Ch5_CantorA

=toc Homework =

Circular and Satellite Motion Lesson 1 (12/13)

 * 1) Speed and Velocity: same value, way different meanings.
 * 2) Similar to the concepts used in kinematics, speed and velocity have the same scalar value but differs with magnitude (in that velocity has magnitude, speed does not). This concept can also be applied to circular motion, where for example it can be at uniform circular motion (a car going constant speed at 10mph). Average speed is calculated by distance/time ==> so technically circumference(2piR)/time, since this is a circle. Average velocity, however, must include direction, and unlike speed, is always changing. This direction is found by the tangent line to the circle, where the force is moving towards the center of the circle. Although direction is always changing, the line of direction will remain tangential to the circle.
 * 3) Acceleration: is it the same in circles as in straight lines?
 * 4) Acceleration equal to the change in velocity ( vf-vi) over the total amount of time passed. Since velocity is a vector, we are looking for the resultant. The direction of acceleration is in the direction of the resultant. If an object is moving at uniform circular motion, acceleration will be towards the center of the circle. A device that is often used to measure acceleration is called the accelerometer. It consists of an object suspended in a fluid (most likely water) and determines if the object has much inertia.
 * 5) Centipede? No, Centripetal!
 * 6) The Centripetal Force Requirement states that for an object moving in a circle, there must be an inward force acting upon it in order to cause its inward acceleration. The unbalanced force required by Newton's first law of motion (inertia) is necessary to keep an object moving in circular motion. The centripetal force of an object can alter the direction without altering speed. This is done by displacement, or the formula of work=force*displacement*cosineTheta. The centripetal force is directed perpendicular to the tangential velocity, meaning that the force can alter the direction of the object's velocity without altering speed. In conclusion, the centripetal force requirement is an inward net force, where centripetal, essentially means direction.
 * 7) What's the difference between centrifugal and centripetal?! I always get confused.
 * 8) Centrifugal, unlike centripetal, means AWAY from the center of the circle. This is a common misconception by people, as they sometimes think that a force is moving OUTWARDS from a circle. THIS IS NOT TRUE! DO NOT believe it! Always remember that CENTRIPETAL refers to the real motion of a circe, not centrifugal.
 * 9) Equations! Equations! Read all about em!
 * 10) Now that were in the circle world, the typical equations slightly differ. Average speed= 2piR/time, while acceleration= 4pi(sq)R/time, force= m/a. Essentially, the equations have the same concepts, but because we're not in a world full of radians and radii, the formulas change!

Circular and Satellite Motion Lesson 2a-c
I chose to talk about circular motion in everyday life with Jessica during school today.
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">How does Newton's Second Law pertain to circular motion?
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">When it comes to circular motion, the equations differ slightly.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">However, it is very similar to kinematics and linear motion.
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">a=m(sq)/R
 * 5) It is of the utmost importance to create FBD when solving these equations.
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">How do amusement parks use physics?
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Loops, small dips and hills, and banking. 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. The most common ride we will look at is the roller coaster.
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The clothoid loop experiences a change in direction. 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.
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,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.
 * 10) From rollercoasters, we can find minimum and maximum speeds based on the theory that humans can only withstand 4gs. So, all designers need to keep this in mind.
 * 11) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">What about athletics?
 * 12) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Circular motion is involved in so many athletic sports: ice skating,baseball, track and field.
 * 13) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Circular motion is defined by the inward acceleration and caused by an inward net force.
 * 14) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Although it does not appear to be so, you can link circular motion (somehow) to every sport.
 * 15) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">the most common circular motion is the "turn"
 * 16) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">some may only be a quarter of a turn and some may be a full turn
 * 17) Contact force has two roles:
 * 18) balancing the downward force of gravity
 * 19) meets the centripetal force requirement for uniform circular motion
 * 20) it normally has two components
 * 21) example: figure skater pushing on the ice, skier making a turn

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Circular and Satellite Motion Lesson 3 (1/3)
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">I discussed the difference of weight on different planets (because of gravity) at the dinner table with my mom.
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">How is there more to gravity?
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Gravity is a force similar to many others, however it is ALWAYS present.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">When an object is being thrown up into the air, gravity acts as a force to slow it down, causing it decrease acceleration and ultimately its speed. However when an object is in free fall, gravity acts as an accelerating force, increasing speed (9.8 m/s/s) and acceleration along the fall.
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Who is Kepler and what are his three laws of planetary motion? How did Newton come into play?
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Johannes Kepler was a German mathematician and an astronomer. His teacher Tycho Brahe helped him gather information about planetary motion around the sun.
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">he couldn't really determine why there was this attraction, but he knew it existed.
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;"> Law of Ellipses
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,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.
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Law of Equal areas
 * 10) <span style="font-family: 'Trebuchet MS',Helvetica,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
 * 11) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Law of Harmonies
 * 12) <span style="font-family: 'Trebuchet MS',Helvetica,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.
 * 13) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Newton discovered the notion of UNIVERSAL GRAVITATION. This relates the cause for heavenly motion to the cause of earthly motion. He found the link by the INVERSE SQUARE LAW.
 * 14) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">the inverse square law states that relationship between the force of gravity between the earth and any other object and the distance that seperates the two centers can be described as: Fg ~ 1/d<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; vertical-align: super;">2.
 * 15) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">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.
 * 16) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">What are Newton's Laws of Universal Gravitation?
 * 17) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Fg ~ m1*m2/d<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; vertical-align: super;">2
 * 18) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">m1= mass of object 1; m2= mass of object 2; d= distance between the two centers
 * 19) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">as the mass of either object increases, the force of gravitational attraction between them also increasesG can also be used in this equation as a constant in the numerator. G= 6.67 * 10 -11 nm 2 /kg 2
 * 20) if the mass of one of the objects is doubled, then the force of gravity between them is doubled
 * 21) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">How does the value of G come into play?
 * 22) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The value of G is 6.67 * 10 -11 nm 2 /kg 2
 * 23) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">For our sake, Fg~ G*m1*m2/d 2
 * 24) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Lord Henry Cavendish discovered the value of G by using a torsion balance, which experimentally determined the relationship between angle of rotation and torsional force.
 * 25) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">the force of g is such a small number when in relation to small masses. However, if the mass is large, the attraction will be greater.
 * 26) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">What is the value of g?
 * 27) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">g= G*M earth /d 2
 * 28) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">g= 2.45 m/s 2
 * 29) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">this same equation used to find the value of g on earth can be applied to other planets with the following subsituted information:
 * 30) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">g= G* M<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; vertical-align: sub;">planet /R<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; vertical-align: sub;">planet <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; vertical-align: super;">2

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The Clockwork Universe 1-4 (1/5)
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">I spoke with Erica, an AP physics student, about the clockwork universe and how it works.
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Who were the "fathers" of discovering the Universe
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Nicolaus Copernicus
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">heliocentric view in which the Earth revolved around the sun
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Galileo supported him although he was denounced
 * 5) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Johannes Kepler
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">modified Copernicus' model
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">said that the planets moved in ellipses, rather than a circular motion around the sun
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Astronomia Nova (New Astronomy) was his book that showed his observational results
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Was mathematics involved?
 * 10) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Yes, Renes Descartes, a very important mathematician of the time (16th century) discovered mathematical equations.
 * 11) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">these equations linked algebra and geometry on the coordinate system
 * 12) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">How did Isaac Newton expand upon these ideas and how did he apply them to physics?
 * 13) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Newton, with his knowledge of physics, was able to connect mathematics along with astronomy, at the right place and at the right time.
 * 14) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Newton had three key points
 * 15) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">deviation from steady motion
 * 16) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">when an object speeds up, slows down, or veers off from direction
 * 17) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">looked for a cause
 * 18) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">for example, slowing down may be caused by braking
 * 19) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">law of universal gravitation
 * 20) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">no matter what two objects it is, every object follows the same pattern
 * 21) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">What was Newton's ultimate law for gravity that still use today?
 * 22) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Newton combined his generation laws of motion with gravity to mathematically demonstrate the elliptical orbit of a planet around the sun.
 * 23) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Additionally, his physics were able to predict that gravitation attractions between heavenly bodies would cause the bodies to somewhat go off track of their elliptical motion around the sun.
 * 24) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Pierre Simon Laplace branched off of his discovery with the study of mechanics. He discovered through determinism that certain things were bound to happen.

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Circular and Satellite Motion Lesson 4 a-c (1/6)
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">I made flash cards to remember these equations.
 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">What are Kepler's Three Laws?
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The Law of Ellipses
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">the path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Law of Equal Areas
 * 5) 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
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Law of Harmonies
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,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
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">What are circular motion principles for satellites?
 * 9) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">a satellite is any object that is orbiting the earth, sun or other massive body and it can be natural or man made. They move in an orbit around
 * 10) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">satellites act in a similar motion to projectiles, as gravity is the only force affecting it
 * 11) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">the motion of satellites can be described by acceleration and velocity
 * 12) these are constantly changing
 * 13) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">however, satellites too move in an elliptical motion, with the central body being at one focus
 * 14) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">How does mathematics factor into gravitational pull?
 * 15) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">We start with this equation Fg= (G*m1*m2)/d 2
 * 16) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Velocity= sqrt((G*mcentral)/R)
 * 17) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Acceleration= (G*Mcentral)/R 2
 * 18) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">T 2 /R 3 = 4π 2 /G*Mcentral

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Circular and Satellite Motion Lesson 4d-e (1/9)

 * 1) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">How does weightlessness have to do with orbit?
 * 2) <span style="font-family: 'Trebuchet MS',Helvetica,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. These "sensations" exist when all contact forces are removed.
 * 3) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Technically, you are momentarily in free fall, where the only force is gravity.
 * 4) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The force of gravity supplies the centripetal force to allow the inward acceleration of circular motion (orbit)
 * 5) What is the relationship between energy in satellites?
 * 6) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">The motion of satellites can be either circular or elliptical. They move at constant speed and remain at the same height.
 * 7) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">Throughout the trajectory, the force of gravity acts in a direction perpendicular to the direction that the satellite is moving, ALWAYS.
 * 8) <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif;">there is no acceleration in the tangential direction, so the satellite remains in circular motion at a constant speed
 * 9) The work-energy theorem states that initial amount of total mechanical energy of a system plus the work done by external forces on a system is equal to the final amount of total mechanical energy on the system.