1. PHY 2048C General Physics I with lab Spring 2011 CRNs 11154, 11161 & 11165 Dr. Derrick Boucher Assoc. Prof. of Physics Session 9, Chapter 8

2. Chapter 8 Homework Due Saturday @ midnight

3. Chapter 8 Practice Problems 9, 11, 27, 29, 33, 39, 43 Unless otherwise indicated, all practice material is from the “Exercises and Problems” section at the end of the chapter. (Not “Questions.”)

4. Topics in this Highlights lecture: Velocity and Acceleration in Uniform Circular Motion Dynamics of Uniform Circular Motion Nonuniform Circular Motion Chapter 8. Dynamics II: Motion in a Plane

5. Uniform Circular Motion Circular motion can be simple or part of a more complex motion. As long as something is going in a circular path (or part of one) the ideas in this chapter will apply.

6. Uniform Circular Motion The acceleration of uniform circular motion points to the center of the circle. Thus the acceleration vector has only a radial component a r. This acceleration is conveniently written in the rtz-coordinate system as

7. Example, Problem 8-12, p. 231

8. Dynamics of Uniform Circular Motion The usefulness of the rtz- coordinate system becomes apparent when we write Newton’s second law in terms of the r-, t-, and z- components, as follows:

9. EXAMPLE 8.4 Turning the corner I

10. Banked curve: A component of the normal force acts in the radial direction: Not as much friction needed OR Faster speeds for a given amount of friction!

11. Banked curve: A component of the normal force acts in the radial direction: Not as much friction needed OR Faster speeds for a given amount of friction!

12. Example, Problem 8-14, p. 231

13. Example, Problem 8-28, p. 232

14. Circular Orbits

15. Newton conceived artificial satellites almost 300 years before they were created.

16. Fictitious Forces If you are riding in a car that makes a sudden stop, you may feel as if a force “throws” you forward toward the windshield. There really is no such force. Nonetheless, the fact that you seem to be hurled forward relative to the car is a very real experience! You can describe your experience in terms of what are called fictitious forces. These are not real forces because no agent is exerting them, but they describe your motion relative to a noninertial reference frame.

19. Centrifugal Force If the car you are in turns a corner quickly, you feel “thrown” against the door. The “force” that seems to push an object to the outside of a circle is called the centrifugal force. It describes your experience relative to a noninertial reference frame, but there really is no such force.

20. Why Does the Water Stay in the Bucket? Imagine swinging a bucket of water over your head. If you swing the bucket quickly, the water stays in. But you’ll get a shower if you swing too slowly. The critical angular velocity ω c is that at which gravity alone is sufficient to cause circular motion at the top. Don’t use as a primary equation: work out Sum of Forces ALWAYS!!!

21. Why Does the Water Stay in the Bucket?

24. Nonuniform Circular Motion

25. The frictional force between the tires and the pavement and the normal force from the banked track keep the bike on the circle. If the bike is accelerating, there is also a tangential component of the acceleration.

26. Nonuniform Circular Motion The force component (F net ) r creates a centripetal acceleration and causes the particle to change directions. The component (F net ) t creates a tangential acceleration and causes the particle to change speed. Force and acceleration are related to each other through Newton’s second law.

27. Example, Problem 8-50, p. 233

28. Chapter 8. Clicker Questions

29. For uniform circular motion, the net force A. points toward the center of the circle. B. points toward the outside of the circle. C. is tangent to the circle. D. is zero.

30. A. n > w. B. n < w. C. n = w. D.We can’t tell about n without knowing v. A car is rolling over the top of a hill at speed v. At this instant,

31. A ball on a string is swung in a vertical circle. The string happens to break when it is parallel to the ground and the ball is moving up. Which trajectory does the ball follow?