Ch5_GreensteinJ

toc = = = = = = = = =Notes 12/13= >
 * Centripetal Force
 * F c
 * "center seeking"
 * Can be N, T, f and/or w
 * Affected by mass, radius & speed
 * More mass = more force
 * Bigger radius = more force
 * More speed = more force
 * Centripetal Acceleration
 * a c
 * Radial Axis
 * Points to the center
 * Tangential axis
 * Perpendicular to radial axis
 * Tangential speed
 * V t

=Notes 12/16=


 * Frequency
 * How many cycles per second
 * f
 * Cycles/second = Hertz (Hz)
 * Period
 * How many seconds per cycle
 * T
 * T = 1/f
 * a c = v 2 /R
 * v = speed
 * R = radius

=Physics Classroom Lesson 1a-e=

At constant speed, maintaining a constant radius from the center of a circle, you reach a condition of uniform circular motion. The circumference is one cycle around the perimeter, also called a period.
 * Speed and Velocity of Circular Motion**

Velocity during circular motion is tangential. 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.
 * Which way is velocity?**

**How do objects accelerate in a circle?**They accelerate towards the center when moving at constant speed. The magnitude is calculated through: **What do you need for centripetal force?** There must be an inward force acting upon it in order to cause its inward acceleration. The word //centripetal // means center seeking **Work = Force * displacement * cosine (Theta) **

**Don't Use the F-Word!**Centrifugal means outward, or away from center. It is the OPPOSITE of centripetal. However, it does not exist. It is really the centripetal force moving towards the circle that may make something appear to move away.

**Mucho Math!**

=Physics Classroom Lesson 2 a-c=

Circular motion pays tribute to Newton's 2nd law. Once again, in order to solve circular motion problems, Newton's equation of F=ma will be necessary. By drawing a free-body diagram of the situation, an x and y axis must be established. Once they have been identified, writing F=ma with applicable forces will allow you to solve.
 * Here's Newton's 2nd Law Again!**



Roller coaster keep customers happy through their rapid ability to change direction of acceleration, and simulate an experience of weightlessness or weightiness. Clothoid loops have a constantly changing acceleration, as well as radius.
 * Who doesn't love a roller coaster?**



Almost all sports involve circular motion. An object moving with an inward acceleration must have a centripetal force. Forces resulting from being in contact with a surface are called contact forces.
 * NASCAR anyone?**

=Physics Classroom Lesson 3 a-e=

Gravity, or the force of gravity, is the force that we observe which interacts between the Earth and nearby objects. It is often known by its acceleration of 9.8 m/s/s, however gravity is much more complex than being simply a number.
 * What is gravity?**

An explanation of gravity is derived from Kepler's 3 laws of planetary motion: By accepting the above concepts, there must be a missing force which causes all this, hence, universal gravitation.
 * Kepler's word is law**
 * 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)

Kepler's law of //universal// gravitation means that all object in the universe are connected through a gravitational force. In order to solve for the force between any two object, we use a modified version of Newton's F=ma equation.
 * Gravity across the Universe**

Nearly 50 years passed after Kepler found the law of universal gravitation before the value of G was found. Lord Henry Cavendish performed a torsion balance experiment, and the value of G found was extremely close to today's accepted value, at 6.67259 x 10-11 N m2/kg2
 * How to find G?**

The acceleration of gravity, g, depends on the law of universal gravitation. Therefore, depending on your distance from the center of the Earth, the value of g changes.
 * g is Always Changing**



=Physical World Clockwork Universe=

Kepler revolutionized people's understanding of our solar system by predicting the elliptical orbit planets follow around the Sun. From this, new advances in math were formed. Coordinate geometry was born, which infused algebraic principles to allow scientists to solve new problems.
 * Krazy Kepler**

For a long time, people had tried to put the world into a mathematical explanation. Newton was the man who accomplished much of this. He did so, however, from an interesting perspective. He believed that universal laws controlled all that we experienced. Rather than focusing on motion, he focused more on acceleration and change of direction. He identified the cause of the change as a force, and found a quantitative relationship. This founded the study of mechanics, and the initialization of his findings predicted where it would develop, called determinism.
 * Newton's Mindset**

=Physics Classroom 4 a-e=


 * Kepler's 3**
 * The path of the planets about the sun is 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)

Satellites are classified as man made or natural. Objects we put into orbit are man made, while the moon, stars, etc. are natural. A satellite is, essentially, a projectile. While they move in elliptical orbits, they still follow many traits of centripetal motion.
 * Different satellites**

The math behind solving these problems involves the modified F=ma formula. It begins with: **Fgrav = ( G • Msat • MCentral ) / R2** which simplifies to...
 * More Math**

for acceleration...

for period...

Weightlessness is the experience of no contact forces, such as in free fall. Technically, a scale does not measure your weight, but rather the normal force on your body. This is why bouncing on the scale changes the reading; the acceleration changes the normal force. Your weightlessness in orbit allows you to feel nothing, yet gravity pulls you towards Earth. You don't actually crash into Earth, since your velocity is tangential.
 * Weightless**

Since work is the exertion of energy, a satellite in orbit is affected by work. When far from the Earth, a satellite experiences positive work (towards the Earth) and when near the Earth, the satellite is pushed away, experiencing negative work. The work-energy theorem shows how energy is conserved, making initial and final work equal. It is as follows: **KEi + PEi + Wext = KEf + PEf or...** **KEi + PEi = KEf + PEf for satellites, since W would be gravity (0)**
 * Energy & Satellites**

= Notes 1/5 =


 * Aristotle 600 BC
 * Early (false) concepts of physical world
 * Copernicus
 * Says Earth is not the center of solar system, Sun is
 * Galileo
 * Begins to challenge Aristotle's theories through logical reasoning
 * Supported Copernicus
 * Got in trouble by Vatican, sentenced to house arrest
 * Looked through first decent telescope
 * Saw the Moon was just a rock
 * Microscopes invented (Leeuwenhoek)
 * People can see tiny parts
 * Newton
 * Observing & writing, but not publishing
 * Robert Hooke asks Newton a question
 * Is the force of gravity inversely proportional to the square of the distance from the sun
 * Yes, Gravity is inversely proportional to the square of the distance
 * Writes Principia
 * Gravity is proportional to the product of the masses & inversely proportional to the distance squared
 * F g ∝ m 1 *m 2 /d 2
 * Called the law of Universal Gravitation
 * F g = G*m 1 *m 2 /d 2
 * G = 6.67 * 10 -11 Nm 2 /Kg 2
 * Kepler
 * Apprentice to Tycho Brahe
 * Brahe wouldn't share his data
 * Brahe dies, and Kepler steals his data
 * Studies it for 14 years
 * Law of Ellipses
 * [[image:http://www.drennon.org/science/ellipse.gif caption="Ellipse. The sun would be at one focus."]]
 * All planets orbit the sun in an elliptical path with the sun at one focus
 * Eccentricity (e)- how far off an ellipse is from being a circle
 * e=0, perfect circle
 * e=1, line
 * e Earth =.06
 * Law of Equal Areas
 * [[image:http://www.drennon.org/science/kepler_sm.gif caption="Animated GIf of Kepler's 2nd Law by Bill Drennon" link="http://www.drennon.org/science/kepler.gif"]]
 * Planets carve out equal area of their orbit in equal times
 * There must be an changing acceleration depending on distance from the sun
 * Law of Harmonies
 * For any planet in our solar system, the ratio of the period squared to the radius cubed is constant
 * **Ta2 / Tb2 = Ra3 / Rb3**
 * Fg = w
 * Force of gravity, gravitational force, gravitational attraction, weight
 * G * m 1 m 2 /d 2 = m 1 g
 * G * m planet /d 2 = g
 * Cavendish
 * solved for G
 * G = 6.67 * 10 -11 Nm 2 /Kg 2