Ch5_VanMaldenJ

=Chapter 5- Circular Motion-= toc

Lesson 1 (A-E)-
Speed and Velocity- Speed and velocity are also relevant when learning about circular motion. The uniform circular motions are present when the object is moving at constant speed. The average speed is calculated by distance (circumference) over time. However, while the speed of the object is constant, its velocity is always changing. Because velocity is a vector, it has a constant magnitude but the direction (being tangent to the circle) is changing at every different location/point on the circle.

Average Acceleration- Average Acceleration can be calculated by using the formula change of velocity over time. Being that acceleration is dependent on change in velocity, it is pointed in the same direction as velocity changes in a circle. When an object in circular motion is being spun at a constant speed, the acceleration of the object is toward the center of the circle.

Centripetal Force Requirement- The Centripetal Force Requirement says that for an object to move in a circle, there must be an inward force acting upon it causing an inward acceleration. This means that a physical force that is pushing or pulling an object towards the center of the circle alters the direction of the object, but does not alter its speed.

Centrifugal vs. Centripetal- A centrifugal force is pushing or moving away from the center of the circle. Objects in circular motion do not experience an outward force because they must undergo an inward force for circular motion to be possible.

Lesson 2- (A-C)

 * Newton’s Second Law states that the acceleration of an object is directly proportional to the net force acting upon the object and inversely proportional to the mass of the object.


 * Net force acting upon the object is directed inwards.
 * It is the friction force that supplies the centripetal force requirement for the car to move in a horizontal circle, without it the car would turn its wheels but would not move in a circle and a circular motion. [[image:http://www.physicsclassroom.com/Class/circles/u6l2a3.gif width="181" height="153" align="right"]]


 * Centripetal acceleration occurs is within the so-called clothoid loops. The radius remain constant.
 * One would experience the greatest speeds at the bottoms of the loop and the lowest speeds at the top of the loop.
 * The acceleration can be described as being centripetal or towards the center of the circle.
 * When loop is not circular, the acceleration of the rider has two components. There is a component that is directed towards the center of the circle (ac) and attributes itself to the direction change; and there is a component that is directed tangent (at)to the track and attributes itself to the car's change in speed.
 * This tangential component is directed opposite the direction of the car's motion as its speed decreases and in the same direction as the car's motion as its speed increases.
 * Motion of a circle-
 * There would also be a centripetal force requirement for such a motion.
 * The upward component of the contact force is sufficient to balance the downward force of gravity and the horizontal component of the contact force pushes the person towards the center of the circle.

Lesson 3 (A-D)

 * Gravity is a force that exists between the Earth and the objects that are near it. As you stand upon the Earth, you experience this force.
 * The force gravity causes an acceleration of our bodies during this brief trip away from the earth's surface and back. Acceleration of gravity (g) is the acceleration experienced by an object when the only force acting upon it is the force 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.
 * Kepler's three laws, which describe the motion of planets about the sun, emerged from the analysis of data carefully collected over a span of several years by his Danish predecessor and teacher, Tycho Brahe. Kepler's three laws of planetary motion can be briefly described as follows:
 * 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)
 * Newton knew that 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. The celestial motions required a cause in the form of an unbalanced force.
 * Newton's related the cause the orbit of the moon about the earth to the falling of an apple to the Earth that led him to his notion of universal gravitation.
 * The force of gravity between the earth and any object is inversely proportional to the square of the distance that separates that object from the earth's center. The force of gravity follows an inverse square law.
 * The relationship between the force of gravity between the earth and any other object and the distance that separates their centers can be expressed by the following relationship.


 * ** ALL ** objects attract each other with a force of gravitational attraction. Gravity is universal. 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.
 * More massive objects will attract each other with a greater gravitational force.
 * As the mass of either object increases, the force of gravitational attraction between them also increases. If the mass of one of the objects is doubled, then the force of gravity between them is doubled.

Reading
>> 1. Newton concentrated not so much on motion, as on deviation from steady motion - deviation that occurs, for example, when an object speeds up, or slows down, or veers off in a new direction.
 * 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, which led to confrontations with the church.
 * The most famous of these must surely have been Galileo, who was summoned to appear before the Inquisition in 1633, on a charge of heresy, for supporting Copernicus' ideas. As a result Galileo invited to renounce his declared opinion that the Earth moves around the Sun.
 * Johannes Kepler (1571-1630) devised a modified form of Copernicanism that was in good agreement with the best observational data available at the time. According to Kepler, the planets //did// move around the Sun, but their orbital paths were ellipses rather than collections of circles. Kepler had no real reason to //expect// that the planets would move in ellipses, though he did speculate that they might be impelled by some kind of magnetic influence emanating from the Sun.
 * 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. We cannot give the details of these laws now, but it is appropriate to mention three key points:

>> 2. Wherever deviation from steady motion occurred, Newton looked for a cause. Slowing down, for example, might be caused by braking. He described such a cause as a force. We are all familiar with the idea of applying a force, whenever we use our muscles to push or pull anything.

>> 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.

Lesson 4 (A-C)
Lesson 4(A-C)

What were Kepler’s three laws?


 * The Law of Elipses- The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus.
 * 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.
 * 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.

What is a foci?


 * Two points on the ellipse whose sum of distance around ellipse is always constant.

What are circular motion principles for satellites?


 * Satellites are 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.
 * Gravity is the only force acting on it
 * Motion of satellites can be described by acceleration and velocity.
 * They move in elliptical motions with central body being at one focus

Lesson 4(D-E)
As you sit in a chair, you experience two forces - the force of the Earth's gravitational field pulling you downward toward the Earth and the force of the chair pushing you upward.
 * The chair pushing up against you is a contact force. They can 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 an action-at-a-distance force.
 * The force of gravity is the result of your center of mass and the Earth's center of mass exerting a mutual pull on each other; this force would even exist if you were not in contact with the Earth.
 * Weightlessness is 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.
 * Weightlessness is only a sensation; it is not a reality corresponding to an individual who has lost weight.
 * Weightlessness has to do with the presence or absence of contact forces.
 * The orbiting astronauts weigh something; that is, there is a force of gravity acting upon their body. Without the force of gravity, the astronauts would not be orbiting in circular motion. It is the force of gravity that supplies the centripetal force requirement to allow the inward acceleration that is characteristic of circular motion.
 * The orbits of satellites about a central massive body can be described as either circular or elliptical.
 * A satellite orbiting about the earth in circular motion is moving with a constant speed and remains at the same height above the surface of the earth.
 * It accomplishes this feat by moving with a tangential velocity that allows it to fall at the same rate at which the earth curves.
 * There is no acceleration in the tangential direction and the satellite remains in circular motion at a constant speed.
 * When the satellite moves away from the earth, there is a component of force in the opposite direction as its motion, which slows it down.
 * When the satellite moves towards the earth, there is a component of force in the same direction as its motion, which speeds it up.
 * [[image:http://hpvanmalju.wikispaces.com/site/embedthumbnail/placeholder?w=345&h=152 width="345" height="152"]]