So this appears in a problem which looks simple enough in its context; It's something like this:
Two discs, A and B, are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ and $2I$ respectively about the common axis. Disc A is imparted an initial angular velocity $2\o...
@JohnRennie Yes sir. But in linear collisions, energy is lost due to permanent deformation. But here where is the deformation sir. The energy is lost as heat, but in the linear case, it is lost as plastic deformation. This is why I'm confused sir.
@yuvrajsingh That's a little bit of distraction introduced by the question setter. It has nothing to do with our question it just spins. And that's it.
:)
May be you can imagine that like, a spring powered toy
@yuvrajsingh I'm asking why should it be conserved when there is a loss in energy. Yes it contradicts with the case of linear collision. But energy loss is of different nature in both cases.
@Intellex well the coupling only happens when the two disks contact each other. If a system like the two disks you're only going to get an elastic coupling if there is somethign flexible in between the two disks that can twist without slipping.
If there's any slipping you'll get energy loss due to friction.
@Intellex lets say the object sits on the x-y plane and you wish to calculate Izfor sake of simplicity. Your infinitely thin slices also have tiny offsets from the x-y plane that need to be taken into account via the parallel axis theorem. This leads to a quadratic term in your infinitesimal which only goes away if the object is 2D
If we can apply the theorem to 2d layers separately. Then we can find the moment of inertias of these layers and then sum them to obtain the MOI of the 3d object.
@Intellex The reason is that although the laminas have the same z axis, they do not have the same x and y axes. So you cannot simply add the moments of inertia (MOI) for the x and y axes for each lamina.
No, as I mentioned you cannot simply add the moments of inertia (MOI) for the x and y axes for each lamina. The x and y axes for each lamina are parallel but they are off-set from each other and from the x, y axes you are using for the 3D object
@JohnRennie sir, when in an n-type a donor state donates an electron to conduction band...a +ve site is created...but it isn't called a hole...Its simply written that its immobile and localized...
@JohnRennie why is it so sir? Can't an electron come and occupy that empty position in the donor?
@user8718165 n-type donor states sit just under the bottom of the conduction band, so the difference between the energy of that state and the bottom of the conduction band is much less than kT. That's why thermal energy is enough to excite the electron from the donor state into the conduction band.
The electron can fall back into the donor state and neutralise it, and indeed that will happen at absolute zero.
But at room temperature the state is ionised due to the thermal energy.
For a while now I've noticed that if I take a cup of hot tea and pour it into two cups and leave it then both cups will cool faster than the single cup.
How is it that nature cools two cups of tea in parallel more quickly? It's still the same amount of tea but it gets cooled quicker if I have two cups
When you divide the liquid into two cups you have a greater surface area to volume ratio.
Since the rate of heat loss is proportional to the surface area, and the heat capacity is proportional to the volume, that means the rate of temperature decrease is faster.
once the container is at the same temperature as the tea, it will stop absorbing heat from it. After that, it will still act as a poor conductor of heat - but that is not a heat capacity effect, and much less significant than the evaporation
@yuvrajsingh the tea will be cooling by evaporation and also by convection through the walls of the teacup. I'm not sure how the relative rates compare, though evaporation i a very efficient cooling process so I'd guess it dominates.
In an intrinsic semiconductor either: - the gap is small enough that some electrons manage to cross it or - there are minority carriers due to defects in the crystal
Remember that the energy of electrons at a temperature $T$ is something like a Boltzmann distribution i.e. the fraction of electrons with energy $E$ is proportional to $f(E) \propto e^{-E/kT}$.
So if the band gap is $nkT$ then the fraction of electrons that can jump to the conduction band is proportional to $e^{-n}$.
@JohnRennie okay sir...got it...let's assume ideal crystal, there the gap will be much larger than kT but after p type doping there will be allowed states near the valence band so more electrons can reach the acceptor state.
How does the e- know whether a state is allowed or not...I mean how does the e- know if it can jump to a state by absorbing a photon sir?
@JohnRennie yeah sir...got it...
@JohnRennie In the intrinsic case...it won't accept a photon of energy kT but after doping it can accept. Does the e- know beforehand that if a state is available or not so it will or won't accept a photon sir?
This might be a stupid question, but nonetheless, it has been bothering me.
If you take a photon, make it go through some atoms in a solid, liquid or whatever, then you have the chance of this photon being absorbed by an electron, and thereby exciting the electron. This requires the photon to ha...
Electrons scatter of lattice vibrations and scatter off other electrons so the energy from the lattice gets randomly distributed over all the electrons.
It's because the energy is randomly distributed that we get a Boltzmann distribution and a small fraction of electrons can get enough energy to cross the gap.
And that's about 40 times kT, so the fraction of electrons thermally excited acoss the gap is proportional to $e^{-40}$ and that's a very, very small number!
So this appears in a problem which looks simple enough in its context; It's something like this:
Two discs, A and B, are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ and $2I$ respectively about the common axis. Disc A is imparted an initial angular velocity $2\o...
