Ch5_souflige

Chapter 5 Circular Motion toc =Notes=

Lesson 1
Method 5: Headline Technique

Headline 1: Velocity and Speed Have Very Different Meanings in Circular Motion

At uniform circular motion, object moves at constant speed around the perimeter of the circle. Speed is measured by circumference over the time period of a revolution. Velocity is a tangential axis that stays perpendicular to the centripetal axis at all points on the circle.

Headline 2: Acceleration is Centripetal!

The misconception is that in uniform circular motion there is no acceleration since the object moves at constant speed; however, acceleration affects velocity, which has a direction. The change in direction means an acceleration takes place. The acceleration is centripetal, its direction is towards the center of the circle.

Headline 3: Centripetal Force Requirement works with inertia

Though it may seem like we are being pushed outward as a car makes a turn, away from the center, in reality we are just experiencing our tendency to keep traveling in a straight line. The car is actually accelerating out from under us.

Headline 4: Centrifugal and Centripetal Centrifugal means outwards from the center, which is not what circular motion is about. Centripetal forces keep objects in their circular paths, not an outward force.

Headline 5: Equations of Circular Motion

Speed: circumference over time. Acceleration: speed squared over radius.

Lesson 2

 * A. Newton's Second Law - Revisited **

These equations show the relationship between net force, acceleration, and mass. Physical situations can apply the law if a free-body diagram is used. We will use Unit 2 principles and circular motion concepts in order to analyze a variety of physical situations involving the motion of objects in circles or along curved paths. The [|mathematical equations discussed in Lesson 1] and the concept of a [|centripetal force requirement] (net force is inwards)will be applied. Consider a car moving in a horizontal circle on a level surface. Friction is centripetal, and normal and weight are on the Y-axis. Draw the free-body diagram and the law can be applied. Other applications may require use of the radius, velocity, etc. Suggested Method of Solving Circular Motion Problems Make sure to think and not memorize. We will focus on the centripetal acceleration within the circular-shaped sections of a roller coaster track. These sections include the clothoid loops (that we will approximate as a circle), the [|sharp 180-degree banked turns], and the [|small dips and hills] found along otherwise straight sections of the track. The most obvious section on a roller coaster where centripetal acceleration occurs is within the so-called ** clothoid loops **. These teardrop shaped loops are simply overlapping circular sections. Radius is larger at bottom than at top. This directly correlates to greatest speeds at the bottoms and lowest speeds at the top. Loops have both centripetal and tangential accelerations that correlate to the objects slowing or speeding up, and direction change. Normal force greatest at bottom and least at top. At various locations along these hills and dips, riders are momentarily traveling along a circular shaped arc. The arc is part of a circle - these circles have been inscribed on the above diagram in blue. In each of these regions there is an inward component of acceleration (as depicted by the black arrows). The magnitude of the normal forces along these various regions is dependent upon how sharply the track is curved along that region (the radius of the circle) and the speed of the car. These two variables affect the acceleration according to the equation ** a = v2 / R ** Circular motion is common to almost all sporting events. Mostly in turns. When a person makes a turn on a horizontal surface, the person often //leans into the turn//. By leaning, the surface pushes upward at an angle //to the vertical//. As such, there is both a horizontal and a vertical component resulting from contact with the surface below. This ** contact force ** supplies two roles - it balances the downward force of gravity and meets the centripetal force requirement for an object in uniform circular motion. The upward component of the contact force is sufficient to balance the downward force of gravity and the horizontal component of the contact force pushes the person towards the center of the circle. Turning motions are not the only situations in sports in which people or objects move in circles. There are certain track and field events - the hammer throw and the discus - in which athletes gather momentum in an object that is to be subsequently thrown. The pre-throw momentum is imparted to the projectile by whirling within a circle. Once momentum has been accumulated, the hammer or discus is launched into the air at an optimum angle in order to maximize the distance it travels.
 * 1) FBD
 * 2) ID given/unknown info and magnitudes.
 * 3) Angled forces -> components
 * 4) Use circular motion equations to find info.
 * 5) Find remaining info.
 * B. Roller Coasters and Amusement Park Physics **
 * C. Athletics **

Lesson 3
How does gravity relate to circular motion?

It is the constant pull downwards. In orbits, gravity is the centripetal force.

What is the Law of Universal Gravitation? Newton's relation of Earthly motion to heavenly motion by means of gravity. It explains all gravity in the universe.

What is the inverse square law? The force of gravity between two objects is inversely proportional to the squared distance between the objects' centers. This is the explanation for both the acceleration of objects in free fall and objects in orbit.

What does the gravitational constant lend to Newton's Law? It gives a constant to the proportionality that the product of the masses over the squared distance of the objects is proportional to the force of gravity between the objects. The constant makes this proportion into an equation.



Cavendish historical context of finding G.

How does g change with location? It decreases as you get further from the surface of the earth.

The Clockwork Universe
Method 5: Headlines

1. Three 16th Century Thinkers Revolutionize the Geocentric Model Copernicus created the heliocentric model in which the planets moved in perfect circles around the Sun. Galileo agreed. Kepler created a similar model but the planets moved in ellipses where the Sun was one of the foci.

2. DesCartes and Coordinate Geometry To underpin Kepler's hypotheses DesCartes had the coordinate grid. X and Y coordinates could directly correlate to geometric problems. More importantly, they made these problems solvable using algebra.

3. Newton's Unifying Laws Newton's greatest achievement was laying down the framework for scientific advancement, particularly in physics. He unified all the past ideas into one cohesive set of laws that culminated with the law of universal gravitation. His focus was not on motion itself but the deviation of steady motion.

4. Newtonian physics and its legacy

Newtonian Physics became the basis for mechanics (the study of force and motion). The Universe began to viewed as predictable, because it seemed that Newtonian physics could explain not only what was currently happening, but what will happen in the future. Determinism became an accepted concept, figuring that the Universe worked on certain laws, and once set into motion could be predicted of its future.

Lesson 4
Headlines Technique

1. Kepler Had Three Laws of Planetary Motion

His first law was that planets move in an ellipse around the sun, where the sun is at one of the foci. His second law states that during the same period of time at any two points in the ellipse the planet and the sun make an equal triangular area. His third law states that their is a specific ratio in the solar system that is the same for all planets -- their periods squared over their average distance to the sun cubed.

2. Satellites obey the laws of Kepler

Satellites (natural or man-made) are projectiles where the centripetal force (and only force) is gravity, while there is a tangential velocity, creating a circular path. An object shot at 8000 m/s or greater would orbit the Earth due to its curvature. Elliptical orbits are created with greater than the required speed for circular orbit. The initial speed takes much of the magnitude of gravity away until it returns back.

3. The Math behind Satellites

Notice that the speed, period, and acceleration are not dependent on the mass of the satellite.

4. Weightlessness Is A Sensation, Not An Absence of Forces The feeling of weightlessness is the same sensation as the one found in free fall; that is, where no contact forces exist (i.e normal force) and the only force is gravity. Also, a scale measures the upward normal force of it on you, not weight; therefore, you lose no weight when in free fall.

5. Analysis of Circular and Elliptical Orbits

In circular orbits the tangential velocity is always perpendicular to the centripetal force of gravity. Therefore, there is always a higher kinetic energy than potential energy. In elliptical orbits, the satellite slows down as it distances itself from the planet, and speeds up as it nears the planet. Therefore, when the satellite is closest to the planet it has the most kinetic energy, and when its the furthest away it has the most potential energy.

Lesson 1 - Work, Energy, and Power
A. Work

After reading the material, answer the following questions: I already understood the meaning of the vectors and the meaning of theta. Theta is between force and displacement.
 * 1) What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.

none.
 * 1) What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
 * 1) What (specifically) did you read that you still don’t understand? Please word these in the form of a question.

What is the significance of work and why does it need its own unit of measurement?

Work, measured in Joules (newtons*1 meter) is a measurement of the amount of displacement caused by a force being exerted on an object. The equation is W=F*d*cos(theta). There is no work being done if the object shows no displacement.
 * 1) What (specifically) did you read that was not gone over during class today?