Recent content by avikarto

You consider a relative velocity between them. Imagine two objects both moving with the same velocity; you would predict no Doppler shift because they are both at rest in the center of momentum frame, for instance.

Why do you feel like the tension must never be larger than the gravitational force? That assumption is in error. Consider, for instance, a system in a plane perpendicular to gravity. You can pull horizontally on an (unbreakable) string attached to an (unmoving) wall with as much force as you...

The normal force is the extra input of force. If the ball were hanging freely, the tension force would equal the gravitational force exactly.

That's just it. As jack action said, friction has nothing to do with this problem. Even without it, there is still the normal force. Thinking about friction won't get you anywhere. Its all about the normal force.

You can't make that supposition. Friction force is a result of the normal force, ##F_f=\mu\cdot F_N##. There IS a normal force, and so there IS a frictional force (unless the coefficient of friction is zero). In any event, you can't just make the normal force vanish.

Some more info for clarification - from different sources, these expressions can be written (for ##\nu=\mu=m##) as... According to Abramowitz & Stegun, EQ 8.6.6, $$P^m_m(z)=\frac{(z^2-1)^{m/2}}{2^m m!}\cdot\frac{d^{2m} (z^2-1)^m}{dz^{2m}}$$ According to Arfken 85, Section 12.5...

The normal force between the ball and the wall produce the horizontal component of the tension in the string. This applies in the example in space as well. As the ball gets pulled down it tries to rotate the string about its pivot point at the wall attachment. Since it cannot rotate due to...

I'd recommend not diving too deeply into the duality topic in your analysis of this particular question. You'll get that info when you need it in your education. For now, just believe that there are discrete photons which carry the energy of your EM wave, and these are the individual things...

Saying that something is a stationary state is equivalent to saying that it is an eigenstate of the system's Hamiltonian. Then, it is clear to see why we say this is a state of definite energy: H |a> = E |a> The Hamiltonian for the free particle is just P^2/m. Its position expectation value...

time=distance/speed t=2d/vx That's all there is to it.

This is really a quantum effect, so it is difficult to explain in terms of physical construction of a wave. Suffice it to say that its all about energy. If you have studied atomic energy levels, then low energy waves might not have the energy required to excite an electron to the n=infinity...

The lower frequency (energy) waves, like radio waves, don't have the energy to knock out electrons from the atoms (ionize the atoms). If the field has enough energy, they can rip an electron off of that atom. This is an action that could change the physical or chemical nature of a molecule in...

Higher energy waves can more easily ionize (or even fully dissociate) the atoms in molecules in our bodies. When these get ionized, they are no longer the molecules that they are supposed to be. That would be one basic-level description. Frequency is proportional to energy. Don't confuse...

I am having trouble understanding the relationship between complex- and real-argument associated Legendre polynomials. According to Abramowitz & Stegun, EQ 8.6.6, $$P^\mu_\nu(z)=(z^2-1)^{\mu/2}\cdot\frac{d^\mu P_\nu(z)}{dz^\mu}$$ $$P^\mu_\nu(x)=(-1)^\mu(1-x^2)^{\mu/2}\cdot\frac{d^\mu...

Specifically, is real*8 still fully compatible this way with newer version compilers? Also, do I lose anything with my simpler definition of pi?