# Search results

1. ### I Decaying Muons on Mt Washington

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...
2. ### 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 lets go...apparently the glass is saved due to this conservation... Relevant Equations Momentum...
3. ### 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 lets go...apparently the glass is saved due to this conservation...
4. ### 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...
5. ### 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...
6. ### 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...
7. ### 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
8. ### 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
9. ### 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 dont see the (r+p) term anywhere in neither the top nor bottom. PS: I...
10. ### 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
11. ### 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 dont know how this is derived \phi_x dx+\phi_y dy=0
12. ### 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
13. ### Is matrix hermitian and its eigenvectors orthogonal?

I calculate 1) ##\Omega= \begin{bmatrix} 1 & 3 &1 \\ 0 & 2 &0 \\ 0& 1 & 4 \end{bmatrix}## as not Hermtian since ##\Omega\ne\Omega^{\dagger}## where##\Omega^{\dagger}=(\Omega^T)^*## 2) ##\Omega\Omega^{T}\ne I## implies eigenvectors are not orthogonal. Is this correct?
14. ### QM Sankar 2nd edition -- gram schmidt process on example 1.3.2

Hi I was trying the gram schmidt process on example 1.3.2 page 43 as shown below u1=(3,0,0), u2=(0,1,2), u3=(0,2,5) v1=u1=(3,0,0) v2=u2-proj_(w1) u2=(0,1,2)-((<0,1,2><3,0,0>)/9)(3,0,0) However the top line inner product gives 0....
15. ### Shankar's QM 2nd Edition

Hi Folks, How do we arrive at equation 1.8.7 page 33. We have ##<i|\Omega-\omega I|V>=0##, given ##I=\Sigma_{j=1}|i><i|## we can write ##<i|\Omega-\omega \Sigma_{j=1}|i><i||V>=0## not sure how to proceed from here...
16. ### Vector Space Basis

Hi Folks, I find this link http://mathworld.wolfram.com/VectorSpaceBasis.html confusing regarding linear independence. One of the requirement for a basis of a vector space is that the vectors in a set S are linearly independent and so this implies that the vector cannot be written in terms of...
17. ### Double Slit Experiment: one at a time

Hi Folks, I am not sure I can appreciate the quantum weirdness that supposedly exist because I do not fully understand the experimental set-up of the double slit experiment. I watched the following which left me with some unanswered questions I have some questions about the experimental...
18. ### Fixed and Moving Reference Frames for adding speeds

Hi Folks, I have some misunderstanding how one can add velocities of different coordinate systems. Consider a planet gear rotating about its own axis and also rotating on its carrier so that the so called velocity of the planet gear relative to the carrier is the planet local velocity minus...
19. ### MATLAB Simplify Matlab for/if statements further

Hi Folks, This loop code is working fine but I would like to simplify it further. Can anyone help? Basically, i need syntax to automate the numbers highlighted in bold. k is a 3*3 matrix, SE_ans is a 3*1 vector, A is a 3*3 identify matrix. The rests are just constants. for i=1:size(k,1)...
20. ### DOUBLE cannot convert the input expression into double array

Hi Folks, I have a symbolic A=18*1*18 array containing symbols/expressions. I want to populate certain entries of this array into another matrix. For example K(1,1)=A(1,1,1) I get the following ??? The following error occurred converting from sym to double: Error using ==> mupadmex Error in...
21. ### Ode45 for solution of 4 d.o.f. problem

Hi Folks, I have made up this code in an attempt to find the response time a 4 dof problem. However, I do not get an oscillatory response as I expect, instead I get a straight line which drops off towards the end. Not sure what is happening..any ideas..? function f = Simple_Planetary(t,y) f =...
22. ### Matrix Operations Query

Hi Folks, I have an inertia tensor D in the old Cartesian system which i need to rotate through +90 in y and -90 in z to translate to the new system. I am using standard right hand rule notation for this Cartesian rotation. ##D=...
23. ### What form for the particular integral of this 2nd order Diff Eqn

Hi Folks, I have the following forced torsional vibration problem of the form ##\displaystyle J_0 \ddot{\theta}+k_t\theta=\frac{a_0}{2}+\sum_{n=1}^{\infty} (a_n \cos n w t+b_n \sin n w t)## I assume the solution of the CF is in the form ##\theta=A \cos nwt+B\sin nwt## but I am not sure what...
24. ### Calculate principle moments of inertia given the moments of inertia along directional vectors

Hi Folks, Is it possible to calculate the principle moments of inertia acting along the principle axes of inertia given the moments of inertia and their directional vectors. Ie , I have the following information Moments of inertia ##J_1, J_2,J_3=18kgm2,15kgm2,6kgm2## and the directional...
25. ### Automotive Car Periodic Vibration/Modulation Captured with App - Some Questions

Hi Folks, Prior to leaving my car in for the annual MOT (UK), there were no vibrations to be felt at any speed. However, to pass the MOT I was advised to replace the 2 front tyres as they were worn. Ever since then, there is a periodic vibration which I can distinctly feel at 85mph but it is...
26. ### Simple Question on Gravity to Earth

Hi Folks, Why does a parachutist experience 0g (assuming falling in a vacuum, no drag) when falling towards the earth? How can he not experience gravity when he is in a gravitational field which is pulling him towards the earth. Im sure this is a classical question but I have not found a...
27. ### Formulating the control volume for a mechanical system

Folks, I am having difficulty correctly representing a mechanical system within a correct "control volume at an instant" in order to identify the various energy balance terms given below ##\displaystyle \dot E_{st}=\frac{d E_{st}}{dt}=\dot E_{in} - \dot E_{out}+ \dot E_g## (1) that...
28. ### MATLAB [MATLAB] Simple Undamped Forced Vibration Problem

Hi Folks, I am trying to replicate a solution in Matlab for the following problem ##\displaystyle \ddot x + \frac{k}{m}x = \frac{F_o}{m} \sin w_ot## using 2 first order linear differential equations in Matlab as shown below tspan=[0 4]; y0=[.02;1]; %Initial Conditions for y(1)=x and...
29. ### Theory of Gearing

Folks, I have a book Gear Geometry and Applied Theory by Litvin. It looks pretty hairy and the diagrams/schematics of the kinematic relations etc are difficult to understand. What branch of mathematics does this fall under, diferential geometry and topology? I think I may need to get...
30. ### Polynomial to represent a linear rectangle element

Folks, I have attached a picture illustrating the labelling of the linear reactangle element which can be represented by the following equation ##u(x,y)=c_1+c_2 x +c_3 y +c_4 xy## (1) ##u_1=u(0,0)=c_1## ##u_2=u(a,0)=c_1+c_2a## ##u_3=u(a,b)=c_1+c_2a+c_3b+c_4ab##...