Ch5_ChiavelliJ

=toc = = **Chapter 5 Wiki ** = = = = = = = = = = = = **Lesson 1: Notes ** = a. //**The Relationship Between Speed & Velocity As It Pertains to Circular Motion **// Uniform circular motion is the motion of an object in a circular path with a constant/uniform speed. Circumference is used to calculate the average speed of circular motion. The formula for average speed is: 

The velocity vector is tangential. At any point in time, the direction of a tangent line drawn to the circle's location is the direction of the velocity vector.

b. **//Acceleration & Circular Motion//** An object engaged in circular motion is accelerating because the direction of the velocity is dynamic. An object moving in circles at a constant speed accelerates towards the center of the circle. An accelerometer can be used to measure the acceleration of an object. This is depicted in the contraption below: c. **//The Centripetal Force Requirement//** If inward acceleration is present, so is an inward force. This is known as the centripetal force requirement. A car starting from rest causes the passenger sensation of accelerating backwards, while a car slowing to a stop would create the passenger sensation of forwards acceleration. In each scenario, the passenger leans in the opposite direction of acceleration. The jerking of the passenger is attributed to its inertia. If a car embarks on a circular orbit, the passenger will experience a sensation of outwards acceleration, when in reality only experiencing the tendency of the body to follow its path tangent to the circular orbit. Centripetal force describes the direction of the force. Work is a force acting upon an object that causes a form of displacement. Work is defined as: Work= Force*displacement*cosine(theta) Understanding that centripetal force is perpendicular to the tangential velocity of the object in a circular path, the force can affect the direction of its velocity vector without changing its magnitude.

d. **//The Big Misconception: Centrifugal//**

<span style="font-family: 'Times New Roman',Times,serif;">Centrifugal is indicative of away from the center or outward. It should not be misunderstood that centrifugal is an outwards force.

<span style="font-family: 'Times New Roman',Times,serif;">e. <span style="font-family: 'Times New Roman',Times,serif;">**//The Math Component//** <span style="font-family: 'Times New Roman',Times,serif;">The acceleration of an object moving in a circular motion can be determined by 2 equations. It can be defined as a= v<span style="font-family: 'Times New Roman',Times,serif; vertical-align: super;">2 /R OR a= 4*pi<span style="font-family: 'Times New Roman',Times,serif; vertical-align: super;">2 *R/T<span style="font-family: 'Times New Roman',Times,serif; vertical-align: super;">2 .<span style="font-family: 'Times New Roman',Times,serif;"> The following equations are relative to net force: <span style="font-family: 'Times New Roman',Times,serif;">

=**<span style="font-family: 'Times New Roman',Times,serif;">Lesson 2: Notes **=

<span style="font-family: 'Times New Roman',Times,serif;">**//Newton's Second Law- A Second Look//**

<span style="font-family: 'Times New Roman',Times,serif;">The use of free body diagrams is critical to solving circular motion problems involving circular or curved paths. Understanding the forces acting on an object is the first key step in determining the correct answer.

<span style="font-family: 'Times New Roman',Times,serif;">**//Applying Circular Motion to Roller Coasters//**

<span style="font-family: 'Times New Roman',Times,serif;">Roller coasters offer insight into the variety of circular motion. These include loops, dips and hills, as well as banked turns. A clothoid loop has a constantly changing radius. <span style="font-family: 'Times New Roman',Times,serif;">

<span style="font-family: 'Times New Roman',Times,serif;">There is a continuous change in direction and speed. For the most part, the direction of the acceleration is directed primarily towards the center of the loop and a small portion devoted the tangent of the track. <span style="font-family: 'Times New Roman',Times,serif;">The free fall and arc relationship transcends to the understanding of circular motion.

<span style="font-family: 'Times New Roman',Times,serif;">**//Let's Talk Athletics//** <span style="font-family: 'Times New Roman',Times,serif;">Any turn is considered a part of a circle. This translates to a variety of applications in terms of athletics, physics, and mathematics. <span style="font-family: 'Times New Roman',Times,serif;">

=**<span style="font-family: 'Times New Roman',Times,serif;">Lesson 3: Notes **=

<span style="font-family: 'Times New Roman',Times,serif;">Universal gravitation is responsible for the motion of the planets and moon in elliptical and circular orbits. The force of gravity between Earth and any object is inversely proportional to the square of the distance that separates the object from Earth's core center. This is known as the inverse square law. It can be expressed as: w= 1/d<span style="font-family: 'Times New Roman',Times,serif; vertical-align: super;">2.
 * <span style="font-family: 'Times New Roman',Times,serif;">//Gravity in Depth// **

<span style="font-family: 'Times New Roman',Times,serif;">**//Newton's Law of Universal Gravitation//** <span style="font-family: 'Times New Roman',Times,serif;">Gravity is universal. The F<span style="font-family: 'Times New Roman',Times,serif; vertical-align: sub;">gravity between 2 objects = m<span style="font-family: 'Times New Roman',Times,serif; vertical-align: sub;">1 *m<span style="font-family: 'Times New Roman',Times,serif; vertical-align: sub;">2 /distance separating the 2 centers. If any mass increases, so will the gravitational force. However if the distance increases, the gravitational force will decrease. The formula can also be expressed as: <span style="font-family: 'Times New Roman',Times,serif;">The result of this equation will be in Newtons of force. The earlier learned equation of F=ma can also be applied in this area of problem solving. Gravitational interactions exist between all objects with an intensity directly relative to the product of their masses.

<span style="font-family: 'Times New Roman',Times,serif;"> **//"G''//** <span style="font-family: 'Times New Roman',Times,serif;">Henry Cavendish established G as the universal gravitational constant using a torsion balance.

<span style="font-family: 'Times New Roman',Times,serif;">By measuring and calculating the necessary values, he was able to determine the value of the constant G.

<span style="font-family: 'Times New Roman',Times,serif;">
 * <span style="font-family: 'Times New Roman',Times,serif;">//A Larger Scope of Application// **

<span style="font-family: 'Times New Roman',Times,serif;">This equation can also be applied in terms of other planets: <span style="font-family: 'Times New Roman',Times,serif;">

=<span style="font-family: 'Times New Roman',Times,serif;">Physics World Lesson 2: Notes =


 * <span style="font-family: 'Times New Roman',Times,serif;">//The Evolution of Modern Scientific Theory// **


 * <span style="font-family: 'Times New Roman',Times,serif;">Heliocentric: **<span style="font-family: 'Times New Roman',Times,serif;">the accepted view that the Earth moves around the sun (Copernicus)

<span style="font-family: 'Times New Roman',Times,serif;">Johannes Kepler revised this theory to declare that the planets move in the orbital motion of an ellipse

<span style="font-family: 'Times New Roman',Times,serif;">The influence of math and science merged with the discovery of geometric and algebraic concepts

<span style="font-family: 'Times New Roman',Times,serif;">Newton was the pioneer who gained momentum and credibility in his concepts


 * <span style="font-family: 'Times New Roman',Times,serif;">Mechanics **<span style="font-family: 'Times New Roman',Times,serif;">: the study of force and motion

<span style="font-family: 'Times New Roman',Times,serif;">**Determinism**: the utilization of Newtonian mechanics to predict numerical values for the questionable components of the universe

=<span style="font-family: 'Times New Roman',Times,serif; text-align: left;">Lesson 4 (a-c): Notes =
 * <span style="font-family: 'Times New Roman',Times,serif;">//Kepler's '3' Law's// **


 * <span style="font-family: 'Times New Roman',Times,serif;">Laws of Planetary Motion: **

<span style="font-family: 'Times New Roman',Times,serif;">**1.** The orbit of the planets about the sun is an ellipse, with the sun being located at one focus (Law of Ellipses)

<span style="font-family: 'Times New Roman',Times,serif;">**2.** A hypothetical line drawn from the center of the sun to the center of a planet will cover equal areas in equal intervals of time (Law of Equal Areas)

<span style="font-family: 'Times New Roman',Times,serif;">Describes the speed of a planet in a position while orbiting the sun

<span style="font-family: 'Times New Roman',Times,serif;">A planet moves faster when nearest to the sun, and slower when farther away

<span style="font-family: 'Times New Roman',Times,serif;">**3.** The ratio of the squares of the periods of any 2 planets is equal to the ratio of the cubes of their average distances from the sun (Law of Harmonies)


 * <span style="font-family: 'Times New Roman',Times,serif;">//Satellite Motion// **

<span style="font-family: 'Times New Roman',Times,serif;">Gravity is the only force acting upon a satellite (a projectile)

<span style="font-family: 'Times New Roman',Times,serif;">In order to enter orbit, a satellite must be launched at a specific speed <span style="font-family: 'Times New Roman',Times,serif;">

<span style="font-family: 'Times New Roman',Times,serif;">The centripetal force can attributed to gravity

<span style="font-family: 'Times New Roman',Times,serif;">

<span style="font-family: 'Times New Roman',Times,serif;">Satellites orbit around a massive body, as opposed to falling into it


 * <span style="font-family: 'Times New Roman',Times,serif;">//The Math Behind Satellite Motion// **

<span style="font-family: 'Times New Roman',Times,serif;">A satellite moving in circular motion around a central body:

<span style="font-family: 'Times New Roman',Times,serif;">Net Force:

<span style="font-family: 'Times New Roman',Times,serif;">Velocity:

<span style="font-family: 'Times New Roman',Times,serif;">Acceleration:

<span style="font-family: 'Times New Roman',Times,serif;">Period:

=<span style="font-family: 'Times New Roman',Times,serif; text-align: left;">Lesson 4 (d-e): Notes = <span style="font-family: 'Times New Roman',Times,serif;">Weightlessness is a sensation experienced when all contact forces are removed
 * <span style="font-family: 'Times New Roman',Times,serif;">//The Orbital Experience and Weightlessness// **

<span style="font-family: 'Times New Roman',Times,serif;">Gravity is a force that acts between the Earth's mass and the mass of other objects that surround it

<span style="font-family: 'Times New Roman',Times,serif;">There is no external contact force pushing or pulling upon the object

<span style="font-family: 'Times New Roman',Times,serif;">The result is a state of perpetual free fall

<span style="display: block; font-family: 'Times New Roman',Times,serif; text-align: left;"> **<span style="font-family: 'Times New Roman',Times,serif;">//Describing Satellite Motion Through Energy// **

<span style="display: block; font-family: 'Times New Roman',Times,serif; text-align: left;"> **<span style="font-family: 'Times New Roman',Times,serif;">Work-Energy Theorem- **the initial amount of total mechanical energy of a system plus the work done by external forces on that system is equal to the final amount of total mechanical energy of the system

<span style="display: block; font-family: 'Times New Roman',Times,serif; text-align: left;"> Can be in potential energy or kinetic energy

<span style="display: block; font-family: 'Times New Roman',Times,serif; text-align: left;">

<span style="display: block; font-family: 'Times New Roman',Times,serif; text-align: left;"> When the external work=0

<span style="display: block; font-family: 'Times New Roman',Times,serif; text-align: left;">

<span style="display: block; font-family: 'Times New Roman',Times,serif; text-align: left;"> The total mechanical energy is conserved

<span style="display: block; font-family: 'Times New Roman',Times,serif; text-align: left;"> In circular orbits, if speed and height is constant, than potential, kinetic, and mechanical energy will be as well

<span style="display: block; font-family: 'Times New Roman',Times,serif; text-align: left;"> In elliptical orbits, speed and height changes, and therefore potential and kinetic energy changes, but total mechanical energy remains the same