Ch5_ChungA

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__**Lesson 1**__

 * a) Speed and Velocity**

Headline: An object moving in circular motion has constant speed but an ever changing velocity!

Paragraph: It turns out that the longer the radius of something in circular motion, the faster it goes. This follows the equation of (2pir)/T. Interestingly, if you double the radius you will also double the speed of the object. It also turns out that the velocity of something moving in circular motion is always changing. This is because at any instantaneous point in time, the direction of the radius will be different. It is essentially tangential to the circular motion of the object.


 * b) Acceleration**

Headline: An object moving in circular motion IS accelerating!

Paragraph: An object moving in circular motion is accelerating. At first, this seems a bit odd because we just defined such an object to have no change in velocity. But is there really no change in velocity? The direction of the velocity vector is always changing and thus the object is accelerating. And if we graph the resultant of two velocities we will see that a circular moving object accelerates towards the center of the circle. Several real world applications prove this to be true and we can measure this through the use of an accelerometer. You can actually make a homemade accelerometer to discuss the concepts just mentioned.


 * c) The Centripetal Force Requirement**

Headline: For objects moving in circular motion, there is a net force (centripetal) acting towards the center which causes it to seek the center!

Paragraph: Any object moving in a circle experiences some sort of force that either pushes or pulls it to the center of the circle. This is called the centripetal force. It is important to note that centripetal force is nothing new... it just simply means that something must be causing an object to move in a circular motion. Interestingly, the work done by an object moving in uniform circular motion is zero degrees. Without centripetal force, an object cannot alter its direction. And because centripetal force is perpendicular to tangential velocity, force can change velocity without changing magnitude.


 * d) The Forbidden F-Word**

Headline: Centrifugal is not Centripetal!!!

Paragraph: Centrifugal forces are not centripetal forces. This is almost always a problem with Physics students because they believe that, when moving in a circle, they are being pushed outwards. Thus it makes sense to them that an outward force must be acting on an object rather than an inward force. This simply is not true. The reason that people feel like they are being pushed outwards from, say, a car is because of Newton's First Law which states that an object in motion tends to stay in motion. The body wants to continue straight, however the car prevents the body from doing so. As such, you actually move inwards. Centripetal force here is at work, not centrifugal.


 * e) The Mathematics of Circular Motion**

Headline: Three Mathematical Properties Help Us With Circular Motion!!!

Paragraph: We will use speed, acceleration, and force to help us analyze the motion of objects moving in circles. The following are the three equations that we will use. Average speed = 2pir/t. Acceleration = (4 x pi^2 x r) / t^2. Fnet = mass x acceleration (the acceleration is the equation in the previous sentence). We can use these equations to help us think about the effects of centripetal force. For instance, through the equations we know that doubling the net force will effectively double the acceleration. We can also use the equations to help us mathematically solve various problems that we may be given.

__**Lesson 2**__

 * What is the relationship between Newton's Second Law and Circular Motion**

Newton's 2nd Law fits in perfectly with circular motion. When you set up an equation, the acceleration for centripetal force going towards the center of a circle would be v^2 / r. Thus, you get an equation that is defined as Centripetal Force = mass times the velocity squared over the radius. When in a circle, the force going towards the middle of the circle would be the frictional force.


 * How do amusement parks fit in with the theme of physics?**

Amusement parks are actually all physics! Roller coaster designers must use physics in order to create safe, yet super exciting rides. For instance, at the top of a loop they have to have the roller coaster attain a minimum speed in order to not fall back down. This is physics. Also, using physics, roller coaster designers can make a person either feel weightless or super weight-y. They do this by manipulating the apparent weight... aka the Normal Force.


 * How is Circular Motion used in athletics?**

Circular motion is mostly used in events that have circles. For instance, a speed skater exemplifies the perfect circular physics question. This is because he is experiencing friction moving towards the center of a circle. Another great example would be a Nascar driver. The ramps in Nascar are designed so that they are banked. This allows for cars to have additional force moving towards the center of the circle, which makes the event much safer for all drivers involved. One thing is certain... sports is almost entirely physics.

__**Lesson 3**__
Headline Method:

Gravity isn't just a name. It isn't simply something causes things to fall. Instead, it has many causes and effects that affect nearly everything in the physical universe. We sometimes deal with Fgrav, the force of gravity and g, the acceleration due to gravity. These two things are very different but work hand in hand.
 * The Name and Force of Gravity**

Johannes Kepler was a very smart and clever man. Using data he obtained from his previous employer, Kepler devised three laws that dictate planetary motion. This took him many years but the effects of his work are too many to count. The first law is the Law of Ellipses, which states that the paths of the planets are elliptical in shape. The next law is the Law of Equal Areas, which states that an imagery line drawn from the center of the Sun to the center of another planet will sweep out equal areas in equal intervals of time. The final law is the Law of Harmonies, which states that the ratio of the squares of the periods of two planets is equal to the ratio of the cubes of their distances from the Sun.
 * Three Laws Dictate Planetary Motion**

Newton was a very smart man who discovered that all objects exert a gravitational force on each other. This is important to note because an apple has the same gravitational force on a planet as the planet has on the apple. This is not an intuitive concept but it is correct none the less. The force of gravity between two objects would be the Universal Gravitational Constant multiplied by the mass of one object and the mass of another divided by their distance (center to center) squared.
 * Gravitation and its Impact on Us**

The value of the gravitational constant was experimentally determined by Lord Henry Cavendish. He essentially discovered the constant using a very neat laboratory experiment involving a torsion balance. He discovered the value of the gravitational constant to be 6.67 x 10^-11.
 * G - Dictates Everything**

The value of g, the acceleration due to gravity, can be determined through analysis of the force of gravity equation. By extrapolating on the equation, we get an expression for the acceleration due to gravity which equals the universal gravitational constant multiplied by the mass of the orbited object divided by the distance squared. It is important to remember here that the distance from the Earth includes the radius of the Earth!
 * g - What is the value of g?**

**Lesson 2 - The Clockwork Universe**
Method 1:

The old fashioned view of the world was that everything revolved around the sun. Copernicus rejected this theory in favor of a heliocentric one, which stated that the earth moved around the sun in a circle. Galileo sided with this theory as well. Unfortunately, the Catholic Church refused to believe this and sentenced Galileo to torture.

In Northern Europe, a scientist known as Kepler postulated that the Earth didn't revolve around the Sun in circles, but rather in ellipses. He came up with this theory by simply observing the stars.

Kepler's ideas started to make sense. This is because people realized that it fit into the ideas of geometry that Rene Descartes postulated. By graphing geometric shapes, one could use algebra to determine motion. Using this, scientists learned how to determine the shapes of circles and lines. This resulted in a branch of geometry known as coordinate geometry.

Newton was in the right place at the right time. He was able to come up with a set of laws that he stated dictated the universe. He believed that deviation occurs in motion when things speed up or slow down. He also believed that when this happened, one must look for a cause. Newton finally proposed the law of universal gravitation by quantifying the force of gravity.

Using his law for gravity, Newton was able to determine that the Earth and other planets did indeed ellipse certain objects like the sun. He also determined that sometimes objects deviated from Keplerian motion. Pierre Laplace build off of Newton's work to revolutionize the science of mechanics.

**1/16/11 - Lesson 4**

 * a-c:**

Method 1:

Kepler devised three laws of planetary motion
 * Law of Ellipses - paths of planets around the sun are elliptical
 * Law of Equal Areas - a line drawn from the center of a planet to the center of the sun will draw out equal areas
 * 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^2/r^3) ratio of every planet is the SAME!!!

A satellite is defined as anything orbiting a massive body. There are several types: man made and natural.

The only thing acting on a satellite is essentially gravity. Thus, we can think of it as a projectile. For instance, if something were shot at the top of Newton's Mountain with enough speed, it could essentially orbit the Earth because the force of gravity would push it inwards and it would orbit at the same rate the Earth curves.

A projectile needs to be launched at 8000 m/s in order to orbit the Earth.

There are several things to remember about the velocity, acceleration, and force vectors of a satellite.
 * Velocity is directed tangential to a circle
 * Acceleration points inward towards the center of a circle (caused by a net force in the same direction as the center)


 * d-e: Headline Method**

A decent amount of people, given the chance, would not pass up the opportunity to lose some extra weight. Unfortunately, this article is not for those people. If you do, however, want to feel what it's like to be super lightweight and weightless, you've come to the right place. It turns out that you can actually become weightless while in orbit. This is essentially the same feeling you get when you are rounding the top of a roller coaster at a high velocity. The feeling of weightlessness is not caused because you lost weight. It is simply a sensation that you feel. Now, when you are in orbit, the weightlessness you feel is a result of the force of gravity which provides centripetal acceleration. Luckily, you will never hit the Earth when this happens!
 * Lose Some Extra Pounds... with Physics!**

So how do you get the game on your TV? With Satellites of course! Satellites make use of very advanced physics. A satellite that orbits the earth moves at a constant speed and at a constant distance from the center of the Earth. This happens because the rate at which it "falls" is the same rate that the Earth curves. When you deal with satellites in elliptical motion, the closer the satellite is to the Earth the faster it moves. The opposite is also true... the further a satellite is from the Earth the slower it will go.
 * Your Dish Network uses Physics!!!**