Wednesday, 6 April 2011
Formule trigonometriche di addizione
Per vedere l'utilità dei numeri complessi, ricaviamo le formule trigonometriche di addizione, nel seguente modo.
ECLIPSING BINARY STARS
"Eclipsing binary stars are just one several types of variable stars. These stars appear as a single point of light to an observer, but based on its brightness variation and spectroscopic observations we can say for certain that the single point of light is actually two stars in close orbit around one another. The variations in light intensity from eclipsing binary stars is caused by one star passing in front of the other relative to an observer. If we assume that the stars are spherical and that they have circular orbits, then we can easily approximate how the light varies as a function of time for eclipsing binary stars. These calculations can be performed in a relatively short computer program."
http://www.physics.sfasu.edu/astro/ebstar/ebstar.html
http://www.physics.sfasu.edu/astro/ebstar/ebstar.html
Stelle doppie- Problema a due corpi
Domanda molto interessante di uno studente sul moto delle stelle doppie. Per discuterlo in dettaglio, dobbiamo avere alcune nozioni che ancora ci mancano, Una bella discussione è fatta da Wiki
http://en.wikipedia.org/wiki/Two-body_problemIl sito mostra alcuni filmati col moto di sistemi binari con diverse masse.
Se cliccate sulla figura, si vede l'animazione
Le due stelle hanno la loro orbita ellittica attorno alla croce rossa che rappresenta la posizione del centro di massa del sistema.
Tuesday, 5 April 2011
Inertial frames of reference
Inertial frame of reference, adapted from Wikipedia, the free encyclopedia
In physics, an inertial frame of reference (also inertial reference frame or inertial frame or Galilean reference frame) is a frame of reference that describes time and homogeneously and isotropically, and in a time independent manner. All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not accelerating.
Measurements in one inertial frame can be converted to measurements in another by a simple transformation (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity). Physical laws take the same form in all inertial frames. In a non-inertial reference frame the laws of physics depend upon the acceleration of that frame of reference, and the usual physical forces must be supplemented by fictitious forces.
The motion of a body can only be described relative to something else - other bodies, observers, or a set of space-time coordinates. These are called frames of reference. If the coordinates are chosen badly, the laws of motion may be more complex than necessary. For example, suppose a free body (one having no external forces on it) is at rest at some instant. In many coordinate systems, it would begin to move at the next instant, even though there are no forces on it. However, a frame of reference can always be chosen in which it remains stationary.
An intuitive summary of inertial frames can be given as: In an inertial reference frame, the laws of mechanics take their simplest form.òIn an inertial frame, Newton's first law (the law of inertia) is satisfied: Any free motion has a constant magnitude and direction.Newton's second law for a particle takes the form:
F = m a
with F the net force (a vector), m the mass of a particle and a the acceleration of the particle (also a vector) which would be measured by an observer at rest in the frame. The force F is the vector sum of all "real" forces on the particle, such as electromagnetic, gravitational, nuclear and so forth. In contrast, Newton's second law in a rotating frame of reference, rotating at angular rate Ω about an axis, takes the form:
F' = m a'
which looks the same as in an inertial frame, but now the force F′ is the resultant of not only F, but also additional terms:
F' = F - 2m Ω x v'-m Ω x (Ω x r')
where the angular rotation of the frame is expressed by the vector Ω pointing in the direction of the axis of rotation, and with magnitude equal to the angular rate of rotation Ω, symbol x denotes the vector cross product, vector r' locates the body and vector v' is the velocity of the body according to a rotating observer (different from the velocity seen by the inertial observer). We assume for the sake of simplicity that the angular velocity is constant in magnitude and direction.
The extra terms in the force F′ are the "fictitious" forces for this frame. (The first extra term is the Coriolis force, the second the centrifugal force). These terms all have these properties: they vanish when Ω = 0; that is, they are zero for an inertial frame (which, of course, does not rotate).
All observers agree on the real forces, F; only non-inertial observers need fictitious forces. The laws of physics in the inertial frame are simpler because unnecessary forces are not present.
In Newton's time the fixed stars were invoked as a reference frame, supposedly at rest relative to absolute space. In reference frames that were either at rest with respect to the fixed stars or in uniform translation relative to these stars, Newton's laws of motion were supposed to hold. In contrast, in frames accelerating with respect to the fixed stars, an important case being frames rotating relative to the fixed stars, the laws of motion did not hold in their simplest form, but had to be supplemented by the addition of fictitious forces, for example, the Coriolis force and the centrifugal force.
The concept of inertial frames of reference is no longer tied to either the fixed stars or to absolute space.
Rather, the identification of an inertial frame is based upon the simplicity of the laws of physics in the frame. In particular, the absence of fictitious forces is their identifying property.
In physics, an inertial frame of reference (also inertial reference frame or inertial frame or Galilean reference frame) is a frame of reference that describes time and homogeneously and isotropically, and in a time independent manner. All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not accelerating.
Measurements in one inertial frame can be converted to measurements in another by a simple transformation (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity). Physical laws take the same form in all inertial frames. In a non-inertial reference frame the laws of physics depend upon the acceleration of that frame of reference, and the usual physical forces must be supplemented by fictitious forces.
The motion of a body can only be described relative to something else - other bodies, observers, or a set of space-time coordinates. These are called frames of reference. If the coordinates are chosen badly, the laws of motion may be more complex than necessary. For example, suppose a free body (one having no external forces on it) is at rest at some instant. In many coordinate systems, it would begin to move at the next instant, even though there are no forces on it. However, a frame of reference can always be chosen in which it remains stationary.
An intuitive summary of inertial frames can be given as: In an inertial reference frame, the laws of mechanics take their simplest form.òIn an inertial frame, Newton's first law (the law of inertia) is satisfied: Any free motion has a constant magnitude and direction.Newton's second law for a particle takes the form:
F = m a
with F the net force (a vector), m the mass of a particle and a the acceleration of the particle (also a vector) which would be measured by an observer at rest in the frame. The force F is the vector sum of all "real" forces on the particle, such as electromagnetic, gravitational, nuclear and so forth. In contrast, Newton's second law in a rotating frame of reference, rotating at angular rate Ω about an axis, takes the form:
F' = m a'
which looks the same as in an inertial frame, but now the force F′ is the resultant of not only F, but also additional terms:
F' = F - 2m Ω x v'-m Ω x (Ω x r')
where the angular rotation of the frame is expressed by the vector Ω pointing in the direction of the axis of rotation, and with magnitude equal to the angular rate of rotation Ω, symbol x denotes the vector cross product, vector r' locates the body and vector v' is the velocity of the body according to a rotating observer (different from the velocity seen by the inertial observer). We assume for the sake of simplicity that the angular velocity is constant in magnitude and direction.
The extra terms in the force F′ are the "fictitious" forces for this frame. (The first extra term is the Coriolis force, the second the centrifugal force). These terms all have these properties: they vanish when Ω = 0; that is, they are zero for an inertial frame (which, of course, does not rotate).
All observers agree on the real forces, F; only non-inertial observers need fictitious forces. The laws of physics in the inertial frame are simpler because unnecessary forces are not present.
In Newton's time the fixed stars were invoked as a reference frame, supposedly at rest relative to absolute space. In reference frames that were either at rest with respect to the fixed stars or in uniform translation relative to these stars, Newton's laws of motion were supposed to hold. In contrast, in frames accelerating with respect to the fixed stars, an important case being frames rotating relative to the fixed stars, the laws of motion did not hold in their simplest form, but had to be supplemented by the addition of fictitious forces, for example, the Coriolis force and the centrifugal force.
The concept of inertial frames of reference is no longer tied to either the fixed stars or to absolute space.
Rather, the identification of an inertial frame is based upon the simplicity of the laws of physics in the frame. In particular, the absence of fictitious forces is their identifying property.
Un esempio su Coriolis
Un esempio fatto con giostra e caramelle sugli effetti di Coriolis al sito
http://www.accademiavelica.it/IT/documentazione/_coriolis/coriolis.2/node2.html
http://www.accademiavelica.it/IT/documentazione/_coriolis/coriolis.2/node2.html
Monday, 4 April 2011
Laboratorio - 4 Aprile
Misura della radioattivita' del fondo naturale con il Geiger. Misura della radioattivita' del KCl. Utilizzo dei fogli Excel per l'analisi dei dati. Istogrammi.
Friday, 1 April 2011
Il sogno di Leonardo
"A research team at Festo has developed SmartBird, a biomechatronic bird that can take off, fly and land autonomously. Festo claims that SmartBird flies, glides and moves through the air like its counterpart in nature — the herring gull — with no additional drive mechanism."
Guardate il filmato al sito:
Festo's biomechatronic bird flies and lands autonomously | News | The Engineer
Festo's biomechatronic bird flies and lands autonomously | News | The Engineer
Vita media ed emivita
La radioattività, o decadimento radioattivo, è un insieme di processi fisico-atomici tramite i quali, alcuni nuclei atomici instabili (radionuclidi) o radioattivi decadono, trasmutano in una specie atomica a contenuto energetico inferiore secondo la legge di conservazione della massa/energia e raggiungendo così uno stato di maggiore stabilità.
Equazione del decadimento esponenziale
Data una quantità il cui valore è N, il decadimento esponenziale è espresso dall'equazione:
λ è un numero detto costante di decadimento. La soluzione di questa equazione è
N(t) è la quantità al tempo t, e N0 = N(0) è la quantità iniziale, al tempo t=0.
In alternativa si può scrivere
dove:
è detta costante di tempo ed è il tempo necessario a ridurre la quantità iniziale di circa il 63,21%.
Il momento esatto in cui un atomo instabile decadrà in uno più stabile è assolutamente casuale e impredicibile. Ciò che si può fare, dato un campione di un particolare isotopo, è notare che il numero di decadimenti rispetta una precisa legge statistica. Il numero di decadimenti che ci si aspetta avvenga in un intervallo dt è proporzionale al numero N di atomi presenti. Questa legge può essere descritta tramite l'equazione del decadimento esponenziale. Oltre alla costante di decadimento λ, il decadimento radioattivo è caratterizzato da un'altra costante chiamata vita media. Ogni atomo vive per un tempo preciso prima di decadere e la vita media rappresenta appunto la media aritmetica sui tempi di vita di tutti gli atomi della stessa specie. La vita media viene rappresentata dal simbolo τ , legato a λ dalla:
che è la costante di tempo.
Un altro parametro molto usato per descrivere un decadimento radioattivo è dato dalla emivita o tempo di dimezzamento t1/2. Dato un campione di un particolare radionuclide, il tempo di dimezzamento ci dice dopo quanto tempo saranno decaduti un numero di atomi pari alla metà del totale, ed è legato alla vita media dalla relazione:
.URANIO 
CESIO 
Thursday, 31 March 2011
Superconductivity from nowhere
"In just over a week scientists will celebrate the centenary of superconductivity: the discovery, in 1911, that some materials cooled towards absolute zero allow electric charge to flow without resistance. But now one physicist believes superconductivity can appear when there is no material at all. According to Maxim Chernodub ... superconductivity can appear – provided there is a very strong magnetic field – in the vacuum of empty space. If Chernodub is correct, the phenomenon could explain the origin of the extensive magnetic-field patterns seen in the cosmos."
Candy floss of rocks
"The earliest rocks in the solar system, from which the terrestrial planets were born, were more like candy floss than hard rock, according to a new analysis carried out by a team including researchers in the UK and Australia. This is the first geological evidence to support the idea that the first solid material in the solar system was extremely porous before it was subsequently compacted into larger bodies, which become the planets we know today."
Earth grew from 'candy floss' rocks - physicsworld.com
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