# Search results for query: *

1. ### LaTeX LaTeX is not working for this code when I Preview

It does not render when I use the preview button. I have read a few threads on this. Seems to be a common problem unfortunately.
2. ### LaTeX LaTeX is not working for this code when I Preview

Not sure how to rectify this. Any ideas? It looks correct via the codecogs website (https://latex.codecogs.com/eqneditor/editor.php) \begin{align} (S \circ R)^{-1} & = \left\{ \left< z, x \right> : \left< z, x \right> \in S \circ R \right\} \\ & = \left\{ \left< z, x \right> : \exists...
3. ### I Surfaces wrapped around a cylinder for 3d printing

Hi All, I am looking to determine how these Vases where modeled using maths on this webpage https://www.3dforprint.com/3dmodel/sine-wave-vase-generator/2116. It looks like the surface is parametrically defined and wrapped around a cylinder. Interestingly he mentions "Sine waves combine to...
4. ### I Muons Decaying on Mt Washington: Expert Answers

Dear Experts, Currently I am reading up on Special Relativity. I struggle to understand how from the perspective of the Muon that the distance to the surface of the Earth is contracted and thus more Muons arrive at the surface based detector. How can this be? To me the physical space is real...
5. ### Angular Momentum of Glass on a String

Hi Folks, Problem Statement How would one use the conservation of angular momentum to explain the attached picture? The rod is held fixed horizontally..the person holds on to the cork and then let's go...apparently the glass is saved due to this conservation... Relevant Equations Momentum...
6. ### Conservation of Angular Momentum

Ah...I understand... homework TYPE questions. Ok. I will know in future! Can this thread be moved or shall I repost? Thanks B
7. ### Conservation of Angular Momentum

Hi. I am not a student and this is not homework. I am reading physicsnin my spare time and occasionally I put a question up to get peoples opinions/help. Please advise how I should proceed for future queries.. Thanks B
8. ### Conservation of Angular Momentum

Hi Folks, How would one use the conservation of angular momentum to explain the attached picture? The rod is held fixed horizontally..the person holds on to the cork and then let's go...apparently the glass is saved due to this conservation...
9. ### To stop a moving object -- Momentum or Kinetic Energy

So in laymans terms if I was to describe a situation to my friend about stopping a 18stone rugby player in his tracks by a sufficient tackle..which would be more appropriate...the energy approach? Or perhaps both are equivalent because to stop him covering more distance instantly is equivalent...
10. ### To stop a moving object -- Momentum or Kinetic Energy

How should I look at the problem at stopping a moving object with the following conditions 1) mass m and speed v 2) 0.5 m and 2v 3)0.5m and sqrt 2 v Simple math tells me the number 2 would require more energy to stop it. I can relate to energy better in terms of how to stop a moving mass...
11. ### Automotive Applying torque to a tube

Then under what conditions does this Torque =inertia times alpha hold that one typically sees in textbooks?
12. ### Automotive Applying torque to a tube

Hi Guys, I have a simple annulus of radius 25mm and 15mm of length 50mm where i applieD a torque of T=100000Nmm. Its inertia about its main axis is I=124.9 kgmm2. Therefore i expect the acceleration to be T/I. Its not clear how to confirm this answer in Msc Adams because when i set simulation...
13. ### MHB Equation for a distributiong force on a half cylinder

Hi Ackbach, This looks good, I think you are moving in the right direction! I have found a pictue online that should clarify my intention. From the picture that we can use as an example. There are approximately 22 nodes circumferentially and 9 nodes axially giving a total of 198 nodes to...
14. ### MHB Equation for a distributiong force on a half cylinder

I created a jpeg of size 145KB which is under 195KB for a jpeg but it still won't load up. 1) It is 7 nodes long 2) Distributing the force circumferentially over 7 nodes and axially over 7 nodes thereby giving total number of 49 nodes 3)Axis is z, correct 4)The total force is acting upwards...
15. ### MHB Equation for a distributiong force on a half cylinder

I cannot attached my sketch as its above max file size unfortunately. I will try again tomorrow
16. ### MHB Equation for a distributiong force on a half cylinder

Folks, I have an FEA applicaton where I need to apply a total force acing vertically upward but to be distributed over half a cylinder (1st n 2nd quadrant). This half cylinder i representd by a set of nodes between 0 \le \theta \le 180 The force will be maximum at 90 degrees and 0 at 0/180...
17. ### Interstellar travel

I should choose my words carefully. I meant "propulsion technology" that major firms are investing in etc at the moment.
18. ### Interstellar travel

but assuming we have the technology it would still be impossible to travel through all that dust without damage? To me, that is the ultimate limitation IMHO!
19. ### Interstellar travel

Hi Folks, What is your opinion on this article? It suggest that interstellar travel is a fantasy. http://www.scientificamerican.com/article/interstellar-travel-as-delusional-fantasy-excerpt/# Yet, I read articles about institutions like NASA investing in various conceptual propulsion...

21. ### Black Hole and Information

Hi Folks, Can somenone explain what "information" is with respect to black holes? I thought it was all about mass and energy from both quantum Mechanics and GR perspective. Why does "information" come into it...sounds unusual to say the least. Thanks B
22. ### MHB Locus of Curves: Solving 4.1.2 with 4.1.10 & 4.1.17

Hi Folks, I am struggling to see how eqn 4.1.17 is determined using eqn 4.1.10 for problem 4.1.2. It is not clear to me what \frac{d\phi}{dt} is. I have inserted the eqns I think might be useful into the one jpeg. Any ideas? Sorry I can't make the picture any clearer given the size limit. Thanks
23. ### Relative Velocity of locus of curves

Hi, This is the best I can do regarding a readable picture where I have pasted the relevant eqns. Thanks
24. ### Relative Velocity of locus of curves

Hi. Ok..I will try another picture again tomorrow. I think there should be enough resolution in the photo when you zoom in. Thanks
25. ### Relative Velocity of locus of curves

Hi Folks, I am struggling to see how eqn 4.1.17 is arrived at using using eqn 4.1.10 at bottom of attachment. Its not clear to me what \frac{d \phi}{dt} is...apart from what is given in eqn 2.1.30... Any ideas? Thanks
26. ### MHB Locus of planer curves

Hi Folks, I am puzzled how entries M_13 and M_23 were obtained in the following matrix M_{2f} as in attached picture. Coordinate systems S1 is attached to bottom left circle, S2 to top left circle and Sf is rigidly attached to the frame. If we assume \phi_{2}=0 we can see that entry 31...
27. ### Implicit Differentiation

I can say I fully understand but perhaps some one can enlighten me regarding what is involved converting derivatives to differentials...for my own understanding and information
28. ### MHB Simplifying Derivatives

Folks, Just struggling to see how this is simplified. \frac{f''(x)}{((1+f'(x)^2)^{1/2}}-\frac{f'(x)^2 f''(x)}{((1+f'(x)^2)^{3/2}}=\frac{f''(x)}{((1+f'(x)^2)^{3/2}} if we let a=(1+f'(x)^2)^{1/2} then I get as far as f''(x)[a^{-1/2}-f'(x)^2a^{-3/2}]=f''(x)[a^{-1/2}-f'(x)^2 a^{-1/2} a^{-1}]...
29. ### Unit Normal for Epicycloid

Ok, great thanks. I should work it out now.
30. ### Unit Normal for Epicycloid

Hi Folks, I got stuck towards the end where it ask to derive the unit normal (eqn 3.2.29 I don't know how they arrived at n_x. I have looked at trig identities...and I have assumed the following n_x=\frac{N_x}{|N_x|} I don't see the (r+p) term anywhere in neither the top nor bottom. PS: I...
31. ### Find Lambda from this arbitrary triangle

Hi RUber, I have it. The extended segment of "a" which forms a right angled triangle with P is Pcos(pi-psi). The tan of lambda is obvious. Thank you very much. I have learned a new way of tacking triangles!
32. ### Find Lambda from this arbitrary triangle

Hi, thanks... This is as far as I got...see attached...
33. ### Find Lambda from this arbitrary triangle

Folks, I am puzzled how one obtains equation 3.2.31 based on the schematic as attached! Can you help? Is there an online source I can refer to to learn how to obtain angles and magnitudes of complex schematics? Thanks
34. ### Implicit Differentiation

Ah ok, So I add in an extra step wrt to x \phi_x+\phi_y \frac{dy}{dx}=0 *by dx to give \phi_x dx+\phi_y dy=0 or wrt to y \phi_y+\phi_x \frac{dx}{dy}=0 *by dy to give \phi_y dy+\phi_x dx=0
35. ### Implicit Differentiation

Sorry, I understand the derivative of a constant is 0 but I still don't see how you get the last term where you have dx and dy by themselves...even if i try \phi_x dx=-\phi_y dy= \frac{dy}{dx}=-\frac{\phi_x}{\phi_y}
36. ### Implicit Differentiation

Folks, Differentiate implicitly \phi(x,y)=0 I get: wrt to x \phi_x+\phi_y \frac{dy}{dx} and wrt to y \phi_y+\phi_x \frac{dx}{dy} however I don't know how this is derived \phi_x dx+\phi_y dy=0
37. ### MHB Unit Normal for Epicycloid

Hi Folks, I got stuck towards the end where it ask to derive the unit normal. I don't know how they arrived at n_x. I have looked at trig identities... n_x=\frac{N_x}{|N_x|}= 1) I don't see the (r+p) term anywhere in neither the top nor bottom. 2) Is the bottom just based on simple trig...
38. ### MHB Implicit Differentiation

I think the last 2 equations are coming from the chain rule so yes I can see that. However, not sure how one arrives at the first equation 3.2.9 by differentiating "both sides"? Thanks
39. ### MHB Implicit Differentiation

Hi, I am referring to eqn 3.2.9 in attached
40. ### MHB Implicit Differentiation

Hi Folks, It is been given that differentiation of \phi(x,y)=0 is \phi_{x} dx+ \phi_{y} dy=0 however I arrive at \phi_{x} dx/dy+ \phi_{y} dy/dx=0 via the chain rule. Where \phi_{x}=d \phi/dx etc What am I doing wrong? Thanks
41. ### MHB Shankar - Simultaneous Diagonalisation of Hermitian Matrices

2) I thought that hermitian matrices were orthgonal as per the 4th point of properties in link wiki https://en.wikipedia.org/wiki/Hermitian_matrix Thats why i didn't orthogonalise them... Eigenvectors of Hermitian Matrix eigenvectors '{''{'2,1,1'}','{'1,0,-1'}','{'1,-1,2'}''}' - Wolfram|Alpha...
42. ### MHB Shankar - Simultaneous Diagonalisation of Hermitian Matrices

Asked to determine the eigenvalues and eigenvectors common to both of these matrices of \Omega=\begin{bmatrix}1 &0 &1 \\ 0& 0 &0 \\ 1& 0 & 1\end{bmatrix} and \Lambda=\begin{bmatrix}2 &1 &1 \\ 1& 0 &-1 \\ 1& -1 & 2\end{bmatrix} and then to verify under a unitary transformation that both can...
43. ### Shankar- Simultaneous Diagonalisation of Hermitian Matrices

Folks, What is the idea or physical significance of simultaneous diagonalisation? I cannot think of anything other than playing a role in efficient computation algorithms? Thanks
44. ### MHB Hermitian Matrix problem

Ok, I see it. Thank you!
45. ### MHB Hermitian Matrix problem

But i calculate \lambda to be the square root of the identity matrix which is the identity matrix to which its eigenvalues \lambda_1=\lambda_2=1 from the characteristic polynomial x^2-2x+1. i don't see where \pm 1 comes from
46. ### MHB Hermitian Matrix problem

We would then have $$I v= \lambda^2 v$$ How do we work out the eigenvalues if we don't know the value of M..? To me, the eigenbasis are determined by first finding the eigenvalues and eigenvectors. Not sure what he means by " going to the eigenbasis of M"!
47. ### MHB Hermitian Matrix problem

Hi Folks, I am looking at Shankars Principles of Quantum Mechanics. For Hermitian Matrices M^1, M^2, M^3, M^4 that obey M^iM^j+M^jM^i=2 \delta^{ij}I, i,j=1...4 Show that eigenvalues of M^i are \pm1 Hint: Go to eigenbasis of M^i and use equation i=j. Not sure how to start this? Should I...
48. ### MHB Eigenvectors of 2*2 rotation matrix

1) Ok, so the eigenvector for \lambda_1=e^{i \theta} is \begin{bmatrix}1\\ i\end{bmatrix} and \lambda_2=e^{-i \theta} is \begin{bmatrix}1\\ 1/i\end{bmatrix} To show these 2 vectors are orthogonal I get the inner product <v_1,v_2>=(1*1)+(i*1/i)\ne 0 but I expect 0...?
49. ### MHB Eigenvectors of 2*2 rotation matrix

Then we get - i v_1+ v_2=0 (1) - v_1-i v_2=0 (2) v_2=i v_1 from 1 v_2=-v_1/i from 2 1) These contradict? How is the eigenvector obtained from this? 2) what if we have a situation where \theta=0? Then \sin \theta=0
50. ### MHB Eigenvectors of 2*2 rotation matrix

Hi Folks, I calculate the eigenvalues of \begin{bmatrix}\cos \theta& \sin \theta \\ - \sin \theta & \cos \theta \end{bmatrix} to be \lambda_1=e^{i \theta} and \lambda_2=e^{-i \theta} for \lambda_1=e^{i \theta}=\cos \theta + i \sin \theta I calculate the eigenvector via A \lambda = \lambda V as...