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= = toc =Physics Classroom Notes=

Lesson 1: Motion Characteristics for Circular Motion
A: Speed and Velocity The Secrets to Circular Speed and Velocity Discovered! Astonishingly, the average speed formula for objects moving in a circle is only a continuation of the formula we all know and love. As opposed to distance over time, it becomes an easy to remember circumference over time. Velocity, however, is a little bit more difficult. As a vector quantity, it needs direction. The direction in a circular object is tangential, meaning that the direction is a line that only touches the circle in the one place that the object is.

B: Acceleration Figuring out Acceleration much easier than thought before! Because velocity is a vector, the direction changes according to the new place on the circle. This becomes a major factor when solving for acceleration, as you have to add or subtract the two direction vectors to figure out the direction of the acceleration. Now, this sounds difficult. But once you do this, it becomes clear that the acceleration always points toward the center of the circle, making it much easier to figure out.

C: The Centripetal Force Requirement The Controversy between Centripetal Force and Outward Acceleration! According to Newton's first law, an object in rest will stay at rest and an object in motion will stay in motion. However, many, not understanding this, will believe that there is an outward acceleration that causes them to move when cars turn. This is not true. This is only because their body is resisting change, and is continuing to go in a straight line.

D: The Forbidden F-Word Contrary to Popular Belief, There is no Centrifugal Force. Centrifugal force is a common misconception believed by many because of a misunderstanding of inertia. People just don't realize that what they are experiencing when they describe things as having a centrifugal force is not that, but the resistance to change their body has. This is Inertia.

E: Mathematics of Circular Motion The Math of Circular Motion Uncovered By using three formulas, we can solve almost any physics problem involving circles. They are:

Lesson 2: Applications of Circular Motion
A: Newton's Second Law - Revisited B: Amusement Park Physics C: Athletics
 * 1) I understood everything in this lesson, as like its title reveals, it was just a review. For example, drawing free body diagrams and using the formulas to solve problems were used in previous chapters. Free body diagrams show all of the forces acting on an object. They, as well as the formulas we know, are essential to solving physics problems. We have to use formulas, like Newton's second law, to solve for the answers.
 * 2) I understand everything.
 * 3) I understand everything.
 * 4) We went over everything here in class.
 * 1) I understood the circular motion of the small dips and hills of a roller coaster. There are sections where there is circular motion, like the top of the hill and the bottom of it. However, they are different in that the center of the circle lies in opposite places. We must be aware of this when we solve problems like this. I also knew the concept that normal force is the feel for a person's weight. We discussed this in the last chapter when talking about elevators, and the same concept applies here. At the top of the hill, you feel weightless because of less normal force. At the bottom, however, there is more normal force than usual, so you feel heavier.
 * 2) I understand everything that we discussed in class that was covered in the reading.
 * 3) No questions.
 * 4) The whole first half was new information about clothoid loops. These are loops whose radius becomes progressively smaller as it goes up, allowing riders to not die when they go on roller coasterss.
 * 1) The part about leaning into a turn I knew already from class. We had previously talked about it, saying that the lean gives you an inward component to the normal force being exerted. This allows for the athlete to turn in the direction of that force. I also knew how to solve these, as we've been doing problems like these for a while. by using the equation Fc = mv^2/r, we can solve for the magnitude of the forces that player is exerting. (add)
 * 2) I understood everything
 * 3) No questions
 * 4) I didn't know that all turns were part of a circle. This is because it had not occurred to me that one turn could be derived from many different circles.

Lesson 3: Circular Motion and Satellite Motion
A: Gravity is More Than a Name (2a) B. The Apple, The Moon, and the Inverse Square Law (2b) C: Newton's Law of Universal Gravitation (2b) D: Cavendish and the Value of G (2b) E: The value of G (2b)
 * 1) I already knew about everything that this lesson talked about. It was an introduction into the unit, and thus went over concepts that I have learned since our physics class began. For example, the acceleration due to gravity is 9.8m/s^2. This number is the same, regardless of the object's mass or apparent speed. Gravity is also responsible for keeping us on the earth, constantly pulling us toward the center.
 * 2) I understood everything.
 * 3) No questions to be answered here.
 * 4) We have gone over this in class.
 * 1) Kepler created three laws: The Law of Ellipses, The Law of equal areas, and the law of harmonies. The first stated that planets moved in elliptical patterns, the second stated that in a given time period, a planet will carve out an area equal to one in a different but equal time period, and the last stated that the ratio of the squares of the periods of two planets is equal to the ratio of the cubes of their average distance from the sun. These provided the framework for Newton's work about universal gravitation. With much thinking and an epiphany from a fallen apple, Newton deduced that gravity must be responsible for Kepler's laws. From there, he discovered the inverse square law, where he said that the force of gravity gets weaker with an increase in distance by an inverse square. So, if something were to be double the distance away, the force would get weaker by a factor of four.
 * 2) I basically understood the whole reading except for the question below.
 * 3) I'm a little bit confused about Newton's cannonball illustration. Why would path C be a circular path, as opposed to an elliptical one? Is this because of perfect match to Earth's curve?
 * 4) I have always thought it was sweet that such a small thing like an apple falling could inspire one of the greatest scientific breakthroughs of the known world.
 * 1) From Newton's second law, we understand that mass is essential when calculating force. Thus, gravity is dependent on the mass of the objects that it is affecting. Newton expressed this in his formula: Fgrav ~ (m1)(m2)/d^2. However, Cavendish, through his experiments found that he could express the proportion through a universal gravitational constant: 6.673x10^-11 Nm^2/ kg^2. This lets us calculate the force directly. However, gravity affects everything, hence the "universal." Thus we can find the force of gravity between anything, though everything will pale in comparison so massive objects like the Earth.
 * 2) I get the material
 * 3) No questions
 * 4) The fact that everything has a gravitational pull was something I had not thought about before. Since it's so small, it's basically an insignificant force, though it's there. The fact that I have a gravitational pull blows my mind.
 * 1) Cavendish set up an experiment where he was able to determine the value of G. He created a torsion balance and found the force of attraction between two spheres that he had used in the experiment. He found a value very close to the accepted value today. Though it's very small, it starts to play a significant role in the force of attraction as masses get extremely large.
 * 2) I understand the reading
 * 3) No questions
 * 4) I thought it was interesting that Cavendish was able to find such a small number with a reasonable amount of accuracy. His experiment was extremely well set up, allowing to do such things.
 * 1) Well, I knew that the acceleration due to gravity is equal to 9.8m/s^2 because we have been using that number for a long time. I also knew from some prior discussions that it can be different depending on your location and your distance from sea level. A person, for example, on Mount Everest will experience a different force of gravity than a person will a mile under the ocean.
 * 2) I get it
 * 3) No questions
 * 4) I think it's pretty interesting to see the relationships between distance and gravity. Newton had said that the relationship was an inverse square relationship, and to see it work out that way on the graph only proves it. He was a smart dude.

The Clockwork Universe (5) + Extra website
The Great Debate Heliocentric or Geocentric? This question was baffling scientists and churches for ages until Copernicus, Galileo, and Kepler all found data to support the heliocentric model of the solar system. Though they faced strict persecution, eventually their ideas won out. Copernicus, the originator, believed that the sun was the center of the solar system, with each planet moving around it in a circular orbit. And though Galileo was forced to denounce, he secretly showed his real allegiance with the famous but possibly untrue statement of "And yet, it moves." Kepler then drove the final nail in the coffin by showing, through Brahe's observations, that each planet moves around the sun in an elliptical orbit.

The man behind the scenes Behind the scenes of all of these scientific breakthroughs however, were crazy developments in mathematics. Rene DesCartes created the two-coordinate system, where anything point could be described with one x and one y. This created a whole new branch of math called coordinate geometry. This new system was a tool that astrologists used to help their own observations and to show mathematic relationships between things.

Newton: the "interpreter of its laws" Without Newton, much of the scientific knowledge we have today would be fragmented - we would have bits and pieces, but nothing would meld together cohesively. We would not have been able to see the relationships between everything if not for the one and only, the man: Sir Isaac Newton. He essentially created a foundation for the future to build upon. He did so, by following a set of laws. He looked, not at motion, but the deviations in motion. When these happened, he looked for a cause - and found one in unbalanced forces. Finally, he was able to quantitatively prove his observations and ideas, most famously in his law of universal gravitation and second law of motion. He created the Clockwork Universe, which states that all the motion and momentum of objects are conserved. It only needed a start (created by God), and then, it could run by itself.

Which is right? Newton's work inspired new ways in which to think about our existence. His work created both mechanics and determinism, though they are seemingly opposite ways to live. Mechanics attempts to explain everything scientifically, and tried to prove that everything works like a machine. Determinism, however, is the belief that the future is ordained. Everything, according to determinism, must have been planned and designed by an intelligent entity. This controversy was significant in its time, though not necessarily today. But it only shows the implications of Newton's work and the enormous impact it made not only on our science, but also on the way we think.

A Revolution in Thinking! This is due to DesCartes' new mechanical view, which stated this: matter is made up of atom, colors occur by the reflection of light waves of differing lengths, bodies obey the law of inertia, and the sun is the center of the solar system. This raised several question about god's relationship with nature. He reasoned that, in the same way kings create laws, God created laws that nature is governed by. Descartes believed in indivisibility. He thought that the human body and mind were two separate entities connected only by the pineal gland.

Lesson 4: Planetary and Satellite Motion
A: Kepler's Three Laws Planetary Motion Unlocked by Kepler! The advent of Kepler's three laws revolutionized the way people thought about planetary motion. His three laws have withstood the test of time to prove accurate even in the modern day. The first, the Law of Ellipses, states that planets move, not in circular orbits, but in elliptical ones. His Law of Equal Areas states that a the line formed by the sun and a planet's center will carve out equal areas in equal amounts of time. This implies that the planet moves fastest when it is closest to the sun, and moves slower when it moves away from the sun. His third law, the Law of Harmonies, states that there is a ratio between every planet that is equal. This is their periods squared over their average distance from the sun cubed. Every planet has the same ratio.

B: Circular Motion Principles for Satellites Projectiles and Satellites - An Oddly Similar Combo Satellites, once you think about it, are the same thing as projectiles. In both cases, they are objects on which gravity is the only force acting on it. The only difference is that satellites will never fall into the Earth due to falling at the same rate the earth is curved. And like projectiles, they obey the same Newtonian laws that projectiles do. Therefore, the math needed to solve satellite problems are simple applications of Newton's law of universal gravitation and uniform circular motion.

C:Mathematics of Satellite Motion The Key to solving Satellite Problems Surprisingly, the only equations we need to solve satellite motion problems are these: Notice how the mass of the orbiting satellite is irrelevant. It cancels out of the equation, and is completely unnecessary to finishing a problem.

Lesson 4 Continued
D: Weightlessness in Orbit The fastest way to lose weight...guaranteed! A sensation of weightlessness is one where there are no contact forces acting on you. However, as simple as this seems, there are many misconceptions. Weightlessness has nothing to do with your weight, but with the presence of contact forces. But wait! You might say that, as gravity acts on everything, weightlessness doesn't really exist. Gravity, though, is an at-a-distance force. You can't physically feel the force, but you know that it is the only thing keeping you anchored to the Earth. There is a big misconception about scales. Some think that it measures the pull of gravity on you. This is just not true. It measures the upward force required to balance your downward one. Astronauts experience a similar weightlessness. The only force acting on them is gravity, which is an at-a-distance force, so they feel weightless.

E: Energy Relationships for Satellites The hidden science behind satellites Satellites, depending on their orbit, have an ever changing or constant energy. This energy can be expressed through the equation KEi + PEi = KEf + PEf. The key here is that all of the energy is conserved. There is no loss. We can represent the energy shifts and changes through what is called a work-energy bar chart. Through them, we can analyze the potential, kinetic, and mechanical energy each satellite has at a given point in time.