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Circular & Satellite Motion

Circular & Satellite Motion. Physics I. Types of Speed. Linear speed is the distance traveled per unit of time . The speed of something moving along a circular path can be called tangential speed because the direction of motion is always tangent to the circle.

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Circular & Satellite Motion

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  1. Circular & Satellite Motion Physics I

  2. Types of Speed • Linear speedis the distance traveled per unit of time. • The speed of something moving along a circular path can be called tangential speed because the direction of motion is always tangent to the circle. • Rotational speed (sometimes called angular speed) is the number of rotations (or revolutions) per unit of time. All parts of the rigid turntable rotate about the axis in the same amount of time Ask your parents about Record players and what speeds they played? Come to class with the answer.

  3. All parts of the turntable rotate at the same rotational speed. • A point farther away from the center travels a longer path in the same time and therefore has a greater tangential speed. • A ladybug sitting twice as far from the center moves twice as fast. Lady Bug Revolution - Phet

  4. Uniform Circular Motion Uniform circular motion is motion along a circular path in which there is no change in speed, only a change in direction. An object moves at a constant speed in a circle: T = Period (seconds) f = Frequency (Hertz) v = Tangential or linear velocity

  5. Notice the difference between period and frequency. What is the period of one lap if 10 laps were covered in 20 seconds? What did you do? • Examples of Period • 10 sec/1 lap = 10 sec • 10 sec/ 2 laps = 5 sec • Examples of Frequency • 10 laps/5 sec • 10 laps/ 20 sec

  6. Suppose that a mass, m, is tied to the end of a string and is being whirled in a horizontal circle as shown in the diagram. What is causing the mass to move in a circle? Why is it considered to be accelerating? Top View: Centripetal Acceleration: “center seeking”

  7. Centripetal Force vs. Centrifugal force?? Centripetal Force – a NET force toward the center Centrifugal Force – an imaginative force an object experiences due to Newton’s first Law of Motion (Inertia). The feel of being pushed out, when instead being pulled in while trying to continue to move in a straight line.

  8. a vo vf If the string breaks, in which direction will the object fly? Tangent to the circle.

  9. Centripetal Force, Fc Circular Motion Applet Fc If a friend is driving the car and makes a hard turn to the right, in which direction do you move if you are in the front passenger’s seat? Why? What forces are acting on you and in what direction?

  10. The centripetal force is exerted BY the door ON you. (Centrally) Sharp Turn in CarWhy do we hit the door? What is the force from the door acting on the rider called? The Normal Force Author: Tippens, P. (2007)

  11. Without a centripetal force, an object in motion continues along a straight-line path. With a centripetal force, an object in motion will be accelerated and change its direction. thephysicsclassroom.com

  12. v = 15 m/s Fc R 250 N 30 m m=? Speed skater Example 1:A skater moves with 15 m/s in a circle of radius 30 m. The ice exerts a central force of 250 N. What is the mass of the skater? Draw and label sketch Solution: Author: Tippens, P. (2007)

  13. Hills & Loops The Physicsclassroom.com

  14. R Disappearing platform at fair. Fc Platform Ride – You Tube (External View) Platform Ride – You Tube (Internal view) Another Example Friction Normal Force Weight What exerts the centripetal force in this example and on what does it act? The normal force from the wall acts as the centripetal force. Friction holds the person up. Author: Tippens, P. (2007)

  15. Spin Cycle on a Washer How is the water removed from clothes during the spin cycle of a washer? Think carefully before answering . . . Does the centripetal force throw water off the clothes? The holes in the drum allow water to “fly” off because of inertia. Author: Tippens, P. (2007)

  16. The Effect of speed on Centripetal Force The model airplane has a mass of 0.90 kg and moves at a constant speed on a circle that is parallel to the ground. Find the Tension in the guideline (17 m) for speeds 19 m/s and 38 m/s. What is counteracting gravity if it is flying parallel to the ground?

  17. Friction and a Car on a Curved Road FN FN If Fc > Ff, then the car will not make the curve. If Fc Ff, then the car will make the curve Critical Point: Fc = Ff Ff Fg Record player demo- Double coins

  18. Vertical Circles In a vertical circle, if Fg is greater than the Fc required to keep the object in a circle, then the object will fall. The critical point is when Fg= Fc. This is used to determine the minimum or maximum speed at which an object can move and stay in the circle.

  19. Circular Motion Practice Problem 1. A coin is placed on a record player at a radius of 15 cm from the center. The rotational speed is set to 45 rpms. • What is the period of one revolution? b. What is the linear speed of the coin? c. How will placing an additional identical coin top of the existing coin affect the centripetal force? d. Recall from earlier demonstrations and lectures: Will adding the extra coin affect whether they will slip off the turntable?

  20. Practice Problems 1. A 1000 kg car completes two revolutions in 1 minute on a circular track with a 1 km radius. • What is the period of one revolution? • What is the car’s linear speed? • What is the centripetal force acting on the car?

  21. Your Turn! 2. A 5 kg mass is traveling a 6 m/s in a horizontal circle with a 60 cm radius. a. What is the centripetal acceleration? b. What is the centripetal force? Ac = 60 m/s2 Fc = 300 N

  22. Newton’s Law of Universal Gravitation Newton discovered that gravity is universal. Everything pulls on everything else in a way that involves only mass and distance. Universal Gravitation Constant: G = 6.67x10-11 Nm2/kg2 F F´ m1 m2 r F = -F´

  23. English physicist, Henry Cavendish determined G by measuring the tiny force between lead masses with an extremely sensitive torsion balance. Cavendish Experiment

  24. g = ? m1 Force of Attraction = Weight Weight m2 Mass of Earth = 5.98 x 1024 kg Radius of Earth = 6.37x106 m

  25. Inverse Square Relationship If r = 3RE, what would be your weight?

  26. Relationship Examples • If the radial distance doubles, then the force of attraction between 2 masses _________________. • If your weight dropped by a factor of 1/16th , then you must be ____ RE away. • If one mass doubled then the force of attraction _____________. • If one mass increased by a factor of 2 and the other mass decreased by a factor of 4, then the force of attraction would be _________________ . • The force of attraction is F. If the radius increased by a factor of 5, the new force would be ______.

  27. Universal Gravitation - Sample Problems 1. A space capsule weighs 500 N on the surface of the earth. How much does the capsule weigh when it is 4.50 x 108 m above the surface of the earth?

  28. 2. A force of 1.2x10-13 N exists between a 30 g mass and an unknown mass. Calculate the second mass if they are 1 m apart.

  29. Your Turn! 3. What is the force of attraction between a 5000g object and a 4000 g object when 30 cm apart? (Don’t forget to convert!!) Pause for Practice Ans: 1.48x10-8 N

  30. Newton & Falling Apple Is the Moon Falling? Hewitt, P. [Illustrations]. Conceptual Physics.

  31. Elliptical Orbits Newton’s Mountain Animation Hewitt, P. [Illustrations]. Conceptual Physics.

  32. Satellite Orbit In order for the satellite to orbit the Earth in a circle, the gravitational force is also the _______________________. Centripetal force

  33. Apparent Weight is zero in orbit because of free-fall but the true weight is determined by Newton’s Law of Universal Gravitation. Satellite Orbit If the satellite is in free fall, why does it not come crashing into the Earth? Zero Gravity with water: http://www.youtube.com/watch?v=r7fEHYkGxd0&feature=related

  34. Kepler’s Laws of Planetary Motion1. The paths of the planets are ellipses with the center of the sun at one focus.2. An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals. Thus the planets move fastest when closest to the sun, slowest when farthest away. 3. Kepler’s Laws Animation

  35. Universal Gravitation – Practice Problems • Two identical masses experience a force of 100 N when placed 20 cm apart. What is the mass of each? • A 5.8x106 kg mass and a 6.4x 105 kg mass experience an attracting force of 2.47x10-4 N. How far apart are the masses?

  36. Bellringer Questions You have 5 minutes to answer the following questions individually. 1. If you weighed 1/16th of your current weight, then you would be located __ Earth radii away. A. 1 B. 2 C. 4 D. 8 • What is the force of attraction between a 20 kg and a 50 kg object located 2 m apart? 1.6x10-8 m 3. ___ measured the constant G. A. Galileo B. Newton C. Cavendish 4. Linear Review Wkst Page 4 The relationship on the curve is A. Linear B. Quadratic C. Inverse 5. Linear Review Wkst Page 4: If a coin and a feather were dropped in a vacuum at the same time, they would have the same A. speed B. Acceleration C. Resistance

  37. Bellringer Questions You have 5 minutes to answer the following questions individually. • A mass travels at 2 m/s in a circle with a radius of 0.9 m. What is the centripetal acceleration? • Linear Review Wkst Page 3: • What is the instantaneous speed of an object that is at its highest point • when it is thrown straight up in the air? • A. 9.8 B. 0 C. 4.9 • 3. Linear Review Wkst Page 3 • When an object is in free fall, it falls a(n) ____ distance with each second. • A. Lesser B. greater C. equal • 4. Linear Review Wkst Page 3 • What is the slope of the graph represent? 4.44 m/s2 acceleration

  38. Bellringer Questions You have 5 minutes to answer the following questions individually. 1. If you weighed 1/16th of your current weight, then you would be located __ Earth radii away. A. 1 B. 2 C. 4 D. 8 • What is the force of attraction between a 20 kg and a 50 kg object located 2 m apart? 3. ___ measured the constant G. A. Galileo B. Newton C. Cavendish 4. The relationship on the curve is A. Linear B. Quadratic C. Inverse 5. If a coin and a feather were dropped in a vacuum at the same time, they would have the same A. speed B. Acceleration C. Resistance

  39. Credits: Cutnell & Johnson Physics. (2004). [Text Art CD]. John Wiley & Sons. Cartoon (Author Unknown). Received from 2007 AP Conference Complimentary Resource CD. Hewitt, P. [Illustrations]. Conceptual Physics. Hwang. F. (200). Circular Motion & Centripetal Acceleration Applet [Simulation]. Retrieved from http://www.phy.ntnu.edu.tw/oldjava/circularMotion/circular3D_e.html Tippens, P. (2007). Chapter 10 Uniform Circular Motion. [PowerPoint Slides]. Received from 2007 AP Conference Complimentary Resource CD. The Physics Classroom. [Animations]. http://www.thephysicsclassroom.com UC Irvine Physics of Music. (n.d.). Simple Harmonic Motion [Simulation]. Retrieved from http://positron.ps.uci.edu/~dkirkby/music/html/demos/SimpleHarmonic Motion/index.html

  40. Demo

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