Ch5_llewellynma

Chapter 5 Honors Physics Max Llewellyn toc

__**Homework**__ Circular Motion Unit Lesson 1
__Topic sentence__: Even though there is one speed there are many different velocities during circular motion. __First Paragraph__: The average speed of something traveling in a circular path is simply the distance, 2piR, over time; however, even though the path of the object is constant, the velocity is not. The object is still changing direction, constantly, and this forms a circle. These velocities are all tangent to the circle.
 * Speed and Velocity**

__Topic sentence__: Even though the speed is constant it doesn't mean there isn't acceleration! __First Paragraph__: Notice how the direction of the object changes even though the speed doesn't, how the velocity is not constant because it is a vector. This change in direction means there must be acceleration present.
 * Acceleration**

__Topic sentence__: Smoke means fire and acceleration means force. __First Paragraph__: This acceleration has to be caused by something right? Well some force, like normal force, tension, gravity, ect, has to act as a centripetal force and constantly push or pull the object in a circular path. If there were no centripetal force then the object would just go straight because of it's inertia. These forces always point toward the center of the circle, never otherwise!
 * The Centripetal Force Requirement**

__Topic sentence__: Centrifugal force doesn't exist. Plain and simple. __First Paragraph__: Centrifugal means on the outside of the circle and they're simply aren't any forces outside the circle. The 'force' that would make someone on an merry go round gone haywire feel like they're being pulled to the outside of the circle is actually the centripetal force pushing them in, not some magic force pulling them out.
 * The Forbidden F-Word**

__Topic sentence__: Everything boils down to newton's laws (maybe that's why they call it Newtonian physics) __First Paragraph__: The mathematics behind how the following equation is derived from newton's three laws are complicated and long winded, trust me I checked. Long story short the acceleration that on object traveling in circular motion is equal to V^2/R. Take my word for it. You can then use this equation for all sorts of fun and games, if that's what your call fun and games.
 * The Mathematics of Circular Motion**

__Topic sentence__: Not going anywhere. __First Paragraph__: F = ma can also be applied in the context Fcentripetal = m * Acentripetal. This means that in any uniform circular motion situation Fc can be calculated by knowing Ac and M. As for which force(s) it is only a simple free body diagram is required to determine that.
 * Newton's Second Law - Revisited**

__Topic sentence__: The physics makes it fun! __First Paragraph__: In any given amusement park there are many different types of physics at work. Circular motion physics take part in things like loops, dip hills and banked turns. Something interesting to observe is that in a full circular loop, assuming the speed is constant and Fc is constant, since Fc must always point towards the circle, when you're at the bottom of the loop normal force has to overcome gravity AND provide for Fc while at the top only gravity is on your side and takes care of Fc so normal force doesn't have to. You might also notice that there is more force on smaller or quicker turns, this is all because of the math above.
 * Amusement** **Park Physics**

__Topic sentence__: Physics physics everywhere! __First Paragraph__: Physics is present all over the universe, that's why it's physics. Even athletes making a turn (even a varying turn, hello calc!) are subject to the laws of physics. Everything that applies above still applies.
 * Athletics**

__**Homework**__ Circular Motion Unit Lesson 3
__Topic sentence__: Gravity, more clingy then your ex __First Paragraph__: The acceleration of gravity is the acceleration that something under the force of gravity, Fgrav, experiences on earth. However this is not the same as the force of gravity itself, merely evidence of it's existence.
 * Gravity is more then a Name**

__Topic sentence__: Flavors of gravity __First Paragraph__: Johannes Kepler used math and science to prove that the planets moved in a elliptical path, but couldn't explain why. Newton proposed the theory of universal gravitation, that gravity spread out over everywhere but wasn't as strong the further away you got. Comparing the acceleration of an apple on the earth's surface to the moon, not on the earth's surface, and found that the ratio of Amoon to Aapple was the same as the inverse of the ratio of DistanceMoon^2 to DistanceApple^2. Thus the inverse square law was born.
 * The Apple, the Moon, and the inverse Square Law**

__Topic sentence__: Weight changes the flavor __First Paragraph__: Not only is distance a factor in the strength of Fgrav but also the masses of both objects in question. Also both the apple and earth were attracted to one another, although the apple was just a lot more moved compared to the earth (Hey! sorta like your ex). He discovered that Fgrav was proportional to the product of the masses divided by the distance separating them. Since that number above is linearly proportional the only thing it takes to make it equal instead is a constant, this is the universeal gravatational constant G, G = 6.673 x 10-11 N m2/kg2
 * Newton's Law of universal Gravitation**

__Topic sentence__: Newton wasn't alone. __First Paragraph__: Even though Newton theorized the existence of G it was never experimentally determined until 1798. Lord Henry Canvish he used a torsion balance that would rotate, but not revolve, a different amount depending on the force causing it to rotate. He put two weights at either end of the apparatus and two more weights in front of them them measured how much the balance rotated because of the gravity pulling the two objects together. Thus science was performed.
 * Cavendish and the Value of G**

__Topic sentence__: How we get g from G __First Paragraph__: If you take the equation of universal gravitation Fgrav = M1 * M2 * G / D^2 and substitute in Mearth for M1, call D pretty much the same relative to the surface of the earth (the changes between the ceiling and the floor doesn't matter that much) and set the whole thing equal to F = M2 A2 you get (Mearth * G * M1) / D^2 = M2 A2, the two M2s cancel out and the rest are now numbers which roughly simplify to g, 9.8 m/s. If you get really far from the center of the earth then g changes but that's another topic.
 * The Value of g**

__**Homework**__ The Clockwork Universe
__Topic sentence__: Copernicus sparked the debate about what the true center of the universe was but that idea took a while to grow in to a fire. __First Paragraph__: Copernicus was the first to propose a __heliocentric__ model of the universe, were everything orbited the sun, not the earth, but his ideas didn't catch on. Galalio at first supported his ideas but was "convinced" by the church to renounce them. Kepler then worked off Copernicus's theory and proposed the planets moved in ellipses but did not know why.
 * Finding the Center**

__Topic sentence__: Even though Kepler could not explain why he was right new advances in mathematics garnered support for his ideas. __First Paragraph__: With René Descartes's advanced in relating geometry to algebra geometry was in turn developed more. Since scientists could now take a more mathematical approach to geometry they could further extend Kepler's ideas.
 * Growing the Flame**

__Topic sentence__: Newton was the right arson in the right dry forest, I'm sure that can't be misinterpreted. __First Paragraph__: Newton was alive in the time when there was both a demand for an explanation of Kepler's laws and the geometrical tools to find them. He focused not on motion but rather on change in constant motion, acceleration. He developed theories that wouldn't be challenged until Einstein, publishing his universal theory of gravitation.
 * The Apex of the Blaze**

__Topic sentence__: Newton's one law for universal gravitation, combined with his general laws of motion, made it possible for him to mathematically predict how a single planet would move around the sun. __First Paragraph__: Aside form this being a great scientific feat it also raised some philosophical questions. As more and more science was developed to predict, well everything, people began to wonder about determinism, the idea that there was only one possible outcome, overriding the idea of free will. This was a controversial topic and is still not settled today.
 * ...It was Always Burning Since the World was Turning**

__**Homework**__ Circular Motion Unit Lesson 4
__Topic sentence__: Kepler's three laws are not only accurate but can be proven so. __First Paragraph__: Kepler's first law simply states that the planets will orbit following an ellipse with the sun at one of the foci, for more information regarding ellipses review conic sections. Kepler's second law, the law of equal areas states that the area carved out by a line from the center of the planet to the center of the sun will be the same for any given time period as the area carved out in that time period at any other location. In other words, if the ellipse was a pie, sliced from planet to sun, no matter where you start if you wait the same time before saying "stop" (when the person cutting the pie cuts the pie) you will always get the same size piece. The third law is the law or harmonies, it states that there is a constant ratio of period squared over radius cubed for any planet that orbits the sun. So if you know the radius and period on any given planet and the radius or period of any other planet you can calculate all your missing information.
 * Kepler's Laws Further Explained**

__Topic sentence__: Before reading this brush up on constant circular motion and sit back in awe at the similar (actually the same) math. __First Paragraph__: A satellite is anything that orbits anything else, natural or not (eg: both the moon and GPS satellites are satellites). While in actuality satellites do not go in perfect circles, unless the ellipse they follow happens to have an eccentricity of 0 (which will happen more often then not in these examples), when talking about averages the same math used in circular motion can be applied to satellite motion by simply remembering that Fgrav exists.
 * Satellitely Familiar**

__Topic sentence__: Remember the math from above, don't forget it. __First Paragraph__: Just reread the above paragraph and remember that Fgrav is often the (only) force pulling toward the planet. Nearly always Fgrav (G*m1*m2/D^2) just equals ma (m*V^2/R^2).
 * Completely New and Never-Before-Seen Material.**

__Topic sentence__: In Earth's orbit nothing about a person's mass changes however they fell weightless none the less. __First Paragraph__: Apparent weight (what a scale would read) only measured the amount of normal force an object is exerting on a plate. On earth there is a constant downward acceleration of -9.8 m/s/s that makes weight seem real. In space if the astronaut is acceleration at the same rate as the spacecraft (both around the earth) relative to each other there is no acceleration and therefor no force. Therefor there is no apparent weight.
 * Going to Space, the New Diet Craze**

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