List of my Publications

Monday, 10 December 2012

By Toutatis!

"Near-Earth asteroid 4179 Toutatis will be passing within 7 million kilometers of Earth on December 12. It's visited us several times before, with a close pass every four years in December. As near-Earth asteroids go, it's a good-sized one, an elongated and lumpy object about 2 by 2 by 4 kilometers in extent."

"Toutatis makes frequent close approaches to Earth, with a currently minimum possible distance (Earth MOID) of just 0.006 AU (2.3 times as far as the Moon). The approach on September 29, 2004, was particularly close, at 0.0104 AU[13] (within 4 lunar distances) from Earth, presenting a good opportunity for observation, with Toutatis shining at magnitude 8.8 when brightest. A more recent close approach of 0.0502 AU (7,510,000 km; 4,670,000 mi) happened on November 9, 2008. The next close approach will be December 12, 2012, at a distance of 0.046 AU (6,900,000 km; 4,300,000 mi), and at magnitude 10.7. ...
Given that Toutatis makes many close approaches the Earth, such as in 1992, 1996, 2000, 2004, 2008, and 2012, it is listed as a potentially hazardous object. ..."

Toutatis  was a Celtic god worshipped in ancient Gaul and Britain.  Today, he is best known through the Gaulish oath/catchphrase "By Toutatis!", invented for the Asterix comics by Goscinny and Uderzo. The spelling Toutatis, however, is authentic and attested by about ten ancient inscriptions.

Wednesday, 10 October 2012

Indiana Jones

Vi ricordate il giovane Indiana Jones che salta giù dal treno del circo?

"An especially interesting case arises when a projectile is hurled from the rear of a fast-moving train or other vehicle. Let us suppose that someone throws a stone, horizontally, down the track from the rear platform of a train speeding along at 60 miles per hour. And suppose that the stone is thrown at an initial speed of 60 miles per hour (relative to the train, of course) . Then, to the people on the train, the stone will appear to follow a perfectly normal parabolic path. But how will it seem to a person standing on the ground alongside the track? Remember that velocity is always relative. The forward motion of the train will just cancel the backward motion of the stone. In other words, the stone will plummet straight down to the ground, with no motion at all in the horizontal direction.
A similar situation arises when a bullet is fired from a speeding aeroplane. A revolver bullet, for instance, has a muzzle velocity of only about 500 miles per hour. If such a bullet is fired from the rear of a modern warplane speeding along at 500 miles per hour, the two velocities cancel, and the bullet at first stands still momentarily then falls straight down as though it had been dropped. On the other hand, if the bullet is fired from the front of the plane, the velocities add, and the speed of the bullet relative to the earth is 1,000 miles per hour. Of course, the machine guns used in warfare fire their bullets at speeds much greater than 500 miles per hour. Moreover, if the target is another moving plane, it is the speed of the bullet relative to this moving target that counts in determining the damage done not the speed relative to the earth. It makes no difference at all whether a revolver bullet stands still with respect to the earth and you run into it with a speed of 500 miles per hour, or whether you are standing still with respect to the earth and the revolver bullet strikes you with this speed. In both cases the effect is the same, and unpleasant for you."

From PHYSICS TELLS WHY, An Explanation of Some Common Physical Phenomena 

the Monkey on the String

Imagine a string passing over a pulley, with a monkey hanging on one end of the string, and an iron bob on the other end balancing the monkey. Monkey and bob are equal in weight, and both are initially at rest. The weight of the string and the friction in the pulley can be neglected.
What happens to the iron bob when the monkey begins to climb up the string? In other words, will the bob rise with the monkey, will it descend, or will it remain stationary?

To solve the problem we must apply Newton's Laws of Motion. When the monkey begins to climb, he is accelerated upward. Therefore, according to Newton's Second Law, the string must not only support the monkey's weight, but it must supply additional force for the acceleration. As a test of this conclusion, you might stand  on bathroom scales sometime when you are going up in an elevator. You will find that as the elevator starts upward, the scales will register several pounds more than your weight. The added push upward on the bottom of your feet serves to accelerate your body. For a simpler experiment, one which can be done less conspicuously, hang a weight on a string, and jerk upward. You will feel a sudden added tension in the string as the mass is accelerated.

Even though the monkey moves upward by his own efforts, there must be an added tension in the string to provide force for the acceleration. By Newton's Third Law the tension in the string must pull equally on the iron bob. Therefore, the bob is accelerated upward just like the monkey. The solution to the problem, then, is this: the monkey and the bob rise together.

When the monkey stops climbing, and thus decelerates, the tension in the string is decreased, and the bob comes to rest at the same time as the monkey. Likewise, if the monkey turns and starts down the string, the bob descends with the monkey.

From PHYSICS TELLS WHY, An Explanation of Some Common Physical Phenomena 

Does a Flying Bird Weigh Anything?

Does a Flying Bird Weigh Anything? ... Suppose that a bird weighing one pound is flying around in a five-pound cage. If you hung the cage on a spring balance,  would the scales record the weight of the cage alone, or the weight of the cage plus the bird? 

There is a story connected with this problem. Some years ago, a graduate student in physics at a large university decided to have some fun at the expense of two of his professors. A newspaper reporter was made a party to the scheme, and was persuaded to call each of the two professors on the telephone in order to ask his expert opinion on a scientific question.

Professor A was asked the following question: If a one-pound bird is flying in a five-pound cage made of thin wire, how much will the combination weigh? "Five pounds," Professor A told the reporter.

Professor B was then called, and a similar, but slightly different question was put to him: If a one-pound bird is flying in a five-pound cage made entirely of glass, how much will the combination weigh? "Six pounds," replied Professor B without hesitation.

The next day, much to the embarrassment of the two prominent professors, headlines appeared in the local paper: UNIVERSITY PROFS DISAGREE ON SCIENTIFIC QUESTION. A carefully misworded account of the questions and answers followed, with the words wire and glass omitted. No doubt everyone would agree that the bird and cage together would weigh six pounds, provided the bird were sitting stationary on its perch. But which of the professors was right in the case of the flying bird? The answer is that they were both right.  Since the bird is not falling, it must be supported by something. That something is the air. Because of the flapping of the bird's wings, the air pushes up on the bird with a force of one pound. The bird must then push down on the air with an equal and opposite force. This downward force of one pound is transmitted through the air to the first solid surface available. Since the wire cage would not have solid walls or floor, the air would push down, not on the cage, but on the ground below. Therefore, as Professor A said, the wire cage plus bird would weigh only five pounds. On the other hand, the glass cage would be impermeable to air, and in this case the weight of the bird must be borne by the cage. Professor B was absolutely correct when he said that the scales would then read six pounds. There is a moral to this story about the bird in the cage. It illustrates the necessity for precise statement in a scientific problem. 

From PHYSICS TELLS WHY, An Explanation of Some Common Physical Phenomena 

Sunday, 23 September 2012

Tuned pendulum

This web page describes the mechanism inside the ancient first seismometer (see this post) of the first century AD.
From seismo.html: "Our seismometer is intended as a demonstrator. The visitor shakes the table to simulate an earthquake. Our pendulum is "tuned" to this input. The crust of the earth absorbs the high frequency content of a quake, the signal from a distant earthquake is in the sub-audio range. In order to detect actual earthquakes the pendulum would need to be several feet in length."

Saturday, 22 September 2012

The world's first seismometer was Chinese

Who was the inventor of the first siesmometer?
 Zhang Heng. He was  (AD 78–139) a Chinese astronomer, mathematician, inventor, geographer, cartographer, artist, poet, statesman. He lived under the Han Dynasty (AD 25–220) of China. He was a  Chief Astronomer, Prefect of the Majors for Official Carriages, and then Palace Attendant at the imperial court.  He invented the world's first water-powered armillary sphere,  improved the inflow water clock by adding another tank and invented the world's first seismometer, which discerned the cardinal direction of an earthquake 500 km away. He improved previous Chinese calculations of the formula for pi. In addition to documenting about 2,500 stars in his extensive star catalogue. Some modern scholars have also compared his work in astronomy to that of Ptolemy (AD 86–161). (Adapted from Wiki)

 A replica of an ancient Chinese Siesmograph  (25-220 CE). Picture taken in July 2004  at Chabot Space & Science Center in Oakland California.
"In 132 CE, after several serious earthquakes in China, astronomer Zhang Heng invented this instrument to warn people of the next one. When the ground shook, it moved a pendulum inside the jug. The pendulum pushed a lever that opened one dragon's mouth. A ball rolled out and into the toad's mouth below, sounding an alarm. The open dragon mouth pointed in the direction of the earthquake, notifying the Emperor."

Thursday, 20 September 2012

Una cosa importante

Una cosa che è importante sapere per la  carriera universitaria degli studenti di Ingegneria è quanto scritto
al link
ACCESSO LM INGEGNERIA Per iscriversi è necessario che lo studente abbia un’adeguata preparazione iniziale .... - Studenti immatricolati presso il Politecnico di Torino a partire dall’a.a. 2007/2008 La media viene calcolata su tutti i crediti con voto in trentesimi con l’esclusione dei peggiori 28 CFU, in considerazione degli sbarramenti applicati dall’Ateneo. Sono ammessi alla LM i candidati per i quali la durata del percorso formativo è inferiore o uguale a 4 anni. Sono ammessi alla LM i candidati per i quali la durata del percorso formativo è superiore a 4 anni ma inferiore o uguale a 5 anni e la preparazione corrisponde ad una media superiore o uguale a 21/30. Sono ammessi alla LM i candidati per i quali la durata è superiore a 5 anni e media superiore a 24.

Nuovo campus a Torino

A Torino c'è un nuovo campou!
"Il Campus Luigi Einaudi aprirà le sue porte il 22 settembre con una grande festa a partire dalle 14.30: una giornata densa di iniziative per scoprire e vivere un’anteprima di quello che sarà un luogo di incontro e scambio tra l’Università e la Città. L’inaugurazione sarà l’occasione per celebrare grandi personaggi che hanno lasciato un’impronta indelebile nella storia dell’Ateneo torinese come in quella di tutto il paese: Luigi Einaudi, con uno spettacolo teatrale inedito dedicato agli aspetti più sconosciuti della sua vita, e Norberto Bobbio, al quale è intitolato il nuovo Polo Bibliotecario."

Il campus in due fasi della costruzione

Tuesday, 24 July 2012

Carlo Promis e l'antica Torino

Carlo Promis e l’antica Torino,
di Amelia Carolina Sparavigna, Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, Duca degli Abruzzi 24, Torino, Italy,

A metà dell’Ottocento, l’antica Torino rivive grazie all’opera di un architetto e archeologo, nonché  docente di quello che diventerà il Politecnico di Torino, Carlo Promis.

La “Storia dell’antica Torino (Julia Augusta Taurinorum)”, uscita nel 1869 a Torino presso la stamperia Reale, è opera di Carlo Promis. Promis fu architetto, archeologo e filologo, Nato nel 1808 e morto nel 1873 a Torino, vi si era laureato nel 1828 in architettura. Come architetto si devono ricordare il progetto urbanistico di Piazza Carlina e la riqualificazione di molte aree e vie della città. Re Carlo Alberto di Savoia, nel 1839, lo nominò regio archeologo. Nel 1860 passò a insegnare architettura nella Regia Scuola di Applicazione per gli Ingegneri, che era stata costituita nel 1859 e che nel 1906 diventerà il Regio Politecnico. Prima istituzione universitaria per la formazione della figura dell’ingegnere è l’attuale Politecnico di Torino.
L’opera di Promis è considerata dagli studiosi suoi contemporanei e da quelli che l’hanno seguito come fondamentale per la conoscenza dell’antica Torino. Il testo è così stato ristampato: l’edizione da me utilizzata è quella del 1969 pubblicata da Edilibri, Andrea Viglongo & C Editori a Torino [1]. In effetti, è utile riportare il titolo completo del libro che è “Storia dell'antica Torino, Julia Augusta Taurinorum: scritta sulla fede de' vetusti autori e delle sue iscrizioni e mura”, che ci dice come Promis, da architetto e archeologo insieme, abbia usato fonti antiche, consistenti nei testi di autori latini e greci, le epigrafi scoperte a Torino, e i resti delle mura che aveva trovato durante i suoi scavi archeologici. ... 

L'articolo completo è pubblicato su Scribd, il 24 Luglio 2012.

Carlo Promis, Storia dell'antica Torino, Julia Augusta Taurinorum: scritta sulla fede de' vetusti autori e delle sue iscrizioni e mura, 1869, Torino, stamperia Reale, 1969, Edilibri, Andrea Viglongo & C Editori, Torino.
Amelia Carolina Sparavigna, The orientation of Julia Augusta Taurinorum (Torino), arXiv, 2012,

© Amelia Carolina Sparavigna, 2012. Tutti i diritti riservati. All rights reserved.

Perimetro della Torino romana segnato su una mappa di Acme Mapper. La posizione delle quattro porte è segnata dai marker (due delle porte esistono ancora). Il Decumano Massimo è inclinato rispetto la direzione cardinale Est-Ovest e coincide con Via Garibaldi. Notate gli isolati coincidenti con le insulae romane. L’ombelico  della città è all’incrocio tra decumano e cardo massimo. Il perimetro della città romana va dalle Porte Palatine a Via della Consolata. Piega a Sud su Via della Consolata e Corso Siccardi. Su questo lato si apriva la Porta Decumana, di cui non rimane nulla. All’angolo di Via Cernaia, il perimetro gira verso la Porta Marmorea, anch’essa smantellata. Su questo lato ci sono Via Cernaia, Santa Teresa e Via Maria Vittoria, Piazza San Carlo. All’angolo dell’Accademia delle Scienze, dove c’è il Museo Egizio, le mura correvano verso Nord, attraversando Piazza Castello, dove c’è la Porta Pretoria, poi l’area del Palazzo reale, ritornando alle Porte Palatine.

Tuesday, 3 July 2012


Higgs Bosons Rumors: Hopes that Cern scientists have found the Higgs Boson were strengthened yesterday when rival American researchers announced their strongest evidence yet of its existence.

Friday, 29 June 2012

Piccole oscillazioni...

"Researchers Terry Hunt and Carl Lipo test a new theory that suggests how ancient Easter Islanders may have used ropes to “walk” the moai to their platforms. Mystery of Easter Island, a new NOVA-National Geographic special, airs Wednesday,"

Friday, 22 June 2012

Alan Turing

Google celebrates the 100th birthday of a computer genius, Alan Mathison Turing (23 June 1912 - 7 June 1954) with a doodle. He is the founder of computer science. He broke the german Enigma-ciphered code.

Thursday, 21 June 2012


Silicene pops out of the plane -
"Researchers in Japan say that they have made 2D honeycomb crystals of silicon that resemble the carbon-based material graphene. This is the second potential sighting of the material dubbed "silicene"; the other was reported in April by an independent group in Europe. The Japanese research suggests it may be relatively easy to alter the structure of silicene by changing the substrate on which it is grown – which could allow different versions of silicene to be produced with a range of useful electronic properties. However, not all scientists agree that this latest material is actually silicene."

Tuesday, 12 June 2012

Ancient Rainfall, Carved in Stone

"Stalactites grow from cave ceilings not as dull cones but often sporting elegant corrugations. In Physical Review Letters, two Italian researchers now explain these mysterious, wavy patterns using standard fluid mechanics. Their theory shows that the horizontal ripples form because spatially periodic patterns arise in the rate of mineral deposits from the water flowing down the stalactite. Starting from this model, climate scientists might in the future use stalactite surface structure to reconstruct variations in precipitation patterns over tens of thousands of years."
Ancient Rainfall, Carved in Stone

Friday, 1 June 2012

Tabella termodinamica

Libro sul calore

L'autore, Giovanni Tonzig, mette a disposizione alcuni capitoli pdf del suo libro.

Le pagine sotto elencate sono disponibili in formato PDF.
Domanda trovata in rete: qualcuno sa spiegarmi per bene come si calcola l'entropia in una trasformazione adiabatica irreversibile???

Bisogna capire cosa significa "entropia in una trasformazione", adiabatica o meno. Agli stati di equilibrio possibili di un sistema termodinamico è associata una funzione (detta appunto "di stato") S, chiamata entropia, che tra le altre caratteristiche ha quella di soddisfare le relazionI:

(1) S(B) – S(A) = ∫ (δQ)/T se l'integrale è effettuato lungo una qualsiasi trasformazione reversibile da A a B;

(2) S(B) – S(A) > ∫ (δQ)/T se l'integrale è effettuato lungo una qualsiasi trasformazione irreversibile da A a B.

In particolare, se A e B sono collegabili da una trasformazione adiabatica reversibile allora S(B) – S(A) = 0, cioè non si ha variazione di entropia. Se tu hai due stati A, B e vuoi calcolare esattamente S(B) – S(A), dovrai cercare una trasformazione reversibile (quindi diversa da ogni trasformazione irreversibile di qualunque tipo che abbia portato il sistema da A a B), e calcolare poi ∫ (δQ)/T lungo questa trasformazione reversibile.
Se poi il sistema è formato da un gas perfetto, tutto si semplifica! In questo caso, sempre e comunque,

ΔS = S2 – S1 = n[Cv·ln(T2/T1) + R·ln(V2/V1)] 

e quindi basta conoscere i valori delle variabili di stato iniziali e finali (p1,V1,T1), (p2,V2,T2).

Esercizio dal documento
Sappiamo che una trasformazione adiabatica reversibile è una isoentropica. Prendiamo uno stato iniziale i ed uno stato finale f di un gas perfetto su un'adiabatica.reversibile: Delta S = S_f - S_i = 0.
Dimostrate che Delta S è zero usando  l'espressione della variazione dell'entropia per un gas perfetto.
Vedi anche:

Transit of Mercury

Very beautiful image at Image Credit: SOHO - EIT Consortium, NASA "The diminutive disk of Mercury, the solar system's innermost planet, spent about five hours crossing in front of the enormous solar disk in 2003 ... the horizon was certainly no problemfor the sun-staring SOHO spacecraft. Seen as a dark spot, Mercury progresses from left to right (top panel to bottom) in these four images from SOHO's extreme ultraviolet camera. The panels' false-colors correspond to different wavelengths in the extreme ultraviolet which highlight regions above the Sun's visible surface."

Here the image from NASA after processing with IRIS

Transit of Venus

"The next transit of Venus, where Venus appears as a dark spot in front of the Sun, will begin at 22:09 UTC on 5 June 2012, and will finish at 04:49 UTC on 6 June.[1] Depending on the position of the observer, the exact times can vary by up to ±7 minutes. Transits of Venus occur in pairs that are eight years apart: the previous transit was in June 2004, and the next pair of transits will occur in December 2117 and December 2125." from Wikipedia

Aristarchus proposed to measure the distance to the Sun using parallax. This approach based on the geometric principles of parallax last for two thousands of years, until Edmond Halley in 1716 proposed to observe the transit of Venus. The use of Venus transits gave an estimate of 1.53×10^13 cm, 2.6% above the currently accepted value, that of l.49 × 10^13 cm. More recently, in 1910, the parallax was measured using the asteroid Eros that passed much closer to Earth than Venus. A transit of Venus happens when this planet passes directly between the Sun and Earth, appearing as a small black disk moving across the Sun bright disk. The duration of such transits is usually measured in hours.
Read  more "Two amateur astronomers at Berkeley", at

Monday, 21 May 2012

Roman Dodecahedron

Solo di recente sono venuta a conoscenza dell'esistenza dei Dodecaedri Romani. Essi sono considerati misteriosi (Wikipedia) poiché non si è ancora trovato un loro uso preciso. Sono state proposte molte teorie: porta-candele (ma all'epoca si usavano le lucerne), dadi per la divinazione (ma questi oggetti hanno le facce con masse diverse e quindi cadono sempre sulla faccia più pesante), strumenti astronomici (per stabilire gli equinozi, ma gli antichi usavano le meridiane) e altro ancora.
Purtroppo non è facile districarsi tra le varie teorie, anche perché spesso non si trovano gli articoli originali da studiare. Quello che appare chiaro è che questi dodecaedri di bronzo sono cavi, con facce che hanno buchi perfettamente circolari di diametri diversi. Cercando in rete ho trovato l'articolo di alcuni archeologi che descrivono con precisione un dodecaedro di bronzo, trovato a Jublains, l'antica Nouiodunum, del secondo o terzo secolo DC. Usando i dati sui diametri dei fori ho creato un modello di cartone. Guardando attraverso il modello ho capito che poteva essere uno strumento ottico per misurare la distanze e funzionare come un telemetro. Come molti telemetri, la misura si basa sui triangoli simili. I dettagli del dodecaedro come strumento telemetrico sono pubblicati in un articolo pubblicato su arXiv (In italiano ).
Il dodecaedro ha quattro differenti range di misura. I dodecaedri cavi, aventi struttura con buchi di diverso diametro, erano strumenti militari per determinare le distanze in balistica. Ed in effetti, questi oggetti sono stati trovati lontano dall'Italia, nei paesi che sono stati al confine dell'Impero. Ho scritto anche un confronto con strumenti medievali e moderni su arXiv,
Il dodecaedro era uno strumento facile da usare. Per cambiare il range di distanza, bastava ruotare il dodecaedro. Se si guardano le foto dei dodecaedri, si vede che avevano delle piccole sferette ai vertici. Esse rendevano più facile la presa dello strumento nelle operazioni veloci.
Durante il Medioevo sono stati creati altri telemetri poiché l'uso del dodecaedro, che era uno strumento dell'esercito romano, si era perso col crollo dell'Impero. Questi oggetti medievali, conosciuti come "fore-staff", erano molto più ingombranti e con parti mobili da cambiare se cambiavano le distanze da valutare. Il dodecaedro romano è in fondo un comodo "telemetro a coincidenza".
Gli archeologi che hanno trovato il dodecaedro a Jublains dicono che esso è un dado per la divinazione. I Romani, come gli Etruschi, avevano dei dadi dodecaedrici per il gioco o la divinazione, ma essi erano molto diversi. Si veda per esempio

 (immagine da Wikipedia)

Recently, I learned that some ancient artifacts, the Roman Dodecahedra, exist. They are considered a "mystery" of archaeology (Wikipedia), because they have not yet received a specific attribution for their use. Many theories have been proposed: candlestick holders (but at that time people used oil lamps), dice for divination (these objects have faces of different masses and therefore they always fall on the heaviest face), astronomical instruments (to determine the equinoxes, but the ancients used sundials), and so on.
Unfortunately it is not easy to study the original items on these theories. What is clear is that these bronze dodecahedra are hollow, with faces that have perfectly circular holes of different diameters.
Searching the Web I found the article written by some archaeologists that accurately describe a dodecahedron made of bronze, found at Jublains, the ancient Nouiodunum, dated to the second or third century AD. Using the data on the diameters of the holes I made a cardboard model. Looking through the model I found it could be an optical instrument for measuring distances, being therefore a rangefinder. Like several rangefinders, the measure is based on similar triangles. The details of the dodecahedron as an instrument for telemetry are published in arXiv (In Italian
The dodecahedron has four different measuring ranges. The dodecahedra, having a structure with holes of different diameters, were military devices to determine distance for ballistics. And in fact, these objects have been found outside of Italy, at the border of  Roman Empire. I also wrote a comparison with medieval and modern instruments, arXiv,
The dodecahedron was  easy to use. To change the range of distance, it was enough to turn the dodecahedron. If you look at pics of dodecahedra, you can see the small knobs. They made easier to grip the tool during quick operations.
During the Middle Ages, rangefinders have been created different from the dodecahedron, which was an instrument of the Roman army. Probably its use was lost with the collapse of the Empire. These medieval objects, known as "fore-staff," were bulkier and had the necessity to change and move some parts of it, for  different ranges. The Roman dodecahedron is basically a  "coincidence rangefinder."
Archaeologists that have found the dodecahedron at Jublains say that it is a dice for divination. The Romans, like the Etruscans, had dodecahedra for the game of dice or divination, but they were quite different. See, for example

Saturday, 19 May 2012

Dioptra - Diottra

Il termine diottra (greco dioptra, da diá = attraverso e opteuo = osservo) è in sé riferibile a qualunque strumento munito di uno o più traguardi forati attraverso cui osservare.... diottra designava anche l'alidada, cioè l'asticciola (arabo al-'idada) girevole imperniata al centro della scala goniometrica tracciata sulla faccia piana anteriore o posteriore di molti strumenti astronomici e topografici antichi. Due pinnule, dette traguardi o mire, fissate perpendicolarmente sull'alidada, permettono di puntare l'oggetto desiderato attraverso i fori in esse praticati. Un indice, sovente costituito dal bordo stesso dell'alidada, mostra sulla scala goniometrica l'angolo fra la linea di vista dell'oggetto mirato e una direzione prefissata che, per esempio, negli astrolabi corrisponde alla verticale del luogo d'osservazione....Nella Sintassi Matematica, o Almagesto, Claudio Tolomeo (II sec. d.C.) attribuisce a Ipparco di Nicea (II sec. a.C.) l'ideazione di uno strumento, detto diottra, per misurare i diametri apparenti del Sole e della Luna. ...Nonostante la testimonianza di Tolomeo e qualche lieve differenza di struttura, lo strumento era già noto a Archimede di Siracusa (287-212 a.C.), che nell'Arenario afferma d'averlo usato per misurare il diametro apparente del Sole....
In un'opera, la Diottra, Erone d'Alessandria (I sec. d.C.) delinea uno strumento portatile – utile applicazione della ruota dentata, della vite e della livella a acqua, – da usare per misurazioni terrestri o astronomiche....
Per talune analogie, si suole riconosce nella diottra di Erone l'antenato del moderno teodolite.
Leggi tutto a

Misura a spanne

Da Wikipedia: "La spanna è un'unità di misura antica, che si basa sulla distanza tra le punte del pollice e del mignolo in una mano di adulto aperta, equivalendo a circa 20 cm. La spanna è suddivisibile in 10 dita o 7,5 pollici o due terzi di piede. Ma in altri sistemi viene invece suddivisa in 10⅔ dita o 8 pollici. ... Per analogia, il concetto di "spanna" viene utilizzato per indicare qualche misura grossolana, da dove molti derivati come "misura spannometrica", cioè "a occhio", "grosso modo", eccetera."

Quali di questi signori misura a spanne?

Friday, 18 May 2012

A cannon initially resting on a frictionless surface of mass m1 = 800 kg (when unloaded) is loaded with a “shot” of mass m2 = 10.0 kg. The cannon is aimed at mass m3 = 7 990 kg, which is connected to a massless spring of force constant k = 4 500 N/m, as in Figure EX5.73a. The cannon is then fired, and the shot inelastically collides with mass m3 and sticks in it, as shown in Figure EX5.73b. The combined system compresses the spring a maximum distance of d = 0.500 m, as in Figure EX5.73c. (a) Determine the speed of m2 just before it collides with m3. (You may assume that m2 travels in a straight line.) (b) Determine the recoil speed of the cannon. (c) The cannon recoils towards the right, and when it passes point A there is friction (with μk = 0.600) between the cannon and the ground. How far to the right of A does the cannon slide before coming to rest? 

A flying squid (family Ommastrephidae) is able to “jump” off the surface of the sea by taking water into its body cavity and then ejecting the water vertically downward. A 0.85-kg squid is able to eject 0.30 kg of water with a speed of 20 m/s. (a) What will be the speed of the squid immediately after ejecting the water. (b) How high in the air will the squid rise? 

The Japanese Flying Squid, otherwise known as Todarodes pacificus, is a invertebrate, and a member of the phylum mollusca, class cephalopoda, and family ommastrephidae. This animal lives in the Northern Pacific ocean. The squid has a siphon–a muscle which takes in water from one side, and pushes it out the other side; in other words: jet propulsion. Squids have ink sacs, which they use as a defense mechanism against possible predators. Squid also have three hearts.

A 45.0-kg girl is standing on a 150-kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.50 m/s to the right relative to the plank. (a) What is her velocity relative to the surface of the ice? (b) What is the velocity of the plank relative to the surface of the ice? 
A rifle with a weight of 30 N fires a 5.0-g bullet with a speed of 300 m/s. (a) Find the recoil speed of the rifle. (b) If a 700-N man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle. 
A 730-N man stands in the middle of a frozen pond of radius 5.0 m. He is unable to get to the other side because of a lack of friction between his shoes and the ice. To overcome this difficulty, he throws his 1.2-kg physics textbook horizontally toward the north shore at a speed of 5.0 m/s. How long does it take him to reach the south shore?

Monday, 14 May 2012

A 40.0-kg child stands at one end of a 70.0-kg boat that is 4.00 m long. The boat is initially 3.00 m from the pier. The child notices a turtle on a rock beyond the far end of the boat and proceeds to walk to that end to catch the turtle. (a) Neglecting friction between the boat and water, describe the motion of the system (child plus boat). (b) Where will the child be relative to the pier when he reaches the far end of the boat? (c) Will he catch the turtle? (Assume that he can reach out 1.00 m from the end of the boat.)

A 5.00-g bullet moving with an initial speed of 400 m/s is fired into and passes through a 1.00-kg block, as in Figure. The block, initially at rest on a frictionless horizontal surface, is connected to a spring with a spring constant of 900 N/m. If the block moves 5.00 cm to the right after impact, find (a) the speed at which the bullet emerges from the block and (b) the mechanical energy lost in the collision.


A simple pendulum is 5.00 m long. (a) What is the period of simple harmonic motion for this pendulum if it is located in an elevator accelerating upward at 5.00 m/s2? (b) What is its period if the elevator is accelerating downward at 5.00 m/s2? (c) What is the period of simple harmonic motion for the pendulum if it is placed in a truck that is accelerating horizontally at 5.00 m/s2
A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. A 0.500-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is pulled horizontally so that it stretches the spring 5.00 cm and is then released from rest at t = 0. (a) What is the force constant of the spring? (b) What are the angular frequency ω, the frequency, and the period of the motion? (c) What is the total energy of the system? (d) What is the amplitude of the motion? (e) What are the maximum velocity and the maximum acceleration of the particle? (f) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s. 


While riding behind a car traveling at 3.00 m/s, you notice that one of the car’s tires has a small hemispherical bump on its rim, as in Figure. (a) Explain why the bump, from your viewpoint behind the car, executes simple harmonic motion. (b) If the radius of the car’s tires is 0.30 m, what is the bump’s period of oscillation?

Tuesday, 8 May 2012

An ancient rangefinder (roman dodecahedron)

According to Wikipedia, "a rangefinder is a device that measures distance from the observer to a target, for the purposes of surveying, determining focus in photography, or accurately aiming a weapon. Some devices use active methods to measure (such as sonar, laser, or radar); others measure distance using trigonometry (stadiametric rangefinders and parallax, or coincidence rangefinders). These methodologies use a set of known information, usually distances or target sizes, to make the measurement, and have been in regular use since the 18th century".
It could be surprising, but probably the Roman Army had a rangefinder. This was the Roman Dodecahedron.

Image courtesy Wikipedia

Just recently, I learned about this “mistery” of archaeology: the roman dodecahedron. After preparing a copy of a specific object, I proposed a paper on arXiv, explaining that it can be used for measuring distance (as a telemeter/rangefinder). (In Italiano a )
 For me, those dodecahedrons having a structure with holes of different sizes, are military instruments to evaluate distances for ballistics. It is simple to use. Of course, later, during the Middle Age, different instruments had been developed for surveying: the dodecahedron was of the Roman Army, and, probably, its use lost after the collpase of the Empire.

Monday, 7 May 2012

Thursday, 3 May 2012

Domanda di teoria - 2013 - Stevino

Discutere la legge di Stevino

Per preparare la risposta, usate il file ppt sul portale

Abbiamo visto che 
  Consideriamo il caso in cui ci sia un'energia potenziale dipendente solo da z.
Si ha che, del gradiente resta solo la derivata rispetto a z:

 Applicazioni notevoli sono i vasi comunicanti e i manometri

Domanda di teoria - 2012

Discutere la statica di fluidi, legando il gradiente della pressione alle forze di volume.

Per preparare la risposta, usate il file ppt sul portale

Wednesday, 2 May 2012

Dodecahedral Sound Source

Some builders of acoustics sources produce dodecahedral loudspeakers. These sources have the characteristic to be omni-directional. This is one of important requirements for the sound source thatcan be create from various spherical polyhedrons. The paper: CHIN. PHYS. LETT. Vol. 27, No. 12 (2010) 124302, Directivity of Spherical Polyhedron Sound Source Used in Near-Field HRTF Measurements, by YU Guang-Zheng, XIE Bo-Sun, RAO Dan, is investigating  the directivities of the spherical  tetrahedron, hexahedron and dodecahedron sound sources.
See also 

Tuesday, 1 May 2012

Domanda di teoria - Energia potenziale forza centrale

Discutere l'energia potenziale e il potenziale di una forza centrale.

Per rispondere alla domanda utilizzate il materiale seguente.

 Discitiamo ora l'energia di una massa m che si muova di orbita circolare attono at un corpo di massa M 
Discutiamo ora il caso della forza Coulombiana