Amr Morsi

The RMS of a sine wave is A/sqrt(2). The average of half a cycle is 2A/pi. Where A is the amplitude of the sine wave.

I think the energy in the strings (energy of all harmonics) is related to the energy of the particle involved. This includes the kinetic energy and the rest energy. Potential energy is included in the factors affecting the strings.

The integration is in the positive direction of theta. That's why it is the green trace.

I think that Fnet is not zero, it is equal to -dp/dt; where p is the momentum of gases. Vdm/dt is an additional term due to the change of the total mass of the rocket. But, it is not the only effect on the acceleration.

Perhaps because the angle phi in your problem is defined upon -pi to pi. So, when crossing pi it is transferred to a negative value. This may be the reason.

You are right Bignose. But, isn't the power here is most significant: (n!)^n. Plus, at large n the sequence turns to zero.

It will get to the result, alejandrito. Where is the difficulty? Is it the right hand side?

Substitute with 8*pi*Tmn instead of Gmn. And, then raise the index n. I think this will come very close to eq 2 and eq 3. Multiplying with gmn will make the equation loose its nature tensor...... It will be scalar.

That's right. Also, when the paper is raised enough, it is got affected by the dynamic pressure of the blown air, and it get pushed down again..... That's why it vibrates.

First, I think that F(x) = -q gradΦ(x), not F(x) = -q divΦ(x), is the correct formula. Second, you have the potential energy of the charge, which when added to the kinetic energy, gives the total energy E, which is a constant. The last equation is function of dr/dt, d(theta)/dt and r. Another equation for theta is r^2 * d(theta)/dt=constant=a, this equation is analogous to conservation of angular momentum. Both differential equations can be solved to find r in terms of t. Try it yourself.

Some experiments have been made, after making the suitable circumistances, to collide two photons and convert them to a pair of electron and proton with the same energy. Such operation can be expected by Quantum Electrodynamics.

You are right ajb. Photons are particles that carry energy (, frequency and phase). By the way, although the rest mass of protons is zero, they do have a motion mass, which is h*(mu)/c^2, where mu is the frequency of the photon.

Why timo? Multiply both sides by [AA]^-1, which gives x=[AA]^-1 . 0=0. Why not?

Multiply both sides by A from the left and then use the notation you introduced, which is A . vo=0. Then you will have A^2 . x = 0 which gives x=0.

Differentiate with respect to n and equate to zero. And, then find the nearest natural number. Note that x will be considered a constant. Also, I think that n! will be considered constant as differentiation is over a small variation around n.

Do you have a relation D>>E or E>>D? This can be used in an approximation which makes it possible to integrate to a closed form.

What Euclidean Norm and Maxnorm have to do here? You can easily get the limit by substituting with x=1 and y=1, you will get lim f(x,y)=1*1=1.

What is meant by "monotone sequence"?

The only discontinuity is at x=-1, which is not included in the domain (0,infinity). Therefore the function is uniformly continuous in(0,infinity).

It is impossible to have c dimensionless in any system of measurement. It will always be length/time. But sometimes, it is omitted, but, it is known implicitly that any velocity term is divided by c. Actually, I think that the reason the velocity of light has this value is two points: 1. The system we use for measurement. 2. It is a universal constant, exactly such as pi. Actually, it is composed of 2 universal constants (epsilon and mu; permittivity and permeability)where c=1/sqrt (epsilon*mu)

What is meant by "gravitational potential energy is gravity source also" is that it is another manifistation (face) of the gravitational energy. The mass of the potential energy is still "M", icarus2. The only relation connecting it with mc^2 is the following relation, which can be deduced from SR (Special Relativity), neglecting GR effects: -GMm/r+gamma*mc^2=E Where E is the total energy of motion of m. This is equivalent to what swansont is saying.

When cooling a material and then heating it, some parts get heated, and thus expanding, more than others. And, that's why it could break. The more quikly the heating, the more liability to breaking.

Since atoms in one molecule are not moving with respect to each other, then magnetic field will not affect the internal structure of the molecule. But, since the whole molecule is vibrating, then the magnetic field will make the polarized molecule to rotate, but, will not increase, nor decrease its velocity (because magnetic force is always perpendicular to velocity).

I totally agree with you. But, what do you mean by "the singularity is a stable form of energy"?

I can find from another question for you, Alejandrito, that you are perfect in calculus, ...... if I didn't misunderstand you.