Ch5_Ordover

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 * Lesson 1: Motion Characteristics for Circular Motion**

1A) Speed and Velocity
Circular Speed and Velocity finally uncovered! The equation for speed of objects in uniform circular motion is merely circumference over time or (2πr)/T. This is the same formula that we always use for speed but distance is changed to circumference because it is around a circle. The speed remains constant, but the velocity does not because the object is always changing direction. To find the direction, you can find the slope of the line tangent to the point where the object is.

1B) Acceleration
Circular Acceleration Myth Explained It is a common misconception that objects in circular motion do not accelerate. Since velocity is always changing, the object must be accelerating. Velocity is a vector, so you must add or subtract the velocity vectors to find the acceleration. After doing this, you will find that acceleration always points towards the center.

1C) The Centripetal Force Requirement
Centripetal Force, Inward or Outward? Since acceleration points inward, their must be a force that causes it to point inward. This is the centripetal force that pushes or pulls an object toward the center of the circle. Some people believe there is an outward acceleration, such as moving towards the side of your car when you make a turn. This is actually just due to inertia because your body will continue moving straight. This makes it seems like there is an outward acceleration, but it is actually centripetal force and it points towards the center of the circle.

1D) The Forbidden F-Word
Centrifugal Force is a Sham! Centrifugal force would be a force that points away from the center of a circle if it existed. It is the opposite of centripetal force, but it does not actually exist. It is merely a misunderstanding of inertia. People believe it exists because they sway the opposite direction when they turn their car. This is actually just inertia because people keep moving in a straight line while their car turn. This causes people to think they are moving away from the turn, but they are not. Centrifugal force is a sham and it does not exist.

1E) Mathematics of Circular Motion
Speed, Force, and Acceleration Equations Discovered! Most circular motion problems can be solved using the equations for speed, force, and acceleration. These are the equations: Speed:

Acceleration:

Force:


 * Lesson 2: Applications of Circular Motion**

2A) Newton's Second Law - Revisited
1) I understood how to draw free body diagrams well and that they showed all the forces acting on an object. In addition, I knew how to use the equations and free body diagrams to solve problems. 2) I understood everything. 3) I understood everything. 4) Everything was gone over during class.

2B) Amusement Park Physics
1) I understood the circular motion of a roller coaster at the hills and valleys. Since normal force equals weight, you feel weightless at the top of a hill because there is less normal force. In addition, you feel heavier at the bottom of a hill because normal force is greater. 2) I understood everything that was discussed in class. 3) I understood everything. 4) There was new information about clothoid loops. These are loops whose radii get smaller as you go up.

2C) Athletics
1) I understood how to use the circular motion equations and trigonometry to solve these problems. In addition, I understood that leaning on a turn gives you an inward component as well and allows you to make sharper turns. 2) I understood everything form class. 3) I understood everything. 4) I was not aware that every turn is part of a circle. Each part of a turn can be part of a different circles with different radii.


 * Lesson 3: Universal Gravitation**

3A) Gravity Is More Than A Name
1) I understood that gravity is the reason for the saying "what goes up, must come down". It is responsible for pulling everything towards the center of the Earth. In addition, acceleration due to gravity is 9.8 m/s^2 on Earth. This value is not affected by mass. 2) I understood everything from class. 3) I understood everything. 4) Everything was gone over in class.

3B) The Apple, The Moon, and The Inverse Square Law
Kepler and Newton's Great Discoveries! Kepler first came up with three laws of motion for planets. They were the Law of Ellipses, The Law of Equal Area, and the Law of Harmonies. However, they did not explain why the planets had this motion. Newton knew that some force must be causing them to do this. He eventually came up with the ideas about universal gravitation.

3C) Newton's Law of Universal Gravitation
Newton Knows All! Newton not only discovered the law of universal gravitation, but he also discovered that gravity exists between all objects, not just Earth. He knew that the force of gravitation got bigger as the mass got larger and the distance got smaller. He came up with the following equation for force of gravity.

3D) Cavendish and the value of G
Cavendish cracks the code! When Newton found the equation for law of universal gravitation, he did not know the gravitation constant. Lord Henry Cavendish found it nearly a century later. He ran an experiment using a torsion balance where he found the relationship between the angle of rotation and the torsional force. He found it to be 6.67 x 10^-11.

3E) The Value of g
Dont Mistake g and G! Gravitational acceleration is 9.8 m/s^2, but that is only on Earth at sea level. It changes depending on how far or close you are to the center of the Earth. It is also different for all different objects and depends on the mass of the object as well. Because of this, the equation for gravitational acceleration is g=Gm/d^2.


 * Lesson 4: Planetary and Satellite Motion**

4A) Kepler's Three Laws
1) I understood Kepler's three laws: The Law of Ellipses, The Law of Equal Area, and The Law of Harmonies. I understood that these laws show the motion of heavenly bodies, but they do not explain why this motion occurs. The idea of gravity was not around until Newton years later. 2) The reading helped to clarify the Law of Equal Area for me. 3) I understood everything. 4) Everything was gone over in class.

4B) Circular Motion Principle For Satellites
1) I understood that satellites are projectiles that orbit large objects. They are projectiles, so they are only affected by gravity and they are always falling. However, their velocity is sometimes great enough that they fall at the same rate that the Earth curves. This causes them to stay the same distance away from Earth without ever crashing. 2) I understood everything from class. 3) I understood everything. 4) I have no questions.

4C) Mathematics of Satellite Motion
1) I understood how to use the three equations to solve problems involving satellite motion. I also understood that none of the three equations have the m of the satellite in them because it is not dependent on mass, just like on Earth. 2) I understood everything from class. 3) I understood everything. 4) Everything was gone over in class.

4D) Weightlessness in Orbit
Quick and Easy Weight Loss SInce gravity is an action-at-a-distance force, and it is the only force that affects you in space, you feel weightless in space. Weightlessness occurs when there are no contact or normal forces acting on you. Weight is determined by the normal force pushing up on you. Therefore you weight different amounts in an elevator. This also means that you are weightless in space.

4E) Energy Relationships for Satellites
The Science of Satellites Satellites can either have a circular or an elliptical path. If they have a circular path, the speed and distance remain constant. Thus, the acceleration of a satellite in circular motion is zero. Satellites on an elliptical path can change speed, and therefore accelerate. The satellite moves faster as it moves toward the Earth and slower as it moves away from the Earth. The speed of these satellites is always changing. The energy of a satellite can be expressed by the work-energy theorem. The equation for this is:
 * KEi + PEi + Wext = KEf + PEf**

The Clockwork Universe
Part 1) The Great Debate Prior to Copernicus, people thought that the Earth was the center of the universe, and that everything orbited the Earth. Then Copernicus came around and suggested that the Earth orbited the sun in a heliocentric model. This caused a lot of controversy, especially from the Catholic Church. Later, Galileo also supported this idea. Finally, Kepler came around and theorized that the planets actually moved around the sun in an elliptical pattern and that some sort of magnetic attraction emanated from the sun.

Part 2) New Type of Math Discovered! During this time period, many advancement in math were being made. One important one was Descartes's discovery of coordinate geometry. He found that any geometry problem could be cast on a coordinate grid and turned into algebra. This helped mathematicians to make discoveries that they could never have done without this.

Part 3) Newton's Luck Newton was lucky that he was born so that he was in his prime during a time of great mathematical advancement, but Kepler's laws were still unexplained. This allowed him to create a framework for the laws of the universe. He looked not just at motion, but how it changed. Based on this, he looked for a cause of this motion. He called these causes forces, which are what we still refer to them as today. Finally, he came up with his law of universal gravitation. Through this single set of laws he laid the foundation for physics.

Part 4) One Law for All Objects Newton came up with his law of universal gravitation and said that it applied to all objects in the universe. Using this, he supported Kepler's idea and showed how all planets move in an elliptical pattern around the sun. He was able to find gravitational attraction between planets. Thus, he took Kepler's idea a step further and said that there is small deviations in the path. This law started the debate between mechanics and determinism. Mechanics was the study of force and motion and it said that the universe was governed by mathematical laws and it was predictable and precise. Determinism took this further and said that once the universe was set it had a predetermined future and could be predicted. This caused a big controversy about free will and wether god existed.