1. © 2010 Pearson Education, Inc. PowerPoint ® Lectures for College Physics: A Strategic Approach, Second Edition Chapter 6 Circular Motion, Orbits, and Gravity

2. © 2010 Pearson Education, Inc. Slide 6-2 6 Circular Motion, Orbits, and Gravity

3. © 2010 Pearson Education, Inc. Slide 6-3

4. © 2010 Pearson Education, Inc. Reading Quiz 1.For uniform circular motion, the acceleration A.is parallel to the velocity. B.is directed toward the center of the circle. C.is larger for a larger orbit at the same speed. D.is always due to gravity. E.is always negative. Slide 6-6

5. © 2010 Pearson Education, Inc. Answer 1.For uniform circular motion, the acceleration A.is parallel to the velocity. B.is directed toward the center of the circle. C.is larger for a larger orbit at the same speed. D.is always due to gravity. E.is always negative. Slide 6-7

6. © 2010 Pearson Education, Inc. When a ball on the end of a string is swung in a vertical circle, the ball is accelerating because A.the speed is changing. B.the direction is changing. C.the speed and the direction are changing. D.the ball is not accelerating. Checking Understanding Slide 6-13

7. © 2010 Pearson Education, Inc. Answer When a ball on the end of a string is swung in a vertical circle, the ball is accelerating because A.the speed is changing. B.the direction is changing. C.the speed and the direction are changing. D.the ball is not accelerating. Slide 6-14

8. © 2010 Pearson Education, Inc. When a ball on the end of a string is swung in a vertical circle: What is the direction of the acceleration of the ball? A.Tangent to the circle, in the direction of the ball’s motion B.Toward the center of the circle Checking Understanding Slide 6-15

9. © 2010 Pearson Education, Inc. Answer When a ball on the end of a string is swung in a vertical circle: What is the direction of the acceleration of the ball? A.Tangent to the circle, in the direction of the ball’s motion B.Toward the center of the circle Slide 6-16

10. © 2010 Pearson Education, Inc. For the ball on the end of a string moving in a vertical circle: What is the direction of the net force on the ball? A.tangent to the circle B.toward the center of the circle C.there is no net force Checking Understanding: Circular Motion Dynamics Slide 6-19

11. © 2010 Pearson Education, Inc. Answer For the ball on the end of a string moving in a vertical circle: What is the direction of the net force on the ball? A.tangent to the circle B.toward the center of the circle C.there is no net force Slide 6-20

12. © 2010 Pearson Education, Inc. When the ball reaches the break in the circle, which path will it follow? Checking Understanding: Circular Motion Dynamics Slide 6-21

13. © 2010 Pearson Education, Inc. Answer When the ball reaches the break in the circle, which path will it follow? C. Slide 6-22

14. © 2010 Pearson Education, Inc. Uniform Circular Motion – Angular Position  In order to describe the position of a particle as it moves around the circle, it is convenient to use the angle  from the positive x-axis.  Thus, we call the angle  the angular position of the particle.   is positive when measured counterclockwise from the positive x-axis   is negative when measured clockwise from the positive x-axis

15. © 2010 Pearson Education, Inc. Angular Position – cont’d.  Rather than measure angles in degrees, mathematicians and scientists usually measure angle  in the angular unit of radians.   (radians) =  Rearranged  (For arc length)

16. © 2010 Pearson Education, Inc. “But, why do we need to learn radians when we already know how to work with degrees!?” -You  Because… MATH.  “Because degrees, technically speaking, are not actually numbers, and we can only do math with numbers. This is somewhat similar to the difference between decimals and percentages. Yes, "83%" has a clear meaning, but to do mathematical computations, you first must convert to the equivalent decimal form, 0.83. Something similar is going on here (which will make more sense as you progress further into calculus, etc).” - Elizabeth Stapel "Radians and Degrees."

17. © 2010 Pearson Education, Inc. Working with radians…  When a particle travels all the way around the circle (one rev)…  It travels: ______

18. © 2010 Pearson Education, Inc. Converting between degrees and radians…  We know…  1 rad = ___   105  = ____ rad

19. © 2010 Pearson Education, Inc. Converting between degrees and radians…  We know…  1 rad = ___   105  = ____ rad

20. © 2010 Pearson Education, Inc. Comparing linear & angular…

21. © 2010 Pearson Education, Inc. Example 6.1

22. © 2010 Pearson Education, Inc. Angular Velocity  is ____________ for an object moving with uniform circular motion.  can be positive OR negative.  Counterclockwise = positive  Clockwise = negative

23. © 2010 Pearson Education, Inc. Linear vs. Circular  Displacement…  (*Note about angular “speed”)

24. © 2010 Pearson Education, Inc. Example 6.2  A steel ball rolls counterclockwise around the inside of a 30.0 cm diameter roulette wheel. The ball completes exactly 2 rev in 1.20 s. a)What is the ball’s angular velocity? b)What is the ball’s angular position at t = 2.00 s?

25. © 2010 Pearson Education, Inc. Example 6.2  A steel ball rolls counterclockwise around the inside of a 30.0 cm diameter roulette wheel. The ball completes exactly 2 rev in 1.20 s. a)What is the ball’s angular velocity? b)What is the ball’s angular position at t = 2.00 s?

26. © 2010 Pearson Education, Inc. Angular Speed cont’d  We can also relate angular speed to period (T ) and frequency (f )!!  If a particle moves around a circle once…

27. © 2010 Pearson Education, Inc. Example 6.3  The crankshaft in your car engine is turning at 3000 rpm. What is the shaft’s angular velocity?

28. © 2010 Pearson Education, Inc. Equation for angular speed

29. © 2010 Pearson Education, Inc. Example 6.5  The diameter of an audio compact disc is 12.0 cm. When the disc is spinning at its maximum rate of 540 rpm, what is the speed of a point (a) at a distance 3.0 cm from the center and (b) at the outside edge of the disc, 6.0 cm from the center?

30. © 2010 Pearson Education, Inc. Revisiting Centripetal Acceleration…  Since we know that…

31. © 2010 Pearson Education, Inc. Uniform Circular Motion Slide 6-23

32. © 2010 Pearson Education, Inc. Example 6.7 (pg. 173)