Ch5_WeissB

=__Chapter 5__=

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Summarization (Method 5) of Circular Motion and Satellite Motion Lesson 1
__Circular Motion is Similar and Different to 1D Motion__ Scientists now say that circular motion has traits that are both like and dislike those of 1D motion. According to them, circular motion is also able to be described in terms of speed and velocity. However, speed for circular motion is calculated as circumference/time, while the direction of the velocity is constantly changing (but is always tangent to the circle).

__Circularly Moving Objects Have Acceleration__ Like 1D motion, acceleration for circular motion can also be measured! However, finding the change in velocity is different. According to scientists, one must find the difference between the final velocity vector and the initial velocity vector by drawing a vector diagram and connecting the two. Once the difference is found, one can easily find acceleration.

__Circular Motion Involves Net Force__ According to scientists, objects that move circularly do so because a net force is acting on them. This (centripetal) net force points towards the center of the circle and causes the acceleration of the object. Because of an object's inertia, this force is needed in order for an object to turn.

__"Centrifugal" Forces Do Not Cause Circular Motion, Scientists Say__ Students everywhere commonly mistake centrifugal forces as acting on circularly moving objects. These forces, which act away from the center of a circle, don't actually do so. Instead, centripetal forces are behind circular motion.

__The Three Equations You Need for Circular Motion__ Scientists today have issued out three equations they say are required for studying circular motion. These are:
 * Average Speed= circumference/time
 * Acceleration= (velocity)^2/radius
 * Acceleration= (4 * (pi)^2 * radius)/(period)^2

Scientists urge students to use these or else they may not understand circular motion.

Summarization (Method 2a) of Circular Motion and Satellite Motion Lesson 2
1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. By the time of this reading, I had already understood the basics of the Second Law. Essentially, it states that net force= mass x acceleration. Also, I had also understood that examples from amusement parks could be used to explain circular motion. In class, many practice problems have included roller coasters, from which we had to find acceleration, normal force, etc..

2. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding. I was a little shaky on how one could find quantities like net force, acceleration, etc. at points on a roller coaster (or any other place where an object is traveling along a vertical circle) that were not at the exact top or bottom of the circle. However, through the use of diagrams, this reading has shown me how to do that.

3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question. Is friction on a circularly moving object ever at an angle?

4.What (specifically) did you read that was not gone over during class today? The concept of clothoid loops was not discussed in class today.

**Summarization (Method 2a) of Circular Motion and Satellite Motion Lesson 3**
1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. Before the reading, I had already understood the basic concept of gravity. For example, I already understood that it is a phenomenon that affects objects on Earth and causes a downward acceleration of 9.8 m/s^2. I also had a grasp of the basics of Kepler's Three Laws from Gizmos. I understood that the orbits of planets were elliptical in shape (with the Sun as one of its foci), that the revolution of a planet will sweep out the same area in the same amount of time, and that the ratio of the squares of the period of planets' revolutions is equal to the ratio of the cubes of the distances of the planets from the Sun.

2. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? The reading helped clarify the fact that gravity is acting as the centripetal force on the planets revolving around the Sun.

3. What (specifically) did you read that you still don’t understand? There was nothing in the reading that I did not understand.

4. What (specifically) did you read that was not gone over during class today? We did not already go over the inverse square law (force of gravity is proportional to (m1xm2)/d^2)

Summarization (Method 1) of The Clockwork Universe (parts 1-4)
In 1543, a century before Newton's birth, Nicolaus Copernicus launched a scientific revolution by rejecting the prevailing Earth-centred view of the Universe in favour of a heliocentric view in which the Earth moved round the Sun. By removing the Earth, and with it humankind, from the centre of creation, Copernicus had set the scene for a number of confrontations between the Catholic church and some of its more independently minded followers. The most famous of these was Galileo (who developed the ideas of motion in terms of velocity, force, and inertia), who was summoned to appear before the Inquisition in 1633, on a charge of heresy, for supporting Copernicus' ideas. He renounced his ideas, though tradition has it that at the end of his renunciation he muttered 'Eppur si muove' ('And yet it moves').

German-born astronomer Johannes Kepler (1571-1630) devised a modified form of Copernicanism that was in good agreement with the best observational data available at the time. According to Kepler, the planets // did // move around the Sun, but their orbital paths were ellipses rather than collections of circles.

Kepler's ideas were underpinned by new discoveries in mathematics like the realization by René Descartes that problems in geometry can be recast as problems in algebra, which led to a mechanical view of nature (and created debates about God's role in nature).

This was the beginning of a branch of mathematics, called // coordinate geometry //, which represents geometrical shapes by equations, and which establishes geometrical truths by combining and rearranging those equations and allowed scientists to go further than the greatest mathematicians of ancient Greece.

Newton's good fortune was to be active in physics at a time when the cause of Kepler's ellipses was still unexplained and the tools of geometry were ripe for exploitation. The new astronomy called for a new physics which Newton had the ability and the opportunity to devise. He was the right man, in the right place, at the right time. Newton's great achievement was to provide a synthesis of scientific knowledge. For the first time, scientists felt they understood the fundamentals, and it seemed that future advances would merely fill in the details of Newton's grand vision.Newton concentrated not so much on motion, as on // deviation from steady motion // - acceleration. He always looked for a cause of this deviation (forces), and he provided a quantitative link between force and acceleration, which led to his law of universal gravitation. He also expanded the ideas of acceleration, inertia, and momentum.

By combining this law with his general laws of motion, Newton was able to demonstrate mathematically that a single planet would move around the Sun in an elliptical orbit, just as Kepler claimed each of the planets did. Moreover, thanks to the understanding that gravity was the cause of planetary motion, Newtonian physics was able to predict that gravitational attractions between the planets would cause small departures from the purely elliptical motion that Kepler had described.

Newton's discoveries became the basis for a detailed and comprehensive study of mechanics (the study of force and motion). The upshot of all this was a mechanical world-view that regarded the Universe as something that unfolded according to mathematical laws with all the precision and inevitability of a well-made clock, whose future development could easily be predicted. This property of Newtonian mechanics is called determinism.

Summarization (Method 2a) of Circular and Satellite Motion Lesson 4a-c
1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. Before the reading, I had already understood Kepler's Laws and the story of how Kepler created them. Kepler used data collected by his mentor Brahe to demonstrate that the planets revolved around the Sun in ellipses (the center of the Sun being one of the foci), that different portions of a planet's revolution will sweep out the same area in the same amount of time, and that the ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the Sun. I also had understood what was meant by a "satellite", an object that is orbiting the earth, sun or other massive body.

2. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding. I was confused about how a satellite could stay in orbit forever. The reading explained that this is due to gravity between the two objects acting as the only centripetal force. Also, the reading explained how the curvature of the body the satellite is orbiting around makes this possible.

3.What (specifically) did you read that you still don’t understand? Please word these in the form of a question. The reading made everything clear; there wasn't anything I didn't understand.

4. What (specifically) did you read that was not gone over during class today? We did not go over how there is a minimum velocity required for a satellite and that satellites stay in orbit due to the curvature of the body it is orbiting around.

Summarization (Method 2a) of Circular and Satellite Motion Lesson 4d-e
1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully. I had already understood the basic concept of weightlessness, which is the sensation that comes from the absence of contact forces. I had also already understood that a satellite moves fastest when it is closest to the object it is orbiting around and moves slowest when it is it is farthest away from the object it is orbiting around.

2. What (specifically did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? The reading helped clarify how weightlessness can be applied to other situations besides roller coasters. At the same time, it helped me understand exactly how velocity changes at different points of an elliptical orbit.

3.What (specifically) did you read that you still don’t understand? Please word these in the form of a question. What other situations can weightlessness be applied to? Why does TME always remain the same in an elliptical orbit?

4. What (specifically) did you read that was not gone over during class today? We did not go over weightlessness from the perspective of an astronaut in space, only when a person is upside on at the top of a roller coaster. We also did not go over the work-energy theorem, which is KEi + PEi + Wext = KEf + PEf.