OpenLLM-France/wikimedia huggingface dataset:
# A-level Physics (Advancing Physics)/Pair Production and Annihilation
## Pair Production

Sometimes, a photon turns into a particle and its antiparticle, for example, an electron and a positron. It could not turn into just an electron, since this would leave the lepton number unbalanced. The photon must have enough energy to create the masses of the two particles. The energy required to create one of the particles is given by:
$E=mc^{2}$,
where m is the mass of the particle, and c is the speed of light (3 x 10$^8$ ms$^{−1}$). However, two particles must be created. Since the two particles are each other's antiparticle, they have identical masses. So, the total energy required is:
$E=2mc^{2}$

## Annihilation

When a particle meets its antiparticle, the two annihilate each other to form 2 photons (due to conservation of momentum) with sum total energy equivalent to the total mass-energy of both particles.
Sometimes, a pair of particles annihilates, but then the photon produces another pair of particles. Also, a photon could produce a pair of particles which then annihilate each other.

## Questions

h = 6.63 x 10$^{−34}$ Js
1. The mass of an electron is 9.11 x 10$^{−31}$ kg. What is the minimum amount of energy a photon must have to create an electron?
2. A 1.1 MeV electron annihilates with a 1.1 MeV positron. What is the total energy of the photon produced?
3. What is its frequency?
4. What is its wavelength?
5. A newly produced electron-positron pair are likely to annihilate almost immediately. Under what circumstances can this be avoided?
Worked Solutions
# A-level Physics (Advancing Physics)/Pair Production and Annihilation/Worked Solutions

h = 6.63 x 10$^{−34}$ Js
1. The mass of an electron is 9.11 x 10–31 kg. What is the minimum amount of energy a photon must have to create an electron?
$E=2mc^{2}=2\times 9.11\times 10^{-31}\times (3\times 10^{8})^{2}=1.64\times 10^{-13}{\mbox{ J}}=1.02{\mbox{ MeV}}$
2. A 1.1 MeV electron annihilates with a 1.1 MeV positron. What is the total energy of the photon produced?
2.2 MeV = 3.52 x 10$^{−13}$ J
3. What is its frequency?
$f={\frac {E}{h}}={\frac {3.52\times 10^{-13}}{6.63\times 10^{-34}}}=5.31\times 10^{20}{\mbox{ Hz}}$
4. What is its wavelength?
$\lambda ={\frac {c}{f}}={\frac {3\times 10^{8}}{5.31\times 10^{20}}}=5.65\times 10^{-13}{\mbox{ m}}$
5. What classical physical conditions might cause a newly produced electron-positron pair to annihilate almost immediately?
Electrons and positrons have opposite charges, and so they attract each other. When they are created, they must have enough kinetic energy to escape each other's attraction. If this is not the case, they will annihilate.
# A-level Physics (Advancing Physics)/Particle Accelerators

Modern experimental particle physics requires particles to be accelerated to very high energies. This is accomplished by passing them through an electric field multiple times, in a similar fashion to an electron gun. Types of particle accelerator include linear accelerators and cyclotrons.

## Linear Accelerators

In a linear accelerator, particles pass through a series of tubes. At either end of each tube are electrodes. An alternating current is used. This means that, when particles pass an electrode to which they are being attracted, the electrode switches charge, and starts to repel the particle. The distances between electrodes increase as you go along the accelerator, since, as the particles accelerate, they travel further per. oscillation of the current.

## Cyclotrons

A cyclotron is like a linear accelerator, except that, instead of using lots of different electrodes, it uses the same two over and over again. The particles move around in a circle due to a magnetic field. The radius of this circle depends on the velocity of the particles. The orbits of the particles are enclosed by two semi-cylindrical electrodes. An alternating current is used to accelerate the particles. When the particles enter one half of the cyclotron, they are pulled back to the other half. When they reach the other half, the current switches over, and they are pulled back to the first half. All the time, the magnetic field keeps them moving in circles. As they gain energy from the electric field, the radii of their orbits increase, and their velocities increase, until the radius is as large as the cyclotron.

## Questions

1. Use the formula for centripetal force to show that the radius of motion depends on the speed of the moving object.
2. A cyclotron with a diameter of 1.5m is used to accelerate electrons (mass 9.11 x 10$^{−31}$kg). The maximum force exerted on an electron is 2.4 x 10$^{−18}$N. What is the maximum velocity of the electrons?
3. What are the problems involved in constructing a large cyclotron?
4. Why don't particles stick to the electrodes when passing through them?
Worked Solutions
# A-level Physics (Advancing Physics)/Motors/Worked Solutions

1. How could you adapt the simple DC motor to use AC?
Connect the coil in the stator in series with the coil in the rotor via a slip-ring commutator. This must be in the correct direction to ensure that the fields created by the two parts of the coil are constantly repelling each other, rather than constantly attracting each other.
2. Why does a three-phase motor have a constant angular velocity?
The vectorial sum of the three currents is constant, so the vectorial sum of the forces on the rotor due to each of the three currents is constant.
3. What is the difference between a split-ring and a slip-ring commutator?
A split-ring makes the current change direction every half-rotation, whereas a slip-ring commutator merely maintains a connection between the moving rotor and the stationary stator.
4. How could the angular velocity of a three-phase motor be increased?
Increase the frequency of the three-phase power.
5. A squirrel-cage motor relies on eddy currents running along the rotor to function. However, if eddy currents run across the rotor, then the force on the rotor is reduced. How may these eddy currents be reduced without reducing the desired eddy currents?
Laminate the plates which connect the rods to each other so that currents are restricted from running in the wrong direction.
# A-level Physics (Advancing Physics)/Orbits

When a planets orbit a star, theoretically, their orbit may be circular. This case is dealt with under circular motion.
In reality, planets orbit in ellipses. An ellipse is a shape which has two foci (singular 'focus'). The total of the distances from any point on an ellipse to its foci is constant. All orbits take an elliptical shape, with the sun as one of the foci. As the planet approaches its star, its speed increases. This is because gravitational potential energy is being converted into kinetic energy.
A circle is an ellipse, in the special case when both foci are at the same point.

## Kepler's Third Law

Kepler's third law states that:
Mathematically, for orbital period T and semi-major axis R:
$T^{2}\propto R^{3}$
This result was derived for the special case of a circular orbit as the fourth circular motion problem. The semi-major axis is the distance from the centre of the ellipse (the midpoint of the foci) to either of the points on the edge of the ellipse closest to one of the foci.

## Questions

| Planet | Mercury | Venus | Earth | Mars |
| Picture | | | | |
| Mean distance from Sun (km) | 57,909,175 | 108,208,930 | 149,597,890 | 227,936,640 |
| Orbital period (years) | 0.2408467 | 0.61519726 | 1.0000174 | 1.8808476 |
1. The semi-major axis of an elliptical orbit can be approximated reasonably accurately by the mean distance of the planet for the Sun. How would you test, using the data in the table above, that the inner planets of the Solar System obey Kepler's Third Law?
2. Perform this test. Does Kepler's Third Law hold?
3. If T$^2$ α R$^3$, express a constant C in terms of T and R.
4. Io, one of Jupiter's moons, has a mean orbital radius of 421600 km, and a year of 1.77 Earth days. What is the value of C for Jupiter's moons?
5. Ganymede, another of Jupiter's moons, has a mean orbital radius of 1070400 km. How long is its year?
Worked Solutions
# A-level Physics (Advancing Physics)/Orbits/Worked Solutions

1. The semi-major axis of an elliptical orbit can be approximated reasonably accurately by the mean distance of the planet for the Sun. How would you test, using the data in the table above, that the inner planets of the Solar System obey Kepler's Third Law?
Divide T$^2$ by R$^3$ and for each planet and see if this value is roughly constant.
2. Perform this test. Does Kepler's Third Law hold?
| Planet | Mercury | Venus | Earth | Mars |
| Picture | | | | |
| Mean distance from Sun (km) | 57,909,175 | 108,208,930 | 149,597,890 | 227,936,640 |
| Orbital period (years) | 0.2408467 | 0.61519726 | 1.0000174 | 1.8808476 |
| ${\frac {T^{2}}{R^{3}}}$ (year$^2$km$^{−3}$ x 10$^{−25}$) | 2.987027815 | 4.85540079 | 2.986972006 | 1.588221903 |
So, Kepler's Third Law does hold for the inner planets, using this rough approximation for the semi-major axis.
3. If T$^2$ α R$^3$, express a constant C in terms of T and R.
$C={\frac {T^{2}}{R^{3}}}$
This is the constant of proportionality. It should be roughly the same for all the planets around the Sun. Alternatively, you can use:
$C={\frac {R^{3}}{T^{2}}}$
We will be using the former to answer the next two questions, but you should be able to get the same answers using the latter.
4. Io, one of Jupiter's moons, has a mean orbital radius of 421600 km, and a year of 1.77 Earth days. What is the value of C for Jupiter's moons?
$C={\frac {T^{2}}{R^{3}}}={\frac {(1.77\times 24\times 60\times 60)^{2}}{(421600000)^{3}}}=3.12\times 10^{-16}{\mbox{ s}}^{2}{\mbox{m}}^{-3}$
5. Ganymede, another of Jupiter's moons, has a mean orbital radius of 1070400 km. How long is its year?
$3.12\times 10^{-16}={\frac {T^{2}}{1070400000^{3}}}$
$T={\sqrt {3.12\times 10^{-16}\times 1070400000^{3}}}=618665{\mbox{ s}}=7.16{\mbox{ days}}$
Which isn't that accurate, due to the approximations that we used.
# A-level Physics (Advancing Physics)/Particle Accelerators/Worked Solutions

1. Use the formula for centripetal force to show that the radius of motion depends on the speed of the moving object.
$F={\frac {mv^{2}}{r}}$
$r={\frac {mv^{2}}{F}}$
So, if F is constant:
$r\propto v^{2}$
2. A cyclotron with a diameter of 1.5m is used to accelerate electrons (mass 9.11 x 10$^{−31}$kg). The maximum force exerted on an electron is 2.4 x 10$^{−18}$N. What is the maximum velocity of the electrons?
$F={\frac {mv^{2}}{r}}$
$v^{2}={\frac {Fr}{m}}={\frac {2.4\times 10^{-18}\times 0.75}{9.11\times 10^{-31}}}=1.97\times 10^{12}{\mbox{ m}}^{2}{\mbox{s}}^{-2}$
$v=1.41\times 10^{6}{\mbox{ ms}}^{-1}$
3. What are the problems involved in constructing a large cyclotron?
Creating a uniform magnetic field over such a large area (for example, the land area enclosed by the LHC) means that cyclotrons have been largely replaced in experimental particle physics by tubes, instead of flat cylinders.
4. Why don't particles stick to the electrodes when passing through them?
There are two reasons. Firstly, alternating current is sinusoidal, so there is no charge on the electrode when the particles are passing through them. Secondly, even if there were charge on the electrode, the net force on the particle would still be 0, since the force would be equal in every direction.
# A-level Physics (Advancing Physics)/Millikan's Experiment

Electrons have a finite charge, which is approximately 1.6 x 10$^{−19}$C. This was first proven by Robert Millikan in 1909. Millikan sprayed drops of oil which were then charged (ionised) either by friction as they were sprayed, or with x-rays. They were then allowed to fall into a uniform electric field.
Once in the uniform electric field, the strength of the field was adjusted in order to keep an oil drop stationary. This was done by hand, looking through a microscope. In a stationary position, the gravitational force and the electric force were balanced - there was no net force on the oil drop. So, at this point:
${\frac {qV}{d}}=mg$
The electric field strength was adjusted by changing the voltage between the two plates. The voltage at which the drops were stationary was measured. The charge on each drop was then calculated. Millikan found that these charges were all multiples of 1.6 x 10$^{−19}$C, thus showing that the charge of each drop was made up of smaller charges with a charge of 1.6 x 10$^{−19}$C.

## Questions

h = 6.63 x 10$^{−34}$ Js
c = 3 x 10$^8$ ms$^{−1}$
g = 9.81 ms$^{−2}$
1. Rearrange the formula above in terms of q.
2. The mass of an oil drop cannot be measured easily. Express the mass of an oil drop in terms of its radius r and its density ρ, and, by substitution, find a more useful formula for q.
3. An oil droplet of density 885kgm$^{−3}$ and radius 1μm is held stationary in between two plates which are 10 cm apart. At what potential differences between the plates is this possible?
4. If the X-rays used to ionise the oil are of wavelength 1 nm, how much energy do they give to the electrons? Why does this mean that the oil drops are ionised?
5. In reality, the oil drops are moving when they enter the uniform electric field. How can this be compensated for?
Worked Solutions
# A-level Physics (Advancing Physics)/Millikan's Experiment/Worked Solutions

h = 6.63 x 10$^{−34}$ Js
c = 3 x 10$^8$ ms$^{−1}$
g = 9.81 ms$^{−2}$
1. Rearrange the formula above in terms of q.
${\frac {qV}{d}}=mg$
$qV=mgd$
$q={\frac {mgd}{V}}$
2. The mass of an oil drop cannot be measured easily. Express the mass of an oil drop in terms of its radius r and its density ρ, and, by substitution, find a more useful formula for q.
$\rho ={\frac {m}{\mbox{Volume}}}$
$m={\mbox{Volume}}\times \rho$
Assuming that the oil drop is spherical:
${\mbox{Volume}}={\frac {4}{3}}\pi r^{3}$
$m={\frac {4}{3}}\rho \pi r^{3}$
$q={\frac {4\pi \rho gdr^{3}}{3V}}$
3. An oil droplet of density 885kgm$^{−3}$ and radius 1μm is held stationary in between two plates which are 10 cm apart. At what potential differences between the plates is this possible?
q must be a multiple of e, the charge on an electron:
$q=ne$, where n is an integer.
$ne={\frac {4\pi \rho gdr^{3}}{3V}}$
$V={\frac {4\pi \rho gdr^{3}}{3ne}}={\frac {4\pi \times 885\times 9.81\times 0.1\times (10^{-6})^{3}}{3\times 1.6\times 10^{-19}\times n}}={\frac {25.7}{n}}$
Then, to find some actual values, take n = 1,2,3 ... , so V = 25.7V, 12.8V, 8.6V ...
4. If the X-rays used to ionise the oil are of wavelength 1 nm, how much energy do they give to the electrons? Why does this mean that the oil drops are ionised?
$c=f\lambda$
$f={\frac {c}{\lambda }}$
$E=hf={\frac {hc}{\lambda }}={\frac {6.63\times 10^{-34}\times 3\times 10^{8}}{10^{-9}}}=1.989\times 10^{-16}{\mbox{ J}}=1.24{\mbox{ keV}}$
This provides the energy required for an electron to escape from its energy level, becoming unbound.
5. In reality, the oil drops are moving when they enter the uniform electric field. How can this be compensated for?
Either:
* Use a slightly stronger potential difference to slow the oil drop down, and then reduce the potential difference to keep the oil drop stationary.
* Measure the voltage required to keep the oil drop moving at a constant (terminal) velocity, using more sophisticated equipment.
# Annotations to James Joyce's Ulysses/Hades/094
## Annotations

Mater Misericordiæ (Latin) Mother of Mercy. The Mater Misericordiæ University Hospital, popularly known as the Mater, was the largest hospital in Dublin in 1904. Located on the corner of Eccles Street, it was founded in 1861.
Ward for incurables there. The Mater Misericordiæ hospital did have a ward for incurables in 1904.

## References

* ↑ Gifford (1988) 113.
* ↑ Gifford (1988) 113.
# Apollo Justice: Ace Attorney/Episode 3: Turnabout Serenade

The whole thing kicks off with what looks like a rock concert. It looks like we are seeing one of Klavier's gigs. He calls for an intermission.

## Case Information

* Time of Crime: July 7th
* Location: Sunshine Coliseum, Lamiroir's Dressing Room
* Defendant: Machi Tobaye
* Victim: Romein LeTouse
* Cause of Death: Gunshot wound to the left shoulder.
* Murder Weapon: .45 caliber handgun.
* Defense Attorney: Apollo Justice
* Prosecution Lawyer: Klavier Gavin

## Characters
### Defense Attorney

Apollo Justice
Apollo was reluctant to go to a concert (let alone Klavier's). He actually saw the victim die right in front of him. Can he manage to defend a person who can't even speak his own language?

### Defendant

Machi Tobaye
A blind and timid piano player, who actually plays it very well. He doesn't speak English, so how can you defend him?

### Victim

Romein LeTouse
A man who is honest and rarely shows pain. Romein was the bodyguard of Lamiroir. You actually hear his last words before dying.

### Prosecution Lawyer

Klavier Gavin
His rock & roll side of his life is depicted in this episode, and of course, things didn't go well like they should have.

### Witness

Lamiroir
Known as "Siren of the Ballad". Lamiroir is modest when it comes to her moving talent. She was a guest singer at the Gavinners concert when the murder occurred.

### Other Characters

Trucy Wright
Your assistant and a magician. Trucy loves to play tricks and can sometimes outright pester Apollo.
Detective Ema Skye
A detective who uses scientific tools to investigate. She actually wanted to be a scientific investigator, but was pushed into the precinct instead. Ema can't really stand Klavier, and is, of course, reluctant to come to the concert from the beginning.
Daryan Crescend
A guitarist of the Gavinners. He can be either be serious or be a jerk depending on which situation he is in.
Valant Gramarye
A brilliant magician, who happens to be Trucy's uncle! What is he doing here?
Phoenix Wright
A man who can't play piano, but can play poker. He seems to be on a personal top secret mission.

## Locations

Wright Anything Agency
This is where you work at.
Detention Center
This is where your clients (in this case Machi) are being held.
Sunshine Coliseum
A fabulous coliseum, where Klavier's concert is held at.
Backstage Hallway
This is the backstage hallway, as the name suggests.
Lamiroir's Dressing Room
The crime scene, here you see everything that occurred.
Klavier's Dresing Room
The title pretty much describes the room.
Coliseum Stage
The Gavinners performed here.
Klavier's Office
Klavier's prosecutor's office. This is where he works. Just look all of the fan stuff here.
Hickfield Clinic
This is where patients are held. Very familiar to Ace Attorney fans.
# American Sign Language/Location
## Location

Of all the possible locations on the body or in space, twelve are used to distinguish signs in ASL:
* the whole face or head,
* the upper face (forehead or brow),
* the mid face (eyes or nose),
* the lower face (chin or mouth),
* the side face (cheek, temple, or ear),
* the neck,
* the trunk (shoulders, chest, and belly),
* the upper arm,
* the forearm (including the elbow),
* the inside of the wrist,
* the back of the wrist, and
* the other (weak) hand: In this case, the weak hand may take one of the simpler handshapes listed above, such as the A, O, B, G, H, V, or L handshapes, but not others such as X or R.
In addition, the sign may be made in 'neutral' space in front of the chest (zero location).
For example, a 5 hand tapping the upper face means 'father', tapping the lower face means it 'mother', and tapping the torso (chest) it means 'fine'.
Signs may be made with two active hands, oriented in a specific way both to each other and to the body locations.

## Referent locus system

In addition to phonological location, there is also indexic location. For example, the 2nd/3rd-person pronouns point to their referent, or to a point in space (a 'locus') that's been set up to represent that referent. Directional (indexic) verbs [see below] are similar. However, no words are distinguished by such divisions of signing space.
A referent locus may be set up by signing a noun and then pointing to a certain spot in sign space. The signer can later refer back to that noun by pointing to its associated location (that is, by using an indexic pronoun), or by incorporating the location into the motion of an indexic verb. For instance, if you point to a spot over your right shoulder when referring to your grandmother in another city, you can then mention her again by pointing over your shoulder instead of repeating 'my out-of-town grandmother'. Perhaps as many as eight loci may be productively used to distinguish pronouns in a conversation, before the speakers become overloaded, whereas English is restricted to three third-person pronouns: he, she, and they.
Nouns can be set up without the need for initially pointing by making a sign for them at a salient point in space near the signer. This is often accompanied by the facial expression that indicates a topic. (See below.) For example, when discussing football, you can sign 'college' on your left (most likely by signing 'college' in neutral space and extending the final hold to the locus you're setting up), fingerspell P-R-O at a locus on your right (that is, off to one side rather than in neutral space), and then ask whether one prefers collegiate or professional games by signing 'you like which?', with the indexic pronoun 'which' oscillating between the two loci.