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Chapter 21

Chapter 21. Angular Momentum. Definitions. P = period in seconds (sec) f = frequency in Hertz (Hz or rev/sec) w = angular speed ( rad /sec) P=1/f w = 2 p f. I = Rotational Inertia.

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Chapter 21

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  1. Chapter 21 Angular Momentum

  2. Definitions • P = period in seconds (sec) • f = frequency in Hertz (Hz or rev/sec) • w = angular speed (rad/sec) • P=1/f • w = 2 p f

  3. I = 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

  4. 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

  5. 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.”

  6. Direction of Motion Centripetal Type of Force Centrifugal Type of Force

  7. Centripetal • …is applied by some object. • Centripetal means "center seeking". Centrifugal • …results from a natural tendency. • Centrifugal means "center fleeing". • This is a fictitious force. Why?

  8. Examples Centripetal Type of Force CentrifugalType of Force • Bucket • Earth’s gravity • Road Friction • Hanger • Space Station Floor • Nature • Nature • Nature • Nature • Nature • water in bucket • moon’s orbit • car on circular path • coin on a hanger • jogging in a space station

  9. Circular Motion • 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.

  10. Centripetal Acceleration • “Turning acceleration” ac = v2/r = w2 r • What are two ways that you can increase the “false gravity” in a spinning space station? • Answers: • Move away from the rotation axis. • Have the space station spin faster.

  11. Moments of Inertia Table 21.2 Hoop or Ring Solid Cylinder

  12. Moments of Inertia Table 21.2 Mass on a Rod m R

  13. Moments of Inertia Table 21.2 Short Barbell Long Barbell

  14. Moments of Inertia Table 21.2 Rectangular Parallelepiped b c a Which axis of a book has the highest moment of inertia?

  15. Moments of Inertia Table 21.2 Solid Sphere Problem 21.6

  16. Problem 21.9 Ff Free Body Diagram FN Fg

  17. Problem 21.9 Ff Free Body Diagram FN Fg [maximum]

  18. Problem 21.9

  19. Problem 21.10 FN Free Body Diagram H2O Fg Note: “Minimum angular speed” means that FN=0.

  20. What if you ran in a spinning space station?

  21. What if you ran in a spinning space station?Would you feel heavier or lighter or no different?

  22. What if you ran the other way? You’d lose “weight”!

  23. Project Two Update • We will now have meetings outside of class time to work on Project Two. • We will meet in room 315A for these meetings. Be sure to sign in when you arrive. • We will attempt to build 2 engines per team, rather than 1 for each person.

  24. Project Two Update • Week 1 • Piston and Pressure Vessel Construction • Week 2 • Crankshaft and Flywheel Construction • Week 3 • Final Adjustments and Testing

  25. Project Two Update • Take 3 minutes to select a meeting time for your team for this week. • Select an alternate time from the list below as well. Tuesday • 12:00 • 4:00 • 5:00 Wednesday • 2:30 • 3:30 • 4:30 • 5:30 Thursday • 11:00 • 12:00 • 5:00 Friday • 12:00 • 1:00 • 2:00 • 3:00 • 4:00

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

  27. 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

  28. 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 • Rolling Double-Cone

  29. 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

  30. 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).

  31. Linear versus Rotational MotionEquation Sheet for Exam 4 • Momentum and Impulse • Conservation of Momentum • Newton’s Second Law • Distance • Speed • Acceleration • vf = vi + at • xf = xi +vit + ½ at2

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