Ch5_TomasofskyN


 * Chapter 5: Circular Motion **toc

=** PC: Lesson 1 Circular Motion and Satellite Motion **=
 * Motion Characteristics for Circular Motion **
 * Method 3 **

a. Speed and Velocity
 * Uniform Circular Motion Never Changes Speed But Does Change Velocity
 * Uniform Circular Motion is motion in a circle, where the radius stays constant. But speed also stays constant too. Moreover, circumference, the distance it takes to complete one whole circle, and time are all related. However, velocity does change in uniform circular motion because velocity, being a vector quantity, not only shows the magnitude but also the direction. The velocity vector is tangential to the direction of the circle.
 * [[image:Screen_shot_2011-12-13_at_3.49.40_PM.png]]
 * [[image:Screen_shot_2011-12-13_at_3.52.22_PM.png]]

b. Acceleration
 * Circular Motion can be at Constant Speed AND Accelerate
 * Circular motion has the constant speed, yet a changing velocity. It is important to remember that acceleration is a change in velocity. Therefore, uniform circular motion also has acceleration! The acceleration is directed towards the center of the circle, as can be seen when analyzing a cork accelerometer.
 * [[image:Screen_shot_2011-12-13_at_3.57.44_PM.png]]
 * There is acceleration ^^^ Velocity changes direction

c. The Centripetal Force Requirement
 * Centripetal Force Also Acts Towards the Circle
 * It has already been established that acceleration is directed towards the center of the circle. With knowledge of Newton's Second Law, when there is acceleration there is a net force. Therefore, the force that is directed towards the center in circular motion is called centripetal force. The centripetal force is unbalanced because without it, an object's inertia would make it continue to move straight. This force has the ability to alter the direction without changing its speed. Moreover, this force is perpendicular to the tangential velocity, showing once again that it can change direction without changing its magnitude.

d. The Forbidden F- Word
 * Centrifugal Should Never Be Spoken
 * Centrifugal means away from the center. There is no centrifugal force in circular motion. The feeling we get of being thrown outward from the center does not mean there is an outward force. Basically, no outward force exists. The net force must be unbalanced towards the center.

e. Mathematics of Circular Motion
 * Speed, Acceleration, and Force take the Main Stage in Circular Motion
 * Speed, acceleration, and force are the things we will be solving for in circular motion math problems. There are three equations to remember (shown below). These equations can be used to problem solve.
 * [[image:Screen_shot_2011-12-13_at_4.11.08_PM.png]] [[image:Screen_shot_2011-12-13_at_4.11.06_PM.png]]
 * [[image:Screen_shot_2011-12-13_at_4.11.29_PM.png]]

= PC: Lesson 2 -- Applications of Circular Motion = Method 3

a. Newton's Second Law -- Revisited
 * How Does Newton's Second Law apply to Uniform Circular Motion Problems?
 * Newton's 2nd Law = f(net) = M * A
 * Net force is always directed inwards towards center of the circle
 * There can be multiple f [[image:http://www.physicsclassroom.com/Class/circles/u6l2a3.gif width="181" height="153" align="right"]] orces acting on multiple axies
 * Remember there is NO vertical acceleration on Y AXIS!!!
 * The force that has acceleration (x axis) is the equal to net force acting on the object
 * In this case, friction
 * The force that has acceleration (x axis) is the equal to net force acting on the object
 * In this case, friction

b. Amusement Park Physics
 * How are amusement parks good demonstrations of physics?
 * Centripetal acceleration occurs in ** Clothoid Loops **
 * Acceleration comes from change in speed and change in direction
 * Increase in height = decrease in kinetic energy and speed
 * And Vice versa
 * Moves through with constant speed (Uniform motion) [[image:http://www.physicsclassroom.com/Class/circles/u6l2b2.gif width="246" height="208" align="right"]]
 * Multiple components of acceleration
 * Ac= Towards center; direction change
 * At = Tangent to track; speed change




 * Top of loop = Normal and gravity both point towards center (centripetal)
 * Small normal force at top
 * Attributes to weightless feeling
 * Bottom of loop = point in different directions

c. Athletics
 * How do athletics demonstrate Uniform Circular Motion?
 * Most common = involving turns
 * Does not have to make a complete circle though
 * Have both horizontal and vertical components
 * Centripetal force requirement
 * Component of force requirement
 * ** Contact Force: ** Balances downward gravity force and acts as centripetal force
 * Also demonstrates Netwton'''s Third Law!
 * For a turn to happen you NEED component of force directing towards the center
 * Can be friction or a component of a diagonal force

= PC: Lesson 3 -- Universal Gravitation = Method 3

a. Gravity is more than a name
 * What does gravity represent?
 * What goes up must come down
 * Physics explains this phenomenon in a universal matter
 * Cause, source, far-reaching implications
 * Gravity is a force and acceleration
 * Summary for the rest of the chapte ** r **

** b. ** The Apple, the Moon, and the Inverse Square Law A B C D
 * ** How can the apple and the moon be used to describe the inverse square law? **
 * Kepler's laws lay groundwork for laws about motion and paths of sun
 * Explanations for laws vary, cause was never defined
 * Newton tried to explain this (apple)
 * Orbit of the moon about the Earth
 * Explained by universal gravitation
 * Universal Gravitation
 * A= shot horizontally will fall to earth with presence of gravity
 * B= shot horizontally with greater speed, ** will travel farthe ** r and then fall to earth
 * C= shot horizontally at great speed, falls ** around ** the earth not into it (satellite, circular motion)
 * D=shot horizontally at even greater speed, begin orbiting the earth (elliptical motion)
 * Can be applied to objects in heavens
 * Affect of gravity is diluted with distance
 * Farther the distance from the center of the Earth, less gravity
 * Force of gravity between earth and object is inversely proportional to the square of the distance that separates that object from the earth's center
 * Inverse square Law
 * [[image:http://www.physicsclassroom.com/Class/circles/u6l3b5.gif width="363" height="124" align="bottom"]]
 * [[image:http://www.physicsclassroom.com/Class/circles/u6l3b5.gif width="363" height="124" align="bottom"]]

c. Cavendish and the Value of G
 * How does Candevish's value of G build upon Newton's laws of universal gravitation?
 * Newton = Gravity is directly proportional to produce of masses, inversely proportional to distance between centers


 * Candevish defined the value
 * Torsion Balance
 * ** G= 6.673 x 10 (^-11) **
 * Value of G is small numerical value
 * Force of gravitational attraction is only appreciable for objects with large mass

d. The Value of G
 * What does the value of G actually represent compared to g?
 * F = m * g vs. [[image:http://www.physicsclassroom.com/Class/circles/u6l3d1.gif width="144" height="52" align="bottom"]]
 * g = acceleration of gravity (9.8) <--- @ sea level
 * Changes with location
 * Value varies inversely with distance from center of earth


 * G= earth rial value (distance from Earth's center)
 * Changes in space

= PC: Lesson 4 -- Planetary and Satellite Motion (A-C) = Method 3

a. Kepler's Three Laws
 * What do Kepler's Three Laws indicate?
 * Law of ellipses (1st)
 * ** Ellipse ** : Special curve where sum of distanes from every point to two other points is a constant
 * Closer points are together, more circular
 * 1. Path of plants around sun is elliptical, center of sun is a focus
 * Law of Equal Areas (2nd)
 * Describes speed of any planet while orbiting sun
 * Constantly changes
 * 2. An imaginary line is drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time [[image:http://www.physicsclassroom.com/mmedia/circmot/ksla.gif width="293" height="145" align="bottom"]]
 * Law of Harmonies (3rd)
 * Orbital period and radius of orbit
 * Compares between motion characteristics
 * T squared: R cubed --> every plant has same ratio
 * 3. Ration of the square of the periods of any two planets is equal to the ratio cubes of their average distances from the sun
 * 3. Ration of the square of the periods of any two planets is equal to the ratio cubes of their average distances from the sun

b. Circular Motion Principles for Satellites c. Mathematics of Satellite Motion
 * How does circular motion apply to satellites?
 * Natural sattelites vs. man-made sattelites
 * Satellites are PROJECTILES
 * Only force is gravity
 * Launced at great speed -- falls towards earth at same rate that the earth curves
 * Allows for orbital motion
 * At every point in projectile, satellite is falling towards earth
 * But never reaches earth
 * For every 8000 m along horizion, earth surface curves downward 5 m
 * 8000 m/s is needed for orbital motion
 * More than 8000 m/s is needed for elliptical motion
 * Satellite motion characteristics = circular motion characteristics
 * Net force = directed inwards, same direction as acceleration
 * [[image:http://www.physicsclassroom.com/Class/circles/u6l4b3.gif width="187" height="236" align="middle"]]
 * Centripetal force = gravity
 * Satelites as elipses
 * Earth is a foci of ellipse
 * Velocity is tangent to the ellipse
 * Acceleration is towards focus of ellipse
 * Net force is same direction as acceleration (towards focus)
 * Component of force (can speed up or slow down)
 * Not constant speed
 * [[image:http://www.physicsclassroom.com/Class/circles/u6l4b7.gif width="343" height="221" align="bottom"]]
 * [[image:http://www.physicsclassroom.com/Class/circles/u6l4b7.gif width="343" height="221" align="bottom"]]
 * What math equations can be used to solve satellite motion equations?
 * Circular motion
 * [[image:http://www.physicsclassroom.com/Class/circles/u6l4b5.gif width="155" height="54" align="bottom"]]
 * [[image:http://www.physicsclassroom.com/Class/circles/u6l4b6.gif width="120" height="47" align="bottom"]]
 * [[image:http://www.physicsclassroom.com/Class/circles/u6l4c1.gif width="137" height="55" align="bottom"]]
 * [[image:http://www.physicsclassroom.com/Class/circles/u6l4c1.gif width="137" height="55" align="bottom"]]

= PC: Lesson 4 -- Planetary and Satellite Motion (d-e) = Method 3

d. Weightlessness in Orbit


 * Why do astronauts experience weightlessness?
 * Force of gravity is action-at-a-distance force
 * Does not require interacting objects
 * Weightlessness
 * No contact forces
 * ex: free fall
 * Only a sensation
 * Elevator Example
 * Normal force is greater with upward acceleration
 * Normal force is less with downward acceleration
 * A=Normal Weight
 * B= More than Normal Weight
 * C= Less tha normal weight
 * D= Weightless(no external contact)
 * Would actually weigh the same amount
 * Only ** sensation ** of flunctuating weight
 * [[image:http://www.physicsclassroom.com/Class/circles/u6l4d4.gif width="432" height="156" align="bottom"]]
 * Astronauts
 * No external contact
 * Gravity is still acting upon their body
 * Centripetal force requirement
 * Allows for inward acceleration
 * Falling towards the Earth, not colliding with it
 * Tangential velocity allows for them to remain in orbital motion
 * In a state of free fall

e. Energy Relationship for Satellites >>>> >>>>
 * What is the energy relationship in a satellite that is moving in an elliptical or ciruclar orbit?
 * Circular motion = constant speed, constant height
 * Tangential velocity (falls at same rate)
 * Gravity = perpendicular
 * Independent and singular
 * No acceleration
 * Constant radius
 * Kinetic energy is constant (depends on speed)
 * Potential energy is constant (depends on height)
 * TME remains constant
 * Elliptical motion =
 * Not perpendicular forces
 * Therefore can accelerate
 * ** Negative work slows down **
 * ** Positive work speeds up **
 * All mechanical energy is conserved
 * Force doing work is internal (is then zero)
 * Kinetic and potential energy changes though
 * Since the speed changes
 * Looses kinetic and gains potential and vice versa
 * TME still remains constant though
 * Work-energy theorem
 * Initial amount of total (TME i) of a system + work done bye external = total mechanical energy (TME f)
 * ** KE i + PE i + W ext = KE f + PE f **

= The Clockwork Universe Reading = Part 1-4 Method 1

__ Part 1: __

The main reason for Newton's prominence was his own intrinsic genius, he was 'in the prime of my age for invention'. In 1543, 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 c ** onfrontations between the Catholic church **. ** Galileo **, was also summoned for supporting Copernicus' ideas.


 * (Earth Centered) & (Sun Centered) & (Elliptical Shape) **

In the Protestant countries of Northern Europe, the German-born astronomer ** Johannes Kepler ** (1571-1630) devised a modified form of Copernicanism. According to Kepler, their orbital paths were ** ellipses rather than collections of circles **. Kepler speculated that they might be impelled by some kind of magnetic influence emanating from the Sun.

__ Part 2: __

René Descartes, that problems in geometry can be recast as problems in algebra. The grid is calibrated (in centimetres) so the position of any point can be specified by giving its ** x- and y- coordinates on the gri ** d. Thus, the x- and y- coordinates of each point on the line obey the equation y = 0.5x, and this is said to be the equation of the line. This is 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 **. So this 'mapping' of geometry into algebra gave scientists new ways of tackling geometrical problems.

__ Part 3 __ Newton's 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. ** For years before Newton, Bits of knowledge were assembled, but there was ** no clear idea how these bits related to one another ** ; He did not claim to have all the answers, but he discovered a convincing ** quantitative framework that seemed to underlie everything else **. For the first time, scientists could fill in the details. At the ** core ** of Newton's world-view is the belief that ** all the motion ** we see around us can be explained in terms of a single set of laws.


 * 1. ** Newton concentrated o ** n deviation from steady motion ** when an object speeds up, or slows down, or veers off in a new direction.


 * 2. ** Wherever deviation from steady motion occurred, Newton looked for a cause. He described such a ** cause as a force **.


 * 3. ** Finally Newton produced a ** quantitative link between force and deviation from steady motion ** and, at least in the case of gravity, quantified the force by proposing his famous ** law of universal gravitation. **

__ Part 4 __

Newton proposed just **one law for gravity** - a law that worked for every scrap of matter in the Universe. 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 orbi**t. Moreover, 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. Newtonís discoveries became the basis for a detailed and comprehensive study of **mechanics** (the study of force and motion). The detailed character of the Newtonian laws was **entirely predictable.** This property called **determinism**. Given an accurate description of the character, position and velocity of every particle in the Universe at some particular moment and an understanding of the forces that operated between those particles, the subsequent development of the Universe could be predicted with as much accuracy as desired.