Ch5_SolimanoM

=Lesson 1 Circular Motion (Method 5)toc= DANGEROUS SPEEDS, INSANE VELOCITY CALCULATIONS!!!!!!!! -Uniform circular motion is an object moving around a circle with a uniform speed! The average speed around a circle is the circumference of the circle/time, when the circumference 2*pi*radius. Thus, average speed = 2*pi*radius/T.

CIRCLES, TANGENTS,AND YOU! -The direction of the velocity vector is always tangential to the circle. So, the magnitude of velocity is the same, while it changes its direction in relation to the circle. The speed of the object is the same, while the velocity is changing.

ACCELERATION AND AN OBJECT MOVING AROUND A CIRCLE!!!! -The acceleration of an object moving around a circle is the rate at which it changes velocity. To solve this around a circle, the tangent velocities are used and are solved for. The acceleration of the object is towards the center of the circle.

WHAT IS THE CENTRIPETAL FORCE REQUIREMENT? -The direction of net force is the same as the acceleration, so there must be an inward pointing force, the centripetal force requirement, to have an inward acceleration. "Centripetal" means "center-seeking". Unbalanced forces are required for an object to move in circles.

THE AUTOMOBILE PASSENGER -A car passenger will often experience a backwards acceleration when accelerating. This is because of inertia, the passenger tries to maintain his motion while the car moves forward. This will also happen when braking, as you will naturally lean forwards. This may seem a net force, but is inertia. This also occurs with turning. When turning, you may experience an outward force, but this is really inertia.

Centripetal force -An object moving in a circle experiences a centripetal force. This is not a new type of force, but rather this describes the direction of the net force, which is towards the center of the circle. Examples of the types of forces that can keep an object in a circle include friction, tension, and gravity. THis can be seen as work, which is a force causing displacement. The work is calculated by force*displacement*cosine theta. The force is directed inward and the velocity is tangent to the circle.

No centrifugal forces -Many people feel an outward force when moving in a circle, and believe they are feeling a centrifugal force. This is not true, as there is no such thing as a centrifugal force. The centripetal forces have specific calculations. The centripetal acceleration equals (v squared)/r. This can replace a in the equation net force = ma.

=Lesson 2 Circular Motion (Method 2a)= 1. From class, I understood the concepts of centripetal force. I knew that the net force of the centripetal force is directed in. There are often three forces acting on the car in the example, weight, normal, and friction. All of these forces are represented by vector arrows.

2. Something that I was not sure of in class was the relationship between a turning object, like in athletics, and its acceleration. I now understand that there are different turns, in which the object can have the same radii or changing radii. I also know that by the object leaning into a turn, he lets the ground push a normal force against him and into the turn. This leaning into the turn not only creates an angled vertical force, but also balances the force of gravity, and thus has two components.

3. I understood all of the information that I read.

4. Something that we did not learn in class was the concept of clothoid loops, or the loops in a roller coaster. In a clothoid loop, the radius constantly changes. The rider of the loop experiences an acceleration from the change in speed and direction. There is an inward acceleration and a tangential acceleration. At the top, the acceleration is directed towards the middle, caused by the inward net force. The forces acted on the passenger can also be solved for using Newton’s second laws,, and by using a = v squared/r when he is at the bottom and top of the roller coaster.

=Lesson 3 (method 5)=

Kepler created the Laws of Ellipses, Equal Areas, and Harmonies. These three laws describe the motion of the planets and the sun, and stated that the planets move in an elliptical manor about the sun, the focus. They further stated that a line drawn from the center of the sun to the planets will “sweep out” equal areas in equal amounts of time, and that there is an equal ratio between the squares of the periods of two planets, and the cubes of their average distances from the sun.
 * Kepler, and his laws**

Kepler did not have a means of describing the motion of the planets. He concluded that this motion was a result of universal gravitation, which he explained in his “newton’s mountain” experiment, where he hypothesized the motions of a cannonball about the earth. He later found that the effect of gravity lessened with distance.
 * Why do the planets move the way they do?**

Isaac Newton knew that the effect of his universal gravity differed with distance. He ultimately expressed the change by saying that the force of gravity between the earth and an object is inversely proportional to the square of the distance that separates the object from the earth’s center. Thus, the force of gravity follows the inverse square law, and is shown by the equation 1/d^2.
 * How is gravity diluted by distance?**

Newton found that gravity is universal, and that all objects attract each other with a force of gravitational attraction. Thus, the gravitational attraction was also dependent on the masses of the objects, and inversely proportional to the square of the distances of both objects. His conclusion was (mass 1 x mass 2)/(d^2) equaled the force of gravity; this can also be modeled with a constant of proportionality by Fgrav = (G x mass1 x mass2)/(d^2).
 * Law of Universal Gravitation**

G is the universal gravitation constant, and was experimentally determined by Henry Cavendish. He measured the effect that lead masses had on the torsional force in a system that featured a rod with two balls attached to the ends of the rod, and thus calculated an experimental value for G. The value of G can vary on earth, based on the density of certain geologic structures.
 * Cavendish and G**

=Circular Motion Lesson 4 (a-e)= What were Kepler’s Three Laws? Kepler proposed three laws, including the Law of Ellipses, the Law of Equal Areas, and the Law of Harmonies. These stated that the planets move around the sun elliptically, and the sun is one focus, a line drawn from the center of the sun to the center of a planet will draw out equal areas in equal amounts of time, and that the ratio of squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun.

Circular Motion and Satellites A satellite is an object that orbits another body, they can be natural or man-made. The satellites are projectiles, the only force acting on them is gravity. The satellites always fall towards the earth.

Acceleration of the satellite The acceleration of the satellite is directed inward because of an inward net force, and keeps the satellite in orbit. The velocities are always tangent to the ellipse on which it moves, as some satellites move in ellipse about the foci of the body it orbits.

What were Kepler’s Three Laws? Kepler proposed three laws, including the Law of Ellipses, the Law of Equal Areas, and the Law of Harmonies. These stated that the planets move around the sun elliptically, and the sun is one focus, a line drawn from the center of the sun to the center of a planet will draw out equal areas in equal amounts of time, and that the ratio of squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun.

Circular Motion and Satellites A satellite is an object that orbits another body, they can be natural or man-made. The satellites are projectiles, the only force acting on them is gravity. The satellites always fall towards the earth.

Acceleration of the satellite The acceleration of the satellite is directed inward because of an inward net force, and keeps the satellite in orbit. The velocities are always tangent to the ellipse on which it moves, as some satellites move in ellipse about the foci of the body it orbits. Solving problems for gravity often involves setting Fg equal to m(squared/r).

Weightlessness, does it exist? Contact forces, like sitting on a chair, and at-a-distance forces, like gravity, exist in our world. Weightlessness is only a sensation, and because of the forces above, does not exist. It is merely when you feel no push or pull on you, however you are always affected by gravity, so you cannot be truly weightless.

Scales and Gravity Scales measure the upward force applied to your body, which can vary in different situations. If there is no acceleration, or constant speed, your weight will stay the same. However, if there is an upward acceleration, say in an elevator, the scale's reading will increase, as you try to maintain your position and the scale moves up. Likewise, if accelerating downwards, the scale's reading will decrease.

Weightlessness and orbit -An object in orbit stays in orbit because of a gravitational force and its tangental velocity. The tangental velocity keeps them in orbit and gravity pulls them towards an object.

=The Clockwork Universe websites (method 5)= The Views Before Newton Before Isaac Newton, Nicolaus Copernicus proposed a heliocentric model of our universe, where the earth moved around the sun. By taking the earth from the center of the universe, he was persecuted by many religious officials. Galileo was persecuted for supporting Copernicus. Kepler soon proposed that the planets moved in ellipses around the sun. Descartes would soon pose a problem to this philosophy, in his development of circles within a coordinate plane. Descartes also proposed that God created math laws that we are governed by

Newton, and His Contributions Newton was able to synthesize the unproved data of Kepler. He proposed a deviation from standard motion as a means of an ellipse forming, meaning a planet could speed up or slow down. He further proposed the law of universal gravitation. He finally stated, by one law, that gravity was the cause of the current planetary motion. Newton further created calculus, and explained colors.

After Newton -Newton's laws became a basis for mechanics, which painted the universe as something under the control of mathematical quantities. It thus could be predicted, using determinism. This idea disturbed many, and for some went against the idea of free will.