Chapter 8

1. Chapter 8 Rotational Motion

2. Forces and circular motion • Circular motion = accelerated motion (direction changing) • Centripetal acceleration present • Centripetal force must be acting • Centrifugal force - apparent outward tug as direction changes • Centripetal force ends: motion = straight line

3. Direction of Motion Centripetal Force Centrifugal Force

4. Centripetal Force • …has different origin (friction, tension, gravity, etc.). • Centripetal means "center seeking". Centrifugal Force(not a real force) • …results from a natural tendencyto keep a state of motion (inertia). • Centrifugal means "center fleeing".

5. What is that force that throws you to the right if you turn to the left in your car? • centrifugal force. • What is that force that keeps you in your seat when you turn left in your car? • centripetal force.

6. Examples Centripetal Force Centrifugal Force • water in bucket • moon and earth • car on circular path • coin on a hanger • jogging in a space station • Bucket • Earth’s gravity • Road Friction • Hanger • Space Station Floor • Inertia • Inertia • Inertia • Inertia • Inertia

7. Circular Motion • Linear speed - the distance moved per unit time. Also called simply speed. • Rotational speed - the number of rotations or revolutions per unit time. • Rotational speed is often measured in revolutions per minute (RPM).

8. Angular Position, Velocity, and Acceleration

9. Angular Position, Velocity, and Acceleration Degrees and revolutions:

10. Angular Position, Velocity, and Acceleration Arc length s, measured in radians:

12. Connections Between Linear and Rotational Quantities

13. Connections Between Linear and Rotational Quantities

14. The linear speed is directly proportional to both rotational speed and radial distance. v = w r • What are two ways that you can increase your linear speed on a rotating platform? • Answers: • Move away from the rotation axis. • Have the platform spin faster.

15. Connections Between Linear and Rotational Quantities

16. Connections Between Linear and Rotational Quantities This merry-go-round has both tangential and centripetal acceleration.

17. Center of Mass • The center of mass of an object is the average position of mass. • Objects tend to rotate about their center of mass. • Examples: • Meter stick • Map of Texas • Rotating Hammer

18. Center of Mass and Balance If an extended object is to be balanced, it must be supported through its center of mass.

19. Center of Mass and Balance This fact can be used to find the center of mass of an object – suspend it from different axes and trace a vertical line. The center of mass is where the lines meet.

20. Rotational Inertia • An object rotating about an axis tends to remain rotating unless interfered with by some external influence. • This influence is called torque. • Rotation adds stability to linear motion. • Examples: • spinning football • bicycle tires • Frisbee

21. The greater the distance between the bulk of an object's mass and its axis of rotation, the greater the rotational inertia. • Examples: • Tightrope walker • Inertia Bars • Ring and Disk on an Incline • Metronome

22. Torque From experience, we know that the same force will be much more effective at rotating an object such as a nut or a door if our hand is not too close to the axis. This is why we have long-handled wrenches, and why doorknobs are not next to hinges.

23. Torque • Torque is the product of the force and lever-arm distance, which tends to produce rotation. • Torque = force ´ lever arm • Examples: • wrenches • see-saws

24. We define a quantity called torque: The torque increases as the force increases, and also as the distance increases.

25. Only the tangential component of force causes a torque:

26. Stability • For stability center of gravity must be over area of support. • Examples: • Tower of Pisa • Touching toes with back to wall • Meter stick over the edge • Rolling Double-Cone

27. Conservation of Angular Momentum • angular momentum = rotational inertia ´ rotational velocity L = I w • Newton's first law for rotating systems: • “A body will maintain its state of angular momentum unless acted upon by an unbalanced external torque.”

28. Conservation of Angular Momentum If the net external torque on a system is zero, the angular momentum is conserved. The most interesting consequences occur in systems that are able to change shape:

29. Examples: • 1. ice skater spin • 2. cat dropped on back • 3. Diving into water • 4. Collapsing Stars (neutron stars)

30. Example Question • Two ladybugs are sitting on a phonograph record that rotates at 33 1/3 RPM. 1. Which ladybug has a great linear speed? A. The one closer to the center. B. The one on the outside edge. C. The both have the same linear speed

31. Example Question • Two ladybugs are sitting on a phonograph record that rotates at 33 1/3 RPM. 1. Which ladybug has a great linear speed? A. The one closer to the center. B. The one on the outside edge. C. The both have the same linear speed

32. Example Question • Two ladybugs are sitting on a phonograph record that rotates at 33 1/3 RPM. 2. Which ladybug has a great rotational speed? A. The one closer to the center. B. The one on the outside edge. C. The both have the same rotational speed

33. Example Question You sit on a rotating platform halfway between the rotating axis and the outer edge. You have a rotational speed of 20 RPM and a tangential speed of 2 m/s. What will be the linear speed of your friend who sit at the outer edge?

34. Example Question You sit on a rotating platform halfway between the rotating axis and the outer edge. You have a rotational speed of 20 RPM and a tangential speed of 2 m/s. What will be the linear speed of your friend who sit at the outer edge? A. 4m/s B. 2m/s C. 20 RPM D. 40 RPM E. None of these