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GALILEI Galileo (1564 1642)

can be considered one of the greatest scientists of modern history and author of the scientific method.
His first important discovery was observing the oscillation of a lamp, discovers the law of the pendulum for small oscillations dell'isocronismo: pendulums of equal length make equal time regardless of fluctuations in their amplitude.
The big news is that Galileo introduced precisely to address the telescope (perhaps not invented by him, but it certainly changed and improved) to the sky and begin the first systematic observations of no more than the naked eye. Initially
advocate of the theory Aristotle - Ptolemy, became convinced of the Copernican theory thanks to these sensational discoveries
- spots on the moon are shadows cast by the mountains (which calculates the height);
- the four 'moons' of Jupiter, that shows that not only the earth can be the center of circular motion;
- The Milky Way is made up of countless stars
- the ring of Saturn
- the phases of Venus that show that this planet "could" turn around Sun;
- the planets are naturally dark because they receive light from the Sun;
- sunspots.

His most important and best known is the "Dialogue Concerning the Two Chief World Systems Ptolemaic and Copernican ". Besides being a great work of popular science, laid the foundations of the new physics through the destruction of the old Aristotelian system. It is set as a dialogue, in fact, among three parties: Salviati is the teacher who acts as the bearer of the new, Sagredo is cultured and free-thinker able to change the view, is a dogmatic Aristotelian Simplicio.
course Galileo knows that, from Earth, he could not show that it is spinning around the sun He bypasses the difficulty of moving along two trails: one part the "principle of inertia" and the other the "principle of relativity".
And from here begins to rise to the need for new physics at the expense of the Copernican Aristotle.

Just in defense of the Aristotelian-Ptolemaic tradition, Galileo was condemned by the church inquisitor of the time and is forced to recant, that the public renunciation and repudiation of his ideas. This painful episode would have created the legend of Galileo, who once stood up after the recantation, hit the ground and murmured: "And yet it moves!"

Towards the end of his life, when she was completely blind, published another of his important wrote: "Discourses and mathematical demonstrations concerning two new sciences"; it is the laws of motion and structure of matter.

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NEWTON (1642-1727)
physicist and mathematician of the greatest of all time.
His most important are the "Philosophiae Naturalis Principia Mathematica," which lists the results of its mechanical and astronomical surveys, as well as lay the foundations of calculus. Among other works include "Optik", a study in which he argued the famous corpuscular theory of light, "Arithmetica universalis and Methodus fluxionum et serierum infinitarum" published posthumously.

The Newton's laws of motion (the one most commonly known as "three laws of motion") are still the basis of classical mechanics. The first law is the principle of inertia states that a body perseveres in its state of rest or uniform rectilinear motion, unless it is compelled to change that state by forces outside the second law, stating that the acceleration of a body is directly proportional to the applied force, allowing the one hand, moment by moment to calculate the position and velocity of the body are known when the initial conditions of motion, on the other hand the definition of one of the most important concepts of physics: the inertial mass . The third law states that for every action there is always an equal and opposite reaction.

's more specific contribution to the description of Newton the forces of nature came from law of universal gravitation: it states that two bodies attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of their distance, this law has vast implications: it introduces the concept of mass gravity, explained the motion of planets around the Sun and the objects inside the Earth's gravitational field, but it is also responsible for the phenomenon of gravitational collapse, leading to the understanding of the phenomenon of blacks holes. The legend wants that the idea of \u200b\u200buniversal gravitation by the fall of an apple suggested to among other things, it would seem authentic.

Among his numerous studies include recognition white light as a result of the superposition of all the colors of the spectrum, the theory of light propagation and the introduction of differential and integral calculus, he was also responsible for understanding the phenomenon of the tides and the precession of the equinoxes. The
Kepler's laws of planetary motion and the theory of Galileo on falling bodies were both confirmed and recognized as consequences of Newton's Second Law of Newton and his law of universal gravitation.

Trivia: In her tomb in Westminster Abbey is this epitaph: "Sibi gratulentur mortales that humani generis decus tantumque exstitisse (mortals rejoice that there has been a such and such great honor of mankind).

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Also I did some concept maps!
you can enlarge or simply give it a try!
laws of dynamics
motions
Galilean relativity

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.. to find in you tube video of Sarah, use this gadget!

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... come to the wiki!

Okay guys! I saw that you worked so hard and I'm glad that you are passionate.
I beg you, put the things we talked about in class on the wiki .. and do not forget to tag (see the tags) for each page.
Remember also that if, for example, Sarah has created a page of the laboratory tagging workshop and some of you think it is more appropriate to another tag, well're ready to add the tags differently.
E 'prorpio their purpose, and do so without fear of making mistakes! So do I!
Vivian, the beautiful logo that you and your group have done and you sent me. As you have seen and I've uploaded my opinion is very comfortable. If someone does not like, however, say that we will try to change it to please everyone! Look
comments!

Great job guys!

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Experiment on the parabolic motion

Material: a rigid plastic tube (which would be blowgun), an electromagnet, a power supply DC power from 0 to 20 V, a ball of iron, a glass marble, electrical cables for connecting two support rods, aluminum foil, two wires terminal, a switch;

Purpose: show that in a parabolic motion of a severe horizontal and vertical motions are independent and that the time of vertical fall is the time of horizontal displacement;

Procedure: mount the tube horizontally on one of the two supports, attaching the electromagnet to the other support, adjusting the height and direction of the blowgun to aim at position to deal with the ball hooked all'elettrocalamita. Secure with scotch tape the wires with terminal ends of the tube, they attach to a strip of aluminum foil, so that it covers the exit hole of the blowpipe.

The structure of the equipment is summarized in the following figure:

all'elettrocalamita Hook the metal ball and use the other as "bullet" in the blowpipe.

Before proceeding with the experience itself must be "calibrated" the pole of the blowgun horizontally and vertically to achieve alignment with the metal ball.

When the ball breaks the foil projectile breaks the circuit and determines the fall of the ball is supported by the electromagnet. The two balls then start at the same time their motion vertical drop. The difference between the two is that the ball projectile, having also a horizontal initial velocity, describes a parabolic motion.

balls collide in a point located at the vertical of the electromagnet. This shows that the downward shift of the metal ball is the same as that of the ball projectile, at the same time interval. In addition, the time taken by the metal ball to fall along the vertical is the same ball used by the projectile along the horizontal line that corresponds to the distance between the electromagnet and exit point from the blowpipe.

A confirmation of impact occurred, in many cases the glass ball breaks.

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Uniform circular motion

a) uniform circular motion

DEF: The motion of a body that is a circle (a circle) with speed (in form) is said constant uniform circular motion. When we refer only to the intensity of the speed we are talking about speed climb.

ATTENTION: The speed is a vector, it is characterized by intensity, direction and orientation.
in uniform circular motion is the intensity of speed to be constant, the direction and to change the time!
NOTE: For each type of trajectory, the velocity vector is always tangent to the trajectory.
Since the form of speed is constant, one might be tempted to consider a motion is not accelerated. But we must remember the definition of acceleration (it is also a carrier!) And note that the difference of two vectors with the same form is not 0. The fact that the speed changes of direction, even if it does not change in intensity, uniform circular motion is therefore an accelerated motion.
For the second principle of dynamics, if the motion is accelerated, then this is a force.

Some important parameters relating to the uniform circular motion are:

1)

PERIOD The period is the time it takes to make a full circle. It is measured in SI (International System) in seconds. It is usually indicated by a capital letter T.
We observe that the concept of time also applies to any motion that they be periodic but the characteristic of, or to "wipe" to the same point after a certain time.

2) FREQUENCY

The frequency indicates the number of revolutions made per unit time. In SI, the frequency is measured in hertz (Hz) and the number of revolutions per second. It is usually denoted by the lowercase Greek letter f or ν. The frequency features in general a periodic phenomenon qualunque.Fra the period and frequency there is a mathematical relationship important:

f = 1 / T;

ie the frequency is the inverse of the period.

3) SPEED 'SCALAR

The velocity scale of uniform circular motion is, as with all speed, measured by the ratio space / Time. If the radius of the circle is R, whereas the entire circumference measure 2 π R and that the total time to tour is the period T, then you will have:
v = s / t = 2 π R / T.
This is the formula of the scalar speed of rectilinear motion. It can also be expressed as a function of frequency taking into account that f = 1 / T. Then you get: v = 2 π R
f.
speed climb, of course, is measured in SI in m / s.

b) centripetal acceleration

The rectilinear motion with uniform acceleration because the direction of its velocity changes point by point. Let's see how this acceleration is calculated and its characteristics.
consider velocity vectors at points A and B respectively, and call them v1 and v2:
means for accelerating the change in velocity per unit time. Dv call with the change in velocity between points A and B for which we have:

v2 = v1 + dv

since the speed at point B is the speed at point A plus the change in speed (all three are vectors!).
For convenience, we report the carrier at point A by a parallel shift. We get :

Remember that the intensity of v1 and v2 are the same and to make the sum of two vectors, you must use the rule of the parallelogram.
We have obtained the vector change in velocity dv that is directed toward the center of the circle along which the motion takes place.
If we divide this vector for the time Dt in which the point is from A to B, we finally obtain the sought acceleration which is itself a carrier who has the same direction and orientation (since the time that we share is a positive number ) of the vector change in velocity dv.
The acceleration is then:

a = dv / dt

. . Please note that we have indicated the acceleration with the "subscript" c. This means that the acceleration "point" toward the center, and this is called centripetal acceleration .
NOTE: This acceleration, at a given point on the circumference, is exactly pointing to the center though, looking at the graph, this would seem true only approximately. In the chart, we took two points (A and B) "somewhat" distant for reasons of simplicity. If we take them "very close" (infinitely close), you would see that dv is directed exactly toward the center and there would then the instantaneous change in speed.

How much is the intensity of centripetal acceleration? Need to derive some basic knowledge of differential calculus, for which we give directly the result. The strength of the centripetal acceleration is: a

c = v ^ 2 / R

where v is the velocity scale of the motion and R the radius of the circle. Also note that here, speed and acceleration are staggered arrangements.
Note that the centripetal acceleration is directly proportional to the square of the velocity and inversely proportional to the radius. This means that if the speed is doubled, the acceleration quadruples and so on. If the radius doubles, the acceleration halved, if the radius by half, the acceleration doubles etc..

c) centripetal force

If a body moves with accelerated motion, it is because it suffers the action of a force (resultant). For the second law of dynamics, the relationship between force and acceleration is given by the formula: F = ma

m is the mass of a scalar, the force and acceleration vectors.
in uniform circular motion, then a force acts, the so-called centripetal force, which is due to the fact that the body along a circular path. If your body does not act force (resultant), the body moves in rectilinear motion (first law of motion ).
The centripetal force is then: F

c = ma c

and will be targeted as the centripetal acceleration, m is the mass of a positive number (multiplying a vector by a positive number, direction and orientation the carrier that you get do not change).

The intensity of the centripetal force will be:

the centripetal force for the same considerations of direct and inverse proportionality that we have done for the centripetal acceleration.

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About the motion of projectiles ... here are two interesting applet:
and a two !

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the motion of a projectile

Galileo was the first in a scientific way to study the motion of a projectile showing that its trajectory is a parabola. The results are published in the work "Discourses and mathematical demonstrations concerning two new sciences."

Obtain the results of Galileo by the equations of motion, taking into account only the gravitational forces acting on the projectile, considered as a material point, and neglecting air friction.

We choose a reference system with the y-axis positive upward, so that the origin of the axes is the point (0 x, y 0) = (0,0) of departure of the projectile; The components will be x = 0, y = - g.

Using the law of fall of a serious, we draw the trajectory of a bullet, making sure it is a parable and then showing some more features.

The velocity vector v at the initial instant t = 0 has form v 0 and is tilted at an angle θ with respect to the positive direction of x, its components are:

v 0x = v 0 cos θ

_{0Y v = v 0} senθ

The law of motion, which expresses the speed is a function of time t (v (t) = v 0 + at).
Since there are no horizontal components of acceleration, the horizontal component of velocity v x remains constant, the vertical component v y change over time because there is a constant downward acceleration (a y = - g):

v x = v 0x

v y = v 0Y - gt

The velocity vector is tangent to the trajectory at each point, its form is not constant and can be obtained by applying the Pythagorean theorem.

The laws of motion describing the motion of the projectile in space are those of a rectilinear motion along x and y uniformly accelerated along, independent of each other. Then the coordinates of the projectile in parametric form (the parameter is the time t) at a generic instant t are:

x (t) = v 0x

t y (t) = v 0Y t - 1 / 2GT ^ 2

From this equation it is possible to obtain the equation of the trajectory in Cartesian form, obtaining t from the first equation and substituting in the second. You get the equation of the trajectory of the bullet:

as you can see that is a downward parabola through the origin of the axes. A drawn representation of motion with the velocity components is shown below.

The vertex of the parabola can be found mathematically by the known relationship V = (-b/2a; -Δ/4a). Arguing from a physical point of view, the vertex of the parabola is obtained by requiring that the velocity along y is 0. It is then the point:

M x represents the abscissa of the point maximum height, y M the maximum height reached by the projectile.

To calculate the range, that is the point at which the bullet falls on the axis of x, y sufficient to impose (x) = 0, ie to the intersection of the parabolic trajectory of the bullet with the x-axis You get two solutions:

The first is obviously the source, the second is the range sought.

The time taken to travel x G is called time of flight (t Flight ) and coincides with twice the time necessary to reach the maximum height y M and return to the soil

t Flight G = x / v = 2x 0x M / v 0x .

Note that the location where the bullet touches the x-axis, the speed is the same in the form at the start but it is symmetrical with respect to x.

The launch angle for maximum range is where you can get as follows:

sen2θ = 1 → 2θ = 90 ° → θ = 45 °.