Ch5_SteeleM

** toc Lesson 1: Motion Characteristics for Circular Motion **

 * a) Speed and Velocity**

__//Learn About the Speed and Velocity of Uniform Circular Motion!//__ All physics students know that v=d/t for linear motion. However, they may not be aware that this equation also works for circles. For a circle v=circumference/time //or// v=2(pi)r/T, where T = the time it takes to make one cycle around the circle. Clever physics students may be thinking right now, "if something is in //uniform// circular motion, how can its velocity be changing?" The answer is this: even though a circle's speed may be constant, the direction is always changing!


 * b) Acceleration**

__//The Truth about Acceleration//__ An object moving in a circle at constant speed is accelerating, because the direction of the velocity vector is changing. Also, objects in uniform circular motion accelerate towards the center of the circle. This is because the acceleration of an object is in the same direction as the velocity change vector (direction = center of circle).


 * c) The Centripetal Force Requirement**

__//Circles Also Abide by Newton's Laws//__ For object's moving in circular motion, there is a net force acting towards the center which causes the object to seek the center. According to Newton's law of inertia, an object in circular motion could never change it's direction without centripetal force (net force). Because centripetal force is perpendicular to the tangential velocity, centripetal force can change the direction of an object's velocity vector without changing its magnitude.


 * d) The Forbidden F-Word**

__//Don't Say the F-Word!//__ Many physics students __mistakenly__ believe that objects in circular motion are experiencing an outward force. This outward force is called centrifugal force (a.k.a the forbidden F-word). In reality, the motion of an object in a circle requires an inward net force. In reality, there must be a net (or unbalanced) force directed INWARD (towards the center of the circle) in order to deviate the object from its otherwise tangential path.


 * e) Mathematics of Circular Motion**

//__Get Smart! Learn the Mathematics of Circular Motion__// With just three equations, we can determine the speed, acceleration, and centripetal force of an object in circular motion. The speed of an object in circular motion can be determined by the equation v=2(pi)r/T, the acceleration by the equation a=v 2 /r, and the centripetal force by the equation F c =ma c (or F c =mv 2 /r). How cool!


 * r = radius, T = period

** Lesson 2: Applications of Circular Motion **

 * a) Newton's Second Law - Revisited**

S = Survey Q = Question R = Read R = Recite R = Review with mom
 * 1) How does one solve circular motion problems?
 * 2) What is an example of a real life situation which combines Newton's second law and circular motion?
 * 1) __Solving circular motion problems__: 1) Construct a FBD. 2) Identify given and unknown information. 3) If any forces are at angles, use vector principles to resolve them into horizontal and vertical components. 4) Use circular motion equations to find unknown information.
 * 2) __Real life situation__: A car moving along a curve.


 * b) Roller Coasters and Amusement Park Physics**

S = Survey Q = Question R = Read R = Recite R = Review with dog.
 * 1) What circular-shaped sections of a roller coaster track make riders experience centripetal acceleration?
 * 2) What are clothoid loops?
 * 3) The centripetal acceleration of an object moving around a clothoid loop has two components. What are the characteristics of these components?
 * 1) __Types of track__: Loops, small dips and hills, and banked turns.
 * 2) __Clothoid Loops__: These types of loops are tear-drop shaped, and therefore the radius is constantly changing. The radius at the bottom is significantly larger than the radius at the top.
 * 3) __Component Characteristics:__
 * **ac** - directed towards center of circle, causes object's change in direction.
 * **at** - directed tangent to the track, causes object's change in speed. Speed decreases --> at directed opposite object's motion. Speed increases --> at directed same way as object's motion.


 * c) Athletics**

S = Survey Q = Question R = Read R = Recite R = Review with mom
 * 1) What is contact force?
 * 2) What does contact force do?
 * 1) __Contact force__: Occurs when a surface pushes upward on an object at an angle //to the vertical//. Both a horizontal and a vertical component result from contact with the surface below.
 * 2) __Role of contact force__:
 * 1) It balances the downward force of gravity
 * 2) It meets the centripetal force requirement for an object in uniform circular motion.
 * The upward component of the contact force is sufficient to balance the downward force of gravity.
 * The horizontal component of the contact force pushes the person towards the center of the circle.

** Lesson 3: Universal Gravitation **

 * a) Gravity is More than a Name**

S = Survey Q = Question R = Read R = Recite R = Review with dad
 * 1) What is acceleration of gravity?
 * 2) What is the force of gravity?
 * 1) __Acceleration of Gravity__: The acceleration experienced by an object when gravity is the only force acting upon it. The acceleration of gravity on earth is approximately 9.8 m/s/s. It is the same value for all objects, regardless of their mass.
 * 2) __Force of Gravity__: The force that attracts a body toward the center of the earth, or toward any other physical body having mass.


 * b) The Apple, the Moon, and the Inverse Square Law**

S = Survey Q = Question R = Read R = Recite R = Review with dog
 * 1) What are Kepler's Laws
 * 2) What were the results of Newton's cannon experiment?
 * 3) What is the Inverse Square Law?
 * 1) __Kepler's Laws__:
 * 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// )
 * 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// )
 * 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// )
 * 1) __Newton's Cannon__:
 * [[image:cannon.gif]]
 * 1) __The Inverse Square Law__:
 * [[image:preportionality.gif]]


 * c) Newton's Law of Universal Gravitation**

S = Survey Q = Question R = Read R = Recite R = Review with dad
 * 1) What is Newton's Law of Universal Gravitation?
 * 2) What are the effects of mass and distance on Fg?
 * 3) What is the universal gravitation constant?
 * 1) __Newton's Law of Universal Gravitation__: **ALL**objects attract each other with a force of gravitational attraction.
 * [[image:G_proprtionaliuty.gif]]
 * 1) __Mass and distance__:
 * [[image:mass_distance.gif]]
 * 1) __Universal gravitation constant__: G = ( 6.673 x 10-11 N m2/kg2 )


 * d) Cavendish and the Value of G**

S = Survey Q = Question R = Read R = Recite R = Review with mom
 * 1) What is the value of G?
 * 2) What does G represent?
 * 1) __The value of G__: G = ( 6.673 x 10-11 N m2/kg2 )
 * 2) __The meaning of G__: G represents the constant of proportionality in Newton's Universal Law of Gravitation equation. 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.


 * e) The Value of g**

S = Survey Q = Question R = Read R = Recite R = Review with mom
 * 1) What is g?
 * 2) Does the value of g change?
 * 3) How can you calculate the value of g?
 * 1) __The meaning and value of g__: g is referred to as the acceleration of gravity. Its value is **9.8 m/s2** on Earth.
 * 2) __The value of g changes__: The value of g varies inversely with the distance from the center of the earth. The variation in g with distance follows an inverse square law - //as the distance is doubled, the value of g decreases by a factor of 4. As the distance is tripled, the value of g decreases by a factor of 9.//
 * 3) __Calculating the value of g__:
 * [[image:g.gif]]

** Lesson: The Clockwork Universe **

 * Part 1**

S = Survey Q = Question R = Read R = Recite R = Review with mom
 * 1) What were Copernicus's views?
 * 2) How did people respond to his views?
 * 3) What were Kepler's views?
 * 1) __Copernicus__: He rejected the prevailing Earth-centred view of the Universe in favor of a **heliocentric** view in which the Earth moved round the Sun.
 * 2) __Response__: Copernicus's views created conflict between the Catholic Church and Galileo (who supported Copernicus's heliocentric view).
 * 3) __Kepler's views__: He expanded on Copernicus's ideas. He postulated that the planets //did// move around the Sun, but their orbital paths were ellipses rather than collections of circles.


 * Part 2**

S = Survey Q = Question R = Read R = Recite R = Review with mom
 * 1) What did René Descartes discover?
 * 2) What was the impact of his discoveries?
 * 1) __René Descartes__: Problems in geometry can be recast as problems in algebra.
 * 2) __Impact__: His his ideas marked 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.


 * Part 3**

S = Survey Q = Question R = Read R = Recite R = Review with mom
 * 1) What did Newton believe?
 * 2) What was the impact of his discoveries?
 * 1) __Newton's beliefs__: All the motion we see around us can be explained in terms of a single set of laws. The three key points of his laws:
 * **1.** //Deviation from steady motion// - deviation occurs when an object speeds up, or slows down, or veers off in a new direction.
 * **2.** Causes of deviation from steady motion occurred - Slowing down might be caused by braking. He described such a cause as a force.
 * **3.** He produced a quantitative link between force and deviation from steady motion. He also quantified the force by proposing his famous law of universal gravitation.


 * Part 4**

S = Survey Q = Question R = Read R = Recite R = Review with mom
 * 1) What was the impact of Newton's Law of Universal Gravitation?
 * 2) Who was Pierre Simon Laplace?
 * 3) What is Newtonian mechanics?
 * 1)  __The impact of Newton's LUG__:  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 orbit, (just as Kepler claimed). He was also able to predict that gravitational attractions between the planets would cause small departures from the purely elliptical motion that Kepler had described.
 * 2) __Pierre Simon Laplace__: He used Newton's laws to develop mechanics (the study of force and motion).
 * 3) __Newtonian Mechanics__: According to Newtonian mechanics, it is possible to predict the entire future behavior of the universe. It is possible to do so if the initial positions and velocities of all the particles in it are known, and the laws describing their interactions are known.

** Lesson 4: Planetary and Satellite Motion **

 * a) Kepler's Three Laws**

S = Survey Q = Question R = Read R = Recite R = Review with mom
 * 1) What is his first law?
 * 2) What is his second law?
 * 3) What is his third law?
 * 1) __Kepler's first law (The Law of Ellipses)__: The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus.
 * [[image:ellipses.gif]]
 * 1) __Kepler's second law (The Law of Equal Areas)__: 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.
 * [[image:Equal_areas.gif width="213" height="217"]]
 * 1) __Kepler's third law (The Law of Harmonies)__: 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.
 * **(T 1 2)/(R13) = (T 2 2)/(R23)**


 * b) Circular Motion Principles for Satellites**

S = Survey Q = Question R = Read R = Recite R = Review with mom
 * 1) What is a satellite?
 * 2) How can the motion of an orbiting satellite be described?
 * 3) How can one describe the motion of a satellite moving in an elliptical path?
 * 1) __Satellites__: Any object that is orbiting the earth, sun or other massive body. Satellites can be categorized as **natural satellites** (ex: moon) or **man-made satellites** (ex: weather forecast).
 * [[image:satellite_newton_cannon.gif width="138" height="166"]]
 * 1) __Motion of an orbiting satellite__:
 * [[image:satellite_motion1.gif width="151" height="194"]][[image:satellite_motion2.gif width="292" height="160"]]
 * 1) Elliptical orbits of satellites:


 * c) Mathematics of Satellite Motion**

S = Survey Q = Question R = Read >> **Fgrav = ( G • Msat • MCentral ) / R 2 ** >> (Msat • v** 2 ** **<span style="background-color: #ffffff; color: #ff0000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: -webkit-center;">) / R = (G • Msat • MCentral ) / R2 ** >> >> R = Recite R = Review with mom
 * 1) What force acts upon a satellite moving in circular motion?
 * 2) How can you solve for the velocity of a satellite in circular motion?
 * 3) How can you solve for the acceleration of a satellite in circular motion?
 * 1) <span style="font-family: Arial,Helvetica,sans-serif;">__Satellites in circular motion__: Centripetal force acts upon a satellite moving in circular motion. The net centripetal force acting upon a satellite orbiting in circular motion is defined by the relationship **<span style="background-color: #ffffff; color: #ff0000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: -webkit-center;">Fnet = ( Msat • v2 ) / R. **
 * 2) __<span style="font-family: Arial,Helvetica,sans-serif;">Solving for velocity __:
 * <span style="background-color: #ffffff; color: #ff0000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: -webkit-center;">Fnet = ( Msat • v** 2 ** **<span style="background-color: #ffffff; color: #ff0000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: -webkit-center;">) / R **
 * 1) Solving for acceleration:
 * **<span style="background-color: #ffffff; color: #ff0000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; text-align: -webkit-center;">g = (G • Mcentral)/R2 **
 * __NOTE__: T<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">he period, speed and the acceleration of an orbiting satellite are not dependent upon the mass of the satellite.


 * d) Weightlessness in Orbit**

S = Survey Q = Question R = Read R = Recite R = Review with dad
 * 1) What are contact forces and non-contact forces?
 * 2) What is weightlessness?
 * 3) What do scales measure?
 * 4) What force makes astronauts feel like they are in free fall?
 * 1) __Contact vs non-contact forces__: Contact forces c<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">an only result from the actual touching of the two interacting objects. The force of gravity acting upon your body is not a contact force; it is often categorized as a non-contact force.
 * 2) <span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">__Weightlessness__: A sensation experienced by an individual when there are no external objects touching one's body and exerting a push or pull upon it. Weightless sensations exist when all contact forces are removed.
 * 3) __Scales__: A scales does not measure your weight.<span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;"> The scale is only measuring the external contact force that is being applied to your body.
 * 4) <span style="font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; line-height: 18px;">Outer space: <span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">The force of gravity supplies the centripetal force requirement to allow the inward acceleration that is characteristic of circular motion. The force of gravity is the only force acting upon their body. For this reason, astronauts are in free-fall.


 * e) Energy Relationships for Satellites**

S = Survey Q = Question R = Read R = Recite R = Review with dad
 * 1) How do satellites in circular motion and elliptical motion differ?
 * 2) What are defining characteristics of satellites in elliptical motion?
 * 3) What is the work-energy theorem?
 * 1) __Satellites in circular vs elliptical motion__:
 * [[image:12.gif]]
 * 1) __Characteristics of satellites in elliptical motion__: <span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">A satellite orbiting the earth in elliptical motion will experience a component of force in the same or the opposite direction as its motion. This force is capable of doing work upon the satellite. Therefore, the force is capable of slowing down and speeding up the satellite. The speed of a satellite in elliptical motion is constantly changing - increasing as it moves closer to the earth and decreasing as it moves further from the earth.
 * 2) <span style="background-color: #ffffff; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px;">__Work-energy theorem__: ** KEi + PEi + Wext = KEf + PEf **
 * <span style="background-color: #ffffff; font-family: Tahoma,Geneva,sans-serif;"> Initial amount of total mechanical energy of a system + the work done by external forces on a system = the final amount of total mechanical energy on the system.