Ch5_LefflerM

=toc = =Chapter 5: Circular Motion =

Lesson 1 Method 5
Understanding the Speed and Velocity of Circular Motion. When an object is moving in a circle, to find the average speed divide the circumference (2*π*r) by the time it takes to make one full pass. The speed and velocity of the moving object are not the same. The speed is constant, but the velocity is constantly changing direction. Depending on the direction, the velocity is a different value. The word for how the velocity and the circle interact is called tangential, which is shown by this picture:

Applying The Concepts of Circular Motion to AccelerationAcceleration changes when the velocity changes, they are directly related. Velocity of an object moving in a circular motion is not constant, so neither is the acceleration. Acceleration points the same way the velocity does (positive/negative), it always points into the circle. Acceleration can be found using an accelerometer. What is the One Requirement to be a Centripetal Force? In order to be an object to move in a circe, it must have an inward force working on it. That force is called centripetal force and is either a push or a pull into the center of the circle. If there is no inward force, the object will move in a straight line, based on Newtons Laws of motion and inertia. The force's acceleration depends on the direction of the object as it moves around the center.

Studies show most people use the F-word incorrectly! Centrifugal forces and Centripetal forces are different. Centrifugal forces try to push/pull away the object from it's curricular path, centripetal forces pull/push the object into the circular path. People tend to think that there is outward forces, when in reality it's just the object wanting to go in a straight path, the centripetal force keeps it in it's path.

Don't Worry, There is Math in this Unit! Speed, force, and acceleration are all used to analyze the motion of objects in circular motion. The equations to find these are average speed = (2πR)/one rotation time, acceleration = v 2 /R, and ∑F = ma.

Lesson 2, Method 5 Newton's Second Law, Applied to Circles with Motion!Newton's Second law can be applied to circular motion, if you know the right way to use it. Newton's second law tells us that ∑F=ma, when dealing with circles, ∑F is always towards the center of the circle. You can tell this by drawing a free body diagram, which is the most important thing to do when solving a circular motion problem. Physics Can Be Fun (Phun)? NO WAY!!!Amusment parks are riddled with lots of fun awesome physics problems. There are clothoid loops, peaks, and valleys; each one has a lot to do with physics. Whenever you are at a peak, valley, or in a clothoid, you are moving in circular motion. depending on where you are in the circular path, you feel heaveir, lighter, or just normal. This is because of the acceleration, which is found with a=v 2 /R. People have Circular Motion Too?Every time someone makes a turn, they are moving in circular motion; when athletes do it, it is much more intense. Skaters deal with this circular motion and the forces that come along with it, buy adding more components to it. This makes it so they are more balanced. They x component of the circle, and the y component will be the force of gravity together.

Lesson 3, Method 5 What in the Name of Gravity? What is gravity and what does it do to us? Gravity is a force that acts on everything, this being said, people are used to acceleration due to gravity, which is 9.8 m/s/s. These are not the same thing, one is a force and another is based off the force and because of it. Gravity and gravitational acceleration will both be used, and explained further in this chapter. Apples, Moons, and Laws OHH MY! How is the force of gravity between Earth and any other object is inversely proportional to the square of the distance that separates the object from Earth's core center? It is all based off of Johannes Kepler analysis of astronomical data which helped him develop three laws to describe the motion of planets. Kepler's Three Laws are: The Law of Ellipses The Law of Equal Areas The Law of Harmonies All this research started because he was hit in the head by a falling apple, which made him think about gravity.
 * The paths of the planets about the sun are elliptical in shape, with the center of the sun being located at one focus.
 * 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 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.

Is Everything Universal? Universal Gravitational is constant and is always equal to 6.673 x 10 -11 Nm 2 /kg 2 which is represented by G. Distance is not the only variable affecting gravitational force. Mass of both objects along with the distance as mentioned before. The force of gravity acting between the earth and any other object is directly proportional to the mass of the earth, directly proportional to the mass of the object, and inversely proportional to the square of the distance that separates the centers of the earth and the object. All objects attract each other with a force of gravitational attraction. When the space between two objects is greater, gravity is weaker, a smaller distance has stronger gravity.

How Does One Use a G? G is the universal gravitational constant. Newton proposed that the gravitational attraction between any two objects is directly proportional to the product of their masses and inversely proportional to the distance between their centers. This is shown in the equaltion Fg = (Gm 1 m 2 )/d 2 The Value of g is WHAT? g is not the easiest thing to find. In order to do it, there are multiple steps. One of the hardest things to do is combining equations. By using the two main equations in this unit, and making them equal each other. (m)(g) = (Gm 1 m 2 )/d 2. The two masses will cancel, then just plug in numbers and the constant G and it is very easy to solve.

The Clock Work Universe, Method 5 The man, the legend who was also a model? For some reason, people think that they are the center of the universe, a man named copernicus changed all that. He theorized that the sun was the center of the universe and we just circled it. People hated this and the church outlawed it. Galileo was sentenced to house arrest because of his support of the idea! Kepler who lived much later, went on the add to the theory, by making a model of our solar system and developing his laws of gravitational motion. Geometry of Algebra? You Decide. Keper's thoughts about planetary motion were fortified by the advances in science around that time. A french Mathematician and scientist Rene Descartes created the coordinate system which made it easier to show algebraic equations as geometric shapes. This showed that Kepler's ideas were right about the shape of the orbitals.

Science wasn't always what it is now you know, ya whippersnappers. People have always tried to explain the world in two ways, one being science and the other religion. Newton helped surge that science explanation of the world with his thoughts about motion. Newton observed motion as not just constant motion, he looked for the turns, speeding up and slowing down. Through those types of motion he was able to better understand the different types of motion and uniform thoughts about it. Newton always looked for a cause for changes and used them to help his understanding. Through his study of motion, he figured out his law of universal gravitation.

What is Determinism and what does it have to do with Anything? Newton's law of gravity worked for every object in the universe from the tiniest grain of sand, to the largest planets in the solar system. When combined with is other laws of motion he was able to fortify Kepler's beliefs mathematically. He showed how to calculate the ellipses of Kepler's diagrams of heavenly bodies. Determinism which is the using Newton's laws to predict the force of gravity and other large forces on earth was helpful in fortifying these theories.

Physics Classroom Lesson 4, Method 5 Kepler's three main laws Law of Ellipses - Planets orbit around the sun in an elliptical patter with the sun being located at one focus Law of Equal Areas - The time it takes to travel any distance on the ellipse is the same for all distances. Law of Harmonies - The periods of any two plantes squared, is equal to the ratio of their average distances from the sun cubed.

Satellites and their motion. While in orbit gravity is the only force that works in Satellites, just like the moon. In order to get a satellite to orbit the earth, it must be launched so that it gets stuck in our gravity belt. Satellites orbit earth, not the other way around because they are to small to be orbited.

Satellites not only have motion, but math to go along with it!

Satellite motion requires the use of math, when you feel the need to solve the problems you can use and combined these equations

Feeling weightless? Maybe your in orbit! People feel weightless when they are not working under any forces, there is not weight, normal, tension, or friction forces. With out these forces, you will be in a state of perpetual free fall.

Satellites Have Energy?!?

Work-Energy Theorem is the initial amount of mechanical energy of an object and the work done by external forces on that system that is equal to the final amount of mechanical energy of the object.

The Equation For The Work Energy Theorem:



If speed and height are constant, all energy will be as well. If you are moving in an elliptical orbit the speed and height changes which results in the change of energy.