Ch5_MalleyJ

Ch5_MalleyJ toc

Lesson 1 Notes: Motion Characteristics for Circular Motion
Method 5: Headline Technique

After reading each passage, imagine that you are a journalist. Newspaper headlines have to grab the reader’s attention, and they must capture the essence of the story in one line. In addition, the first paragraph (usually only 2 – 4 sentences) includes all of the major points, with the rest of the article fleshing out those points fully. Your job is to generate the headline and first paragraph only. Do this for each concept presented in the passages that you are assigned to read (generally, each webpage from TPC).

a.) Speed and Velocity

 * **Headline**: Hey, Watch Your Velocity, Even If You're At Constant Speed!
 * **Article**: Uniform circular motion, the motion of an object in a circle with a constant or uniform speed, is one of many forms of circular motion. With a uniform speed and circumference, you are able to calculate the average speed of object by doing circumference/time (circumference being 2πr). Additionally, the direction of the vector is very important, and the best word to describe this is tangential, because the direction of the velocity vector at any instant is in the direction of a tangent line drawn to the circle at the object's location.

b.) Acceleration

 * **Heading**: Acceleration Has Vectors Too
 * **Article**: Object moving in circles at a constant speed accelerate towards the center of the circle, and the device used to measure this is usually called an accelerometer.

c.) The Centripetal Force Requirement

 * **Heading**: Work is Force Times Distance Times Cosine of Theta, so Homework's Not Really Work!
 * **Article**: An object in uniform circular motion experiences an inward net force. This inward force is sometimes called the centripetal force, where this big c-word describes its direction. Without this centripetal force, it would be impossible for an object to alter its direction. The idea that the centripetal force is directed perpendicular to the tangential velocity means that the force has the ability to alter the direction of the object's velocity vector without altering its magnitude.

d.) The Forbidden F-Word

 * **Heading**: Centrifugal Doesn't Exist To Us
 * **Article**: An object moving in circular motion is at all times moving tangent to the circle, so the velocity vector for the object is directed tangentially. To make circular motion, there must be a net or unbalanced force directed towards the center of the circle in order to deviate the object from its otherwise tangential path, which is inward - a centripetal force WITH A P, NOT AN F. This F-word means //away// from the circle, which isn't what we want to deal with.

e.) Mathematics of Circular Motion

 * **Heading**: So Many Equations, So We're Here to Help!
 * **Article**: The equation for average speed is known (average speed = 2πr/t), as is the equation for acceleration (acceleration = 4π 2 r/t 2 ). However, now expanding upon the net force equation, we know that F net = m*(4π 2 r/t 2 ) which is the same for our purposes as F net m*v 2, assuming there's a constant mass and radius.

a.) Newton's Second Law - Revisited

 * Circular motion can be used for many different purposes to analyze different situations
 * Using the equations from Newton's second law, you can find all sorts of variables that you can't get from the givens alone
 * Friction and acceleration problems also come back to make circular motion problems complete
 * There's no set formula for solving these things - just do what you know and eventually it'll work out

b.) Roller Coasters and Amusement Park Physics

 * There's all kinds of circular motion in amusement parks - sharp turns and small dips and hills can be found in nearly every track
 * The thrill of these isn't necessarily the speed - it's the weightlessness - so you need to use physics to figure out how to achieve this
 * __clothoid loops__: where centripetal acceleration occurs inside
 * [[image:u6l2b2.gif]]
 * there's a change in speed in this loops because it's two circles - the FBDs change too!!
 * in a sense, the forces are in a sort of tug-of-war
 * Weightlessness does not mean that there is no weight force!!

c.) Athletics

 * Circular motion can be witnessed at a variety of sporting events
 * __contact force__: supplies two roles - balances the downward force of gravity and meets the centripetal force requirement for an object in uniform circular motion
 * The same basic problem solving approach can be applied again here
 * Even the discuss and throwing events can be explained using this type of physics to describe the speed-radius-acceleration relationship

a.) Gravity is more than a Name

 * Gravity is associated with nearly everything that moves or falls downwards
 * The acceleration and force of gravity are different, but you should be accustomed to using both by now
 * Gravity itself is not affected by mass

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

 * Kepler's Three Laws of Planetary Motion
 * The Law of Ellipses: 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 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.
 * 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.
 * Circular motion requires a centripetal force and is not linear
 * 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
 * Altering the separation distance results in an alteration in the force of gravity acting between the objects (the two quantities are inversely proportional, so an increase in one will cause a decrease in the other)

c.) Newton's Law of Universal Gravitation

 * Universality - the concept that that all objects attract each other with a force of gravitational attraction - gravity is universal
 * Concluded through this: [[image:u6l3c1.gif width="302" height="149"]]
 * 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
 * Since gravitational force is inversely proportional to the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces
 * Universal Gravitation Constant
 * [[image:u6l3c3.gif]]
 * Perturbation - tendency to deviate from its otherwise smooth path

d.) Cavendish and the Value of G

 * G is a very small value (given above)
 * Cavendish's Torsion Balance explains the forces between two objects that makes them rotate

e.) The Value of g

 * g is referred to as the acceleration of gravity (9.8 m/s/s)
 * at twice the distance from the center of the earth, the value of g = 2.45 m/s/s
 * the acceleration of gravity of an object is a measurable quantity
 * the value of g is independent of the mass of the object and only dependent upon location - the planet the object is on and the distance from the center of that planet

a.) Kepler's Three Laws

 * Kepler's three laws of planetary motion are stated in a previous notes section, please refer back to it for specific details of the actual laws
 * Kepler's first law explains that planets are orbiting the sun in a path described as an ellipse
 * an ellipse is a special curve in which the sum of the distances from every point on the curve to two other points is a constant
 * the two other points are known as the foci - the closer they are, the more closely the ellipse resembles a circle
 * all planets orbit the sun in a path that resembles an ellipse, with the sun being located at one of the foci of that ellipse
 * Kepler's second law describes the speed at which any given planet will move while orbiting the sun
 * the speed is constantly changing
 * a planet moves fastest when it is closest to the sun and slowest when it's furthest
 * the law of equal areas shows the triangles that make up the points of a circle (basically)
 * an imaginary line drawn from the sun to any planet sweeps out equal areas in equal amounts of time
 * Kepler's third law compares the orbital period and the radius of orbit of a planet to those of other planets
 * makes a comparison between the motion characteristics of different planets
 * the ratio of the squares of periods to the cubes of their average distances from the sun is the same for every one of the planets

b.) Circular Motion Principles for Satellites

 * satellite - something that orbits the earth, sun, or other large massive body
 * can be either natural or man-made
 * the moon is a //natural// satellite
 * a satellite is a projectile which falls //around//the earth instead of into it
 * at every point along its trajectory, a satellite is falling toward the massive body; yet, because the massive body curves, it never reaches it
 * velocity, acceleration, and force are all made up of vectors - so they have sign and direction that changes in the trajectory
 * satellites encounter inward forces and accelerations and tangential velocities
 * even moving in elliptical motion, there's a tangential velocity and an inward acceleration and force

c.) Mathematics of Satellite Motion

 * the period, speed, and acceleration of a satellite are only dependent upon the radius of orbit and the mass of the central body that the satellite is orbiting
 * the mass of projectiles has no affect upon the acceleration towards the earth and the speed at any instant
 * when air resistance is negligible and only gravity is present, the mass of the moving object becomes a non-factor - same deal with orbiting satellites

d.) Weightlessness in Orbit

 * people feel weightless because there is no external force pushing or pulling upon their body, not because there is no weight
 * action-at-a-distance force - can't be felt and therefore would not provide any sensation
 * contact forces - actually touching whatever is being acted upon
 * inward acceleration is a characteristic of circular motion

e.) Energy Relationships for Satellites

 * orbits of satellites about a central massive body can be described as either circular or elliptical
 * 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
 * internal and external forces are different
 * work-energy bar chart represents the energy of an object by means of a vertical bar
 * the same principles of motion that apply to the objects on earth - Newton's laws and the work-energy theorem - also govern the motion of satellites in the heavens

Part One

 * __heliocentric__: having the sun as the center of the solar system
 * Copernicus first proposed this, but his ideas weren't widely spread
 * Galileo was basically forced in to his death after refusing to say that what Copernicus proposed wasn't true
 * in the Keplerian system, a planet follows an elliptical orbit, with the Sun at one focus of the ellipse
 * however, Kepler was unable to explain why this happened - and the people wanted an explanation

Part Two

 * Kepler's ideas were further supported by René Descartes
 * his ideas about graphing started the study of coordinte geometry, which gave scientists a new way of tackling geometric problems

Part Three

 * Newton has the ability and opportunity to come up with a reason why for Kepler's plan
 * Newton created laws to explain theories, ones that would later be supported by basically every experiment ever
 * concentrated on deviation from steady motion - deviation that occurs when an object goes in a different direction or changes speed
 * universal gravitation law

Part Four

 * Newton proposed only one law for gravity - as this was part of his grand vision
 * combined this law with his general laws of motion - this made it possible for him to demonstrate mathematically that a single planet would move around the Sun in an elliptical point
 * predicted that gravitational attraction between the planets would cause small departures from the purely elliptical motion that Kepler had described
 * mechanics - the study of force and motion
 * determinism - predictability
 * doctrine of free will - asserts that human beings are free to determine their own actions