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Circular Motion

Learn about Earth's rotation, satellite movements, centripetal force and acceleration, tangential velocity, frequency, and arc length in circular motion. Solve problems and explore real-life examples. Study centripetal force in various scenarios and see its application in car curves, loop-the-loop, and rotor rides.

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Circular Motion

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  1. Circular Motion Physics Mrs Coyle

  2. Earth rotates about its axis • Satellite revolves about the earth

  3. Part I-Intro to Circular Motion • Tangential Speed and Velocity • Frequency and Period • Centripetal Force • Centripetal Acceleration

  4. Characteristics of Circular Motion • Tangential (linear) Velocity • Frequency • Period

  5. Frequency, f :#revolutions per unit time • f = # rev / time Units: • (1/sec)=sec-1=Hertz (Hz) • rpm (#rev/min) • rps (#rev/sec) r

  6. Period • Period T : time for 1 revolution • Unit: sec, min, h • Relating Frequency and period • f= 1 T

  7. Arc Length • Arc Length s (unit: meter) • Distance traveled along a circular path. s

  8. Average Tangential (Linear) Speed v= s t Unit: m/s v= 2pr/T = 2prf

  9. Uniform Circular Motion • Linear(tangential speed is constant) • v=constant

  10. Tangential (Linear) Velocity The tangential velocity vector is tangent to the circle at the point of study. v v

  11. Problem 1 A biker travels once around a circular track of radius 20.0m in 3s. Calculate: • the average tangential speed • the frequency • the period Answers: 41.9m/s, f=0.33Hz, T=3s

  12. Record Player

  13. Problem 2 A coin sits 0.10m from the center of a record player spinning at 45rpm. • What is the frequency in Hertz? • What is the period? • What is the linear speed? Answer: 0.75Hz, 1.33s, 0.47m/s

  14. Merry-go-Round

  15. How does the v vary with r? • The linear speed increases as r increases. Example: • How does your linear speed change when you are on a merry-go-round and you move away from the center?

  16. How does the f vary with r? • f does not depend on r Example: • How does your frequency change when you are on a merry-go-round and you move away from the center?

  17. Centripetal Force, Fc= m v2 r • Is a center seeking force. (Always points to the center.) • Is perpendicular to the tangential velocity at any given instant. • It is not an extra force. An existing force represents the centripetal force.

  18. What forces represent the centripetal force in these examples? • Car on bend of road. • Coin on record player. • Child on merry-go-round. • Ball tied on a string.

  19. Centripetal Acceleration, ac= v2 r • Has same direction as centripetal force.(Always points to the center). • Is perpendicular to the tangential velocity at any given instant.

  20. Centripetal Force Fc=mac

  21. Problem 3 A child on a merry-go-round sits 1.5m from the center. They spin 3 times in one min. The mass of the child is 40kg. Find the friction(centripetal force) acting on the child. Answer: 5.9N

  22. Part II More Centripetal Force Problems • Car Rounding a Curve • Loop-the- loop • Rotor

  23. What force plays the role of the centripetal force when a car rounds a curve?

  24. Car Rounding a Bend

  25. Example 1: Car Rounding a Curve • A car is travelling with a speed of 45km/h on a circular horizontal track of radius 50m. What is the minimum coefficient of friction, so that the car stays on the track? • Answer: 0.3

  26. What force plays the role of the centripetal force when a ball is on the top of a loop-the-loop?

  27. Loop the Loop

  28. Example 2: Loop-the-loop • What is the critical velocity of a ball at the top of the loop of radius .3m so that it completes the loop? • Answer: 1.7m/s

  29. Rotor Ride

  30. Rotor Ride • http://www.youtube.com/watch?v=J7k8Oz_73mw&feature=player_embedded#

  31. What force plays the role of the centripetal force in the rotor ride? • http://upload.wikimedia.org/wikipedia/commons/7/7d/Rotormidcyclelunapraksyd.JPG

  32. Example 3: Rotor • A brave student rides in a rotor of radius 5m whose floor drops when it reaches a speed of 20mi/h. What is the coefficient of friction between the student and the wall of the rotor, so that the student does not fall? Answer: 0.6

  33. Recap

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