Ch5_AronskyA

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 **Chapter 5: Circular Motion**

=Lesson 1 Summary: = 12/13
 * 1) //Speed and Velocity are Back Yet Again//
 * 2) The concepts of speed and velocity can be applied to circular motion. For example, an object can have uniform circular motion as it is going at a constant speed and the average speed can still be calculated by distance over time, but being a circular, it is now written as circumference/time (2 X pi X radius/time). However, while the speed of an object is constant, the velocity is changing because as it is a vector, it takes into account direction. Velocity is always tangent to the circle and as an object turns, the tangent line will always be facing in a different direction.
 * 3) //Acceleration, We Could NEVER Forget About You!//
 * 4) Acceleration is calculated by the change of velocity over time (vf-vi/t). The acceleration is dependent upon the velocity change and is in the same direction as the velocity change. Objects at constant speed moving in circles accelerate towards the center of the circle. A device used to measure acceleration, called an accelerometer, consists of an object suspended in a fluid and determines if the object has much inertia.
 * 5) //Centripetal-Man: Common Force in Disguise//
 * 6) The centripetal force requirement states that an object moving in a circle, must have an inward force acting upon it in order to cause its inward acceleration. There must be an unbalanced force for all objects moving in a circular motion because of Newton's first law. The centripetal force, the force pushing or pulling an object towards the center of the circle, changes the direction of the object without changing its speed. As this force is perpendicular to the tangential velocity, it is able to change the object's velocity but not its magnitude.
 * 7) //Be Careful Using the F-Word!//
 * 8) The word centrifugal means away from the center of the circle and should not be confused to the similar word centripetal! Objects in circular motion do not experience an outward force. Thus, the inward force, or centripetal force, is necessary for circular motion. Don't get them mixed up!
 * 9) //Breaking News: Discovery of Equations in the Circle World//
 * 10) Speed, acceleration, and force are used to determine motion of objects in circles. Average speed is found by the equation of circumference over time (2 pi radius/ t), while acceleration can be calculated by 4pi(sq)R/time. Net force is still determined by mass times acceleration, in which the acceleration can be substituted with the equation mentioned previously. We're switching into radian and pi mode, it's circle time.

=Lesson 2 Summary: = Applications of Circular Motion - 12/22


 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">//How is Newton's Second Law applied to circular motion?//
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif;">a=V(sq)/R instead of a = F/m
 * 3) <span style="font-family: Tahoma,Geneva,sans-serif;">Consider a car on a turn - the friction force is the centripetal force because it causes the wheels to move in a circle
 * 4) <span style="font-family: Tahoma,Geneva,sans-serif;">Necessary to create FBD
 * 5) <span style="font-family: Tahoma,Geneva,sans-serif;">Determine magnitude of any known forces and label FBD
 * 6) <span style="font-family: Tahoma,Geneva,sans-serif;">Use circular motion to determine unknown info
 * 7) Use remaining info to solve for requested info
 * 8) <span style="font-family: Tahoma,Geneva,sans-serif;">//How is physics applied to amusement parks?//
 * 9) <span style="font-family: Tahoma,Geneva,sans-serif;">Circular motion with loops, small dips and hills, and banking.
 * 10) <span style="font-family: Tahoma,Geneva,sans-serif;">Physicist have to calculate max speeds and minimum speeds, as well as accelerations for different rides such as roller coasters, log flumes, and ferris wheels.
 * 11) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"><span style="font-family: Tahoma,Geneva,sans-serif;">The clothoid loop experiences a change in direction (tear-drop shape). It is a series of overlapping and adjoining circular sections. The radius of these circular section decrease as it approaches the top of the loop.
 * 12) <span style="font-family: Tahoma,Geneva,sans-serif;">Acceleration is experienced because of change in speed and direction
 * 13) <span style="font-family: Tahoma,Geneva,sans-serif;">At the bottom of the loop, the track pushes upwards upon the car with a normal force. However, at the top of the loop the normal force is directed downwards; since the track (the supplier of the normal force) is above the car, it pushes downwards upon the car.
 * 14) <span style="font-family: Tahoma,Geneva,sans-serif;">Able to find minimum and maximum speeds based on the theory that humans can only withstand 4gs
 * 15) <span style="font-family: Tahoma,Geneva,sans-serif;">//How is physics applied to athletics?//
 * 16) <span style="font-family: Tahoma,Geneva,sans-serif;">Involved in ice skating, baseball, track and field.
 * 17) <span style="font-family: Tahoma,Geneva,sans-serif;">Circular motion is characterized by the inward acceleration and caused by an inward net force.
 * 18) <span style="font-family: Tahoma,Geneva,sans-serif;">Most common example of circular motion in sport is "the turn"
 * 19) <span style="font-family: Tahoma,Geneva,sans-serif;">some may only be a quarter of a turn and may be a full turn
 * 20) <span style="font-family: Tahoma,Geneva,sans-serif;">Contact force has two roles:
 * 21) <span style="font-family: Tahoma,Geneva,sans-serif;">balances the downward force of gravity
 * 22) <span style="font-family: Tahoma,Geneva,sans-serif;">meets the centripetal force requirement for uniform circular motion
 * 23) <span style="font-family: Tahoma,Geneva,sans-serif;">upward component balances gravity and horizontal pushes person towards center of circle
 * 24) <span style="font-family: Tahoma,Geneva,sans-serif;">example: figure skater pushing on the ice, skier making a turn

=<span style="font-family: Tahoma,Geneva,sans-serif;">Lesson 3 Summary: = <span style="font-family: Tahoma,Geneva,sans-serif;">Universal Gravitation

<span style="font-family: Tahoma,Geneva,sans-serif;">//Part A: Gravity is More Than a Name:// <span style="font-family: Tahoma,Geneva,sans-serif;">Gravity is the thing that causes objects to fall to Earth. Gravity must be understood in terms of its cause on the structure and the motion of the objects in the universe. We have become accustomed to calling gravity the force of gravity and have even represented it by the symbol F grav. In fact, many students have become accustomed to referring to the actual acceleration of such an object as the acceleration of gravity. On and near Earth's surface, the value for the acceleration of gravity is approximately 9.8 m/s/s. It is the same acceleration value for all objects, regardless of their mass (and assuming that the only significant force is gravity). <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">//Part B: Apple, Moon, and Inverse Square Law// <span style="font-family: Tahoma,Geneva,sans-serif;">In the early 1600's, mathematician and astronomer Johannes Kepler analyzed known astronomical data in order to develop three laws to describe the motion of planets about the sun. Kepler's three laws of planetary motion can be briefly described as follows: <span style="font-family: Tahoma,Geneva,sans-serif;">The cause for how the planets moved as they did was never stated. Kepler could only suggest that there was some sort of interaction between the sun and the planets that provided the driving force for the planet's motion. To Kepler, the planets were somehow "magnetically" driven by the sun to orbit in their elliptical trajectories. There was however no interaction between the planets themselves. <span style="font-family: Tahoma,Geneva,sans-serif;">Newton knew that there must be some sort of force that governed the heavens; for the motion of the moon in a circular path and of the planets in an elliptical path required that there be an inward component of force. Circular and elliptical motion was clearly departures from the inertial paths (straight-line) of objects. And as such, these celestial motions required a cause in the form of an unbalanced force. <span style="font-family: Tahoma,Geneva,sans-serif;">The inverse square law proposed by Newton suggests that the force of gravity acting between any two objects is inversely proportional to the square of the separation distance between the object's centers. That is, an increase in the separation distance causes a decrease in the force of gravity and a decrease in the separation distance causes an increase in the force of gravity. Furthermore,the factor by which the force of gravity is changed is the square of the factor by which the separation distance is changed.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The paths of the planets about the sun are elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses)
 * <span style="font-family: Tahoma,Geneva,sans-serif;">An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas)
 * <span style="font-family: Tahoma,Geneva,sans-serif;">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. (The Law of Harmonies)

<span style="font-family: Tahoma,Geneva,sans-serif;">//Part C: Newton's Law of Universal Gravitation// <span style="font-family: Tahoma,Geneva,sans-serif;">Newton compared the acceleration of the moon to the acceleration of objects on earth. Believing that gravitational forces were responsible for each, Newton was able to draw an important conclusion about the dependence of gravity upon distance. This comparison led him to conclude that the force of gravitational attraction between the Earth and other objects is inversely proportional to the distance separating the earth's center from the object's center. But distance is not the only variable affecting the magnitude of a gravitational force. <span style="font-family: Tahoma,Geneva,sans-serif;">But Newton's law of universal gravitation extends gravity beyond earth. **ALL** objects attract each other with a force of gravitational attraction. This force of gravitational attraction is directly dependent upon the masses of both objects and inversely proportional to the square of the distance that separates their centers. <span style="font-family: Tahoma,Geneva,sans-serif;">Since the gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a greater gravitational force. If the mass of one of the objects is doubled, then the force of gravity between them is doubled; and so on. <span style="font-family: Tahoma,Geneva,sans-serif;">Since gravitational force is inversely proportional to the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces. The constant of proportionality (G) is known as the universal gravitation constant. The value of G is found to be 6.673 x 10^-11. The units on G may seem rather odd; nonetheless they are sensible. When the units on G are substituted into the equation above and multiplied by m 1 • m 2 units and divided by d 2 <span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Tahoma,Geneva,sans-serif;">units, the result will be Newton’s. Knowing the value of G allows us to calculate the force of gravitational attraction between any two objects of known mass and known separation distanc e.

<span style="font-family: Tahoma,Geneva,sans-serif;">//Part D: Cavendish and Value of G//

<span style="font-family: Tahoma,Geneva,sans-serif;">Newton's law of universal gravitation proposed that the gravitational attraction between any two objects is directly proportional to the product of their masses and inversely proportional to the distance between their centers. Cavendish's apparatus for experimentally determining the value of G involved a light, rigid rod about 2-feet long. Two small lead spheres were attached to the ends of the rod and the rod was suspended by a thin wire. Cavendish had calibrated his instrument to determine the relationship between the angle of rotation and the amount of torsional force. Once the torsional force balanced the gravitational force, the rod and spheres came to rest and Cavendish was able to determine the gravitational force of attraction between the masses. By measuring m 1, m 2 , d and F grav , the value of G could be determined. Cavendish's measurements resulted in an experimentally determined value of 6.75 x 10 -11 N m 2 /kg 2. Today, the currently accepted value is 6.67259 x 10 -11 N m 2 /kg 2. The value of G is an extremely small numerical value. Its smallness accounts for the fact that the force of gravitational attraction is only appreciable for objects with large mass.

<span style="font-family: Tahoma,Geneva,sans-serif;">//Part E: Value of G// <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 13px;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Tahoma,Geneva,sans-serif;">The value of g is dependent upon location. There are slight variations in the value of g about earth's surface. These variations result from the varying density of the geologic structures below each specific surface location. They also result from the fact that the earth is not truly spherical; the earth's surface is further from its center at the equator than it is at the poles. This would result in larger g values at the poles. As one proceeds further from earth's surface - say into a location of orbit about the earth - the value of g changes still. <span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 13px;">

=<span style="font-family: Tahoma,Geneva,sans-serif;">Clockwork Universe Summary = <span style="font-family: Tahoma,Geneva,sans-serif;">1/9/12

<span style="font-family: Tahoma,Geneva,sans-serif;">1. Who are important figures involved with works of the universe? <span style="font-family: Tahoma,Geneva,sans-serif;">2. What did Renes Descartes do? <span style="font-family: Tahoma,Geneva,sans-serif;">3. What was Newton's law of gravity that worked for everything in the universe? <span style="font-family: Tahoma,Geneva,sans-serif;">4. What is the clockwork universe?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Copernicus: heliocentric view in which the Earth revolved around sun
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Galileo: supported Copernicus's theory; all bodies accelerate at same rate regardless of size or mass; came up with laws of motion
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Newton: expanded on Galileo; acceleration is caused by force, inertia is resistance to change in velocity
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Johannes Kepler: modified Copernicus by saying that planets move in ellipses rather than in circular motion around the sun; Astronomia Nova (his book) showed his observational results
 * <span style="font-family: Tahoma,Geneva,sans-serif;">he was a mathematician in 16th century that discovered mathematic equations
 * <span style="font-family: Tahoma,Geneva,sans-serif;">linked algebra and geometry on the coordinate system
 * <span style="font-family: Tahoma,Geneva,sans-serif;">mapping of geometry into algebra gave scientists new ways of tackling geometrical problems
 * <span style="font-family: Tahoma,Geneva,sans-serif;">he combined his generation laws of motions with gravity to mathematically demonstrate the elliptical orbit of planet around sun
 * <span style="font-family: Tahoma,Geneva,sans-serif;">his physics were able to predict that gravitation attractions between planets would cause the bodies to somewhat go off track of their elliptical motion around sun
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Pierre Simon Laplace branched off his discovery with study of mechanics - discovered through determinism that certain things were bound to happen
 * <span style="font-family: Tahoma,Geneva,sans-serif;">nature is only this lifeless matter in motion; life is an phenomenon of this matter in motion and is not essential to nature
 * <span style="font-family: Tahoma,Geneva,sans-serif;">we can call things living but we really mean that their parts are so disposed as to behave automatically in accord to physical laws of necessity
 * <span style="font-family: Tahoma,Geneva,sans-serif;">**total momentum of universe is conversed, interactions redistribute the momentum, but the total never changes**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">**God only starts the clock, then it runs by itself for the rest of time**

=<span style="font-family: Tahoma,Geneva,sans-serif;">Lesson 4 Summary = <span style="font-family: Tahoma,Geneva,sans-serif;">**//Planetary and Satellite Motion (a-c)//**

<span style="font-family: Tahoma,Geneva,sans-serif;">1. What are Kepler's Three Laws? <span style="font-family: Tahoma,Geneva,sans-serif;">2. What are circular motion principles for satellites? <span style="font-family: Tahoma,Geneva,sans-serif;">3. What are the mathematics of satellite motion?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">//Law of Ellipses//: path of planets about sun is elliptical in shape, with center of sun being located at one focus
 * <span style="font-family: Tahoma,Geneva,sans-serif;">//Law of Equal Areas//: even though planets move fastest when closest to the sun and their speeds are constantly changing, if an imaginary line is drawn from center of sun to center of planet will sweep out equal areas in equal intervals of time
 * <span style="font-family: Tahoma,Geneva,sans-serif;">//Law of Harmonies//: ratio of squares of periods of any two planets is equal to ratio of cubes of their average distances from sun
 * <span style="font-family: Tahoma,Geneva,sans-serif;">satellites: any objects that are orbiting the Earth, sun, or other massive body and can be natural or man made; move in an orbit about object (ex: moon)
 * <span style="font-family: Tahoma,Geneva,sans-serif;">satellites act in similar motion to projectiles because gravity is the only force acting on it
 * <span style="font-family: Tahoma,Geneva,sans-serif;">motion of satellites can be described by acceleration and velocity
 * <span style="font-family: Tahoma,Geneva,sans-serif;">velocity: directed tangent to circular at every point
 * <span style="font-family: Tahoma,Geneva,sans-serif;">acceleration: directed towards center of circle
 * <span style="font-family: Tahoma,Geneva,sans-serif;">satellites moves in elliptical motion with central body being at one focus
 * <span style="font-family: Tahoma,Geneva,sans-serif;">G: 6.673 X 10^-11
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Mcentral: mass of central body about which satellite orbits
 * <span style="font-family: Tahoma,Geneva,sans-serif;">R: radius of orbit for satellite
 * <span style="font-family: Tahoma,Geneva,sans-serif;">the force of gravity = (G*m1*m2)/d 2
 * <span style="font-family: Tahoma,Geneva,sans-serif;">velocity = sqrt((G*Mcentral)/R)
 * <span style="font-family: Tahoma,Geneva,sans-serif;">acceleration= (G*Mcentral)/R 2
 * <span style="font-family: Tahoma,Geneva,sans-serif; vertical-align: super;">the period, speed, and acceleration of a satellite are only dependent upon radius of orbit and mass of central body that satellite is orbiting

<span style="font-family: Tahoma,Geneva,sans-serif;">**//Planetary and Satellite Motion (d-e)//**

<span style="font-family: Tahoma,Geneva,sans-serif;">1. What does weightlessness in orbit mean? <span style="font-family: Tahoma,Geneva,sans-serif;">2. What are the energy relationships for satellites?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">weightlessness is a sensation experience by a person when there are no external objects touching one's body or exerting a push on it; exist when all contact forces are removed
 * <span style="font-family: Tahoma,Geneva,sans-serif;">momentarily in free fall, where gravity is the only force
 * <span style="font-family: Tahoma,Geneva,sans-serif;">force of gravity supplies centripetal force to allow the inward acceleration of circular motion (orbit)
 * <span style="font-family: Tahoma,Geneva,sans-serif;">earth orbiting astronauts are weightless in orbit
 * <span style="font-family: Tahoma,Geneva,sans-serif;">motion of satellites is circular or elliptical and they move at constant speed and remain at same height
 * <span style="font-family: Tahoma,Geneva,sans-serif;">throughout trajectory, the force of gravity acts in a direction perpendicular to direction that satellite is moving
 * <span style="font-family: Tahoma,Geneva,sans-serif;">there is no acceleration in tangential direction so the satellite remains in circular motion at constant speed
 * <span style="font-family: Tahoma,Geneva,sans-serif;">work energy theorem: initial amount of total mechanical energy of a system + the work done by external forces on a system = to final amount of total mechanical energy on the system