studiot

Why would you restrict this to solid matter? Do you mean what is usually called solid state physics or do you mean some form of continuum mechanics? Have you done any counts to see if there is enough frequency of posting to warrant separating this stuff out into its own forum?

Well, that is not the relativistic view. Relativity proves time is hyperbolic. Spacetime's basic group is the Poincare group. Time is not right circular. What proof do you have that they are incompatible for you to be able to say this?

An electric current is what happens when there is a net movement of electric charge in a particular direction. Charge is regarded as being 'carried' by various bodies, also called charge carriers. It does not exist by itself. Two types of carrier you will encounter in biology are electrons (negative carrier) which are sub atomic particles (smaller than atoms and part of them) and ions which are atoms (or molecules) with an excess of electrons (negative carrier) or a deficiency of them (positive carrier). Positive charges moving in one direction are equivalent to negative charge moving in the opposite direction. Your instructor meant the movement of electrons when referring to charge current and the movement of ions when referrring to ionic current. Ionic currents normally occur in solution, since ionisation is one way that solutes can dissolve in solvents.

You have made that mathematical statement several times, but there is the view that time is a simply useful parametrisation for many equations.

c) The position vector is the vertical value of the y coordinate of the mass. The seismometer works by having a rigid frame. That is the dimension d does not alter during the motion. So the position vector for the mass can be obtained by noting that the base of the frame is at y, the top at y+d and the mass a distance x down from the top. Can you make an equation of this ? d) The mass suffers two vibrations, the one due to the seismic excitation ( the y) and the one due to its own resonance The (x). The result depends upon the relative constants of the dashpot and the spring, which control the resonant response and how close it is to the excitation frequency. Does the force of gravity make any difference? Remember also (it was what you deduced in parts A & B) that the ground force Asin(wt) does not act directly on the mass. Are any of the forces acting on the mass actually sinusoidal? Further is Y not a force but a distance ?

If two objects are in relative motion does not the separation change, unless that relative motion is zero?

But that velocity is perpendicular to r so are they in relative motion?

Go on.

What were parts A and B? They usually hang together so one leads on to the next. What exactly do you not understand about C and D? You have noted that despite the two axes shown in the sketch this is a one dimensional problem (ie x is not horizontal)? Finally I take it that the spring and dashpot are vertically aligned through the centre of gravity of the mass, so there is no twisting of the mass.

In relation to time and the foregoing discussion about physical and real, consider the following: In space, positions x, (x+10) and (x-10) are all physical and real since I can move my boat from one to the other and back again as many times as I like and place it in any one of them if I am a good enough sailor. But in time I can only observe my boat in the present. I cannot move it to the future or the past or observe it there. So does this make the present physical and real, but the future and past non-physical and non-real?

There is the issue of the motion. Apparent mass gain appears to observers in relative motion. What is the relative motion of two observers at say r/2 and r from the centre of rotation? Does their separation alter?

Of course, John is quite right, the only entity for which A = -A is zero so you are just working on keeping zero to itself. I was thinking about the general trig sum of two angles. CAST is a way of remembering which trig function is positive in which quadrant, here is a list.

Consider alpha = 20 degrees and beta = 50 degrees. Are you really offering that cos (20+50) = - cos (70) ? Some of these statements depend upon which quadrant your sum ends up in, have you heard of CAST?

Does Hooke's law matter? By the looks of things rkt was suggesting calibration. I was going to suggest something like that myself, along with what we used to call a spud gun (that used a coil spring).

[math]I = \int {\frac{{du}}{{1 - {u^2}}}} [/math] [math] = \frac{1}{2}\ln \frac{{1 + u}}{{1 - u}}[/math] [math] = \frac{1}{2}\ln \frac{{1 + \sin x}}{{1 - \sin x}}[/math] [math] = \ln |\tan \left( {\frac{\pi }{4} + \frac{x}{2}} \right)|[/math] [math] = \ln |\sec x + \tan x|[/math]

Well done for doing it yourself. +1

Because you have made d(1/cosx) in your line 1 equal to sinx in your line 2 rather than sinx/cos2x So work your integration by parts out again.

You have the right idea with your 1/1 but with the wrong part of the integral [math]I = \int {\frac{1}{{\cos x}}dx} [/math] [math] = \int {\frac{{\cos x}}{{{{\cos }^2}x}}dx} [/math] [math] = \int {\frac{{\cos x}}{{1 - {{\sin }^2}x}}dx} [/math] If we make the substitution sinx=u [math] I = \int {\frac{{du/dx}}{{1 - {u^2}}}} dx = \int {\frac{1}{{1 - {u^2}}}} du[/math] This has three different (logarithmic and trigonometric) forms. Does this help?

What makes you think there is a single most fundamental branch of mathematics? Why should this be so, after all the Hindus thought that the world was carried on four elephants and even neolithic man placed his lintels on two supports. There are many different ways you could divide maths into branches. One such is maths is the study of number and shape. This was certainly true early maths, although the study of Geometry was indeed codified first, this could not have happened without some numebr theory. Here is an interesting viewpoint from one of the world's most famous mystical poets. Coleridege was also responsible for this poem about the first proposition on Euclid's first book of fomal geometry. http://blogs.ams.org/mathgradblog/2013/06/05/euclid-coleridge-poem-2/ More recently we have categorised the subject into two branches Analysis and Synthesis. Synthesis is interesting because it leads to the idea of cmputability, a modern notion. In modern times a good source for your research would be the Cambridge University text "Computability and Logic" by Boolos and Jeffrey go well

Just out of interest what do you mean by this? To balance the forces (is force balance on the GCSE? syllabus) in an infinite ocean it is a relatively simple calculation as CharonY suggests, although you must know a good deal of underlying physics to do this. But to measure the viscosity using stokes law requires some quite sophisticated corrections for real world apparatus.

I am having real trouble reconciling GCSE with first year university, which is where a student would normally meet the Stokes falling ball viscometer. Google provides many hits on stokes visometer here is a university lab from one. http://www.engr.uky.edu/~egr101/ml/ML3.pdf This gives the fully corrected formula. A simpler one is viscoscity, f =[math]\frac{{2{r^2}g}}{{9\nu }}({\rho _s} - {\rho _L})[/math] ps and pL are the sphere and liquid densities respectively r is the sphere radius v is the terminal velocity. I can't see that you could be expected to produce a derivation of even this simplified equation for GCSE

Actually that was the question. The kilograms were an example, as shown by the opening words "for example". The infinitesimal in the example was dm, which dimensionally correctly refers to mass. Since you have revised your question (1) from how many numbers make 1 kg? to How many infinitesimals (I will take that as dm) make 1 kg? and I said I would answer a properly posed question here is my answer. (1) An uncountable number. Perhaps I should point out here that is because the domain is R3. For the series I posted on the other hand the answer is a countable number. I already did answer your second question, quite specifically. You still have not answered any of mine.

Actually it is on topic since it addresses the OP. You have already been told by a moderator that your approach is off topic. Although you have not answered my question, I will answer yours (1) The question is flawed since the units are different on either side of the equation. Couch your question correctly and I will try again. (2) For the purpose of many physical models (already described) yes that is true. It is not a belief system, but a matter of definition.

Are you saying that the following are not true and should not therefore be taught to final high school / tech college / first year undergrads as they have been for more than the last hundred years? [math]\bar x = \frac{{\iiint {\rho xdxdydz}}}{{\iiint {\rho dxdydz}}}[/math] [math]{I_{xx}} = \int {\rho ({y^2} + {z^2})dv} [/math]

No, physics was not implied, maths was explicity called for since the OP not only posted in the maths section as opposed to the physics one, but further chose an area of pure maths over applied maths. In any case your argument that an infinite number of physical points cannot make up 10 kg is suspect. A vast area of physics, including most of classical physics is predicated upon the premise that you can indeed either infinitely divide a finite piece of matter or alternatively assemble a finite piece from an infinite number of parts. This underlies classical statics and dynamics, continuum mechanics, and even the angular momentum of quantum particles is derived from continuum mathematical analysis. Can you tell me any reason why, if each of the numbers in my series posted above was a mass coefficient, I could not assemble 1.6 kg from the first series and 1.2 kg from the second and any other value by suitable scaling?