = div (velocity)...
I am reading a book of Fundamental Energy Systems.
The author describes the rate of change in head for a turbomachine as:
$$ \frac{1}{2}[(V_1^2-V_2^2)+(U_1^2-U_2^2)+(V_{R2}^2-V_{R1}^2)] = H =U_1V_{u1} - U_2V_{u2} $$
and the static effect as:
$$SE =(U_1^2-U_2^2)+(V_{R2}^2-V_{R1}^2) $$
However...
I was looking at Kirchoffs Laws:
"A solid, liquid or dense gas produces a continuous spectrum".
I would expect objects to produce an emission spectrum since we would be observing the photons that come from spontaneous emission of electrons in excited states. This photons are specific to the...
I am unsure as to how to apply binding energy since we did not see this in class. I did take his advice into account. But got the same answer in the end.
What is the author meaning by that, I literally just read in section 5.1, that the depending on the energy loss of the electrons that make up the substance, this energy will be released as photons. Since this is particular for each atom, it explained how we can tell which element is wich.
So if...
Yeah it was supposed to be MeV. My mistake there.
I did check several websites including Wikipedia, it states that the mass is less than 0.12 eV/c^2. So since it is not a concrete number and the mass is so small it seems mass less I arrived to the conclusion that perhaps I should not include it...
Summary: The problem states Tritium decay into Helium, an electron and an electron neutrino.
Questions of the problem: a) To write an expression for the single particle transformation that occurs at the nucleus.
to which i wrote: n -> p + e + v
b) Is to calculate the energy released by the...
I was reviewing physics stuff and I've managed to confuse myself.
I was reading about work (principles of ohysics, serway&jewtt):
-work is an energy transfer
-if work is done on a system and W is positive, energy is transferred to the system; if W us negative, energy is transferred from the...
Hey guys, so I am reading this book and on pages 89-90, the author says:
"Increasing temperature correspond to a decreasing slope on Entropy vs Energy graph", then a sample graph is provided, and both in that graph and in the numerical analysis given in page 87 the slope is observed to be an...
Sorry about that, I could not track the post I had done already. Here is the sketch of how I am working it out on my mind.
https://imgur.com/spbCzfS
Since he says: 'the tangential component of g (the component normal to the true grav force)'
The thing is in page p.347 Taylor, it is said that the component is:
g_tan = Omega^2*Rsin(theta)cos(theta) However the angle between the centrifugal Force and the axis normal to the direction of the grav Force is actually 90 - theta, I am not really getting where I am going wrong understanding...
I do not understand why the tan component for a gravity affected by the centrifugal force:
g = Ω^2 * R * sinθ * cosθ
So I tried to draw this: using a "big" X-shaped axis where the / component goes along the main gravity direction while \ points normal to / this direction. Then the centrifugal...
Would you guys mind doing a diagram for this? I do not know why I am not getting it. I tried doing a diagram myself, I ended up with an X looking diagram with x-axis going from NW to SE (having this shape \ ). And the y-axis would be this element: / (So g_0 is pointing along this axis). With...
I am a bit confused on the projection aspect, I can only recall projection involving cos(theta) so would you mind explaining how to derive that projection?
Homework Statement
Acceleration experienced by an astronaut in a rotating space station.
Homework Equations
What force would he experience is his own rotating frame of reference.
The Attempt at a Solution
Newton's second Law for a rotating frame is:
mr'' = F net+ Fcor + Fcf
Fnet (In the...
Hey guys, I reading over Taylor's Classical Mechanics book. Chapter 9, Centrifugal Acceleration Section.
In p.346 he mentions that for a free fall acceleration:
g = g_0 + Ω^2 * Rsinθ ρ
Where its radial component would be...
A total derivative dU = (dU/dx)dx + (dU/dy)dy + (dU/dz)dz. I am unsure of how to use latex in the text boxes; so the terms in parenthesis should describe partial differentiations.
My question is, where does this equation comes from?
I assume Griffiths was aware of this and added a whole Appendix, explaining linear algebra applied to complex numbers. However it was in this section where my question came from. As a reminder, elementary linear algebra does not involve complex numbers, which is what triggers the use of the...
Personally I liked the QM book better that the Electrodynamics one. I found that in the Edynamics one, he normally skips a lot of steps during his examples or proofs, and also makes a lot of references to problems that are provided; however, one does not normally have the time to work all of...
So from what I understand, the Inner product definition for complex numbers is just a different definition from the actual dot product? Since properties are lost if the 'usual definition' of dot product
Hey guys, as an update, I continued reading on the Linear Algebra Apendix, as in the Matrix section he states: "The inner prodect of two vectors cab be written very neatly as a matrix product: <a|B>=(a+)b ."
The plus is intended to be a dagger, that is the Hermitian Conjugate. Which meas that...
Thank you guys, I think I just got confused with the notation since we have been using * for conjugates. And he normally does in the book too, thank you!
Hey, I am currently reading over the linear algebra section of the "introduction to quantum mechanics" by Griffiths, in the Inner product he notes: "The inner product of two vector can be written very neatly in terms of their components: <a|B>=a1* B1 + a2* B ... " He also took upon the...
Its potential would be stronger the closer this one is to it? And how can a Potential go towards infinity, I feel pretty lost on the subject. Thank you for the help btw!
So I have been wondering:
The potential for a point charge at the origin, is described as:
(Using the reference point at infinity): V=1/(4πε) * q/r
My question is, what happens to this Potential the closer we are to the point charge, and so the closer we would get, the Potential seems to go...
Yeah it comes with a diagram, but i do not see how multiplying L by the displaced angle, I can end up with the length of the arc. Like, how the unit conversion works. for that? With the diagram I can see where the the restoring force in the pendulum comes from though.
1. Homework Statement
Hey guys, I am reading my Physics book, in that specific section it says "the restoring force must be directly proportional to x or (because x=(theta)*L) to theta"
Homework Equations
The Attempt at a Solution
I have tried to look for that x=(theta)*L relationship...