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PHYS16 – Lecture 24

PHYS16 – Lecture 24. Ch. 10 & 11 Rotation. Announcements. Final Exam and Midterm Exam test times No consensus on midterm – didn’t realize during room picking for next year No consensus on Final As of right now exams will be given as before, during lab and during our final exam time.

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PHYS16 – Lecture 24

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  1. PHYS16 – Lecture 24 Ch. 10 & 11 Rotation

  2. Announcements • Final Exam and Midterm Exam test times • No consensus on midterm – didn’t realize during room picking for next year • No consensus on Final • As of right now exams will be given as before, during lab and during our final exam time. • Problem 9 on homework, Friction =10.5 kN

  3. Ch. 10 & 11 Rotation • Angular Motion • Angular displacement, velocity, & acceleration • Constant acceleration problems • Angular Inertia • Angular Energy • Rotational Kinetic Energy • Angular Force & Torque • Angular Momentum & Collisions

  4. Rotation pre-question • Two ponies of equal mass are initially at diametrically opposite points on the rim of a large horizontal turning disk at a fair. The ponies both simultaneously start walking toward the center of the disk. As they walk what happens to the angular speed of the disk? (Ignore friction.) • Angular speed increases • Angular speed decreases • Angular speed stays constant

  5. Angular Momentum & Collisions

  6. Angular Momentum • Angular momentum (L) – momentum of a rotating object • Angular momentum is conserved if there are no external torques

  7. Discussion Question: Rotating person • When I rotate in a chair with two weights extended and then bring the weights in, what happens to my angular speed? ΔL=0 and L=Iω Holding arms out increases I. If L stays the same, and I increases then ω decreases. What about Kinetic Energy?

  8. Discussion Question: Rotating person • What if I am at rest in a chair and I spin up a bicycle wheel, will I start to rotate? Which direction? ΔL=0 , so as long as there is no outside torques then yes, I will rotate. Direction will be opposite to wheel. http://www.phys.unt.edu/~klittler/demo_room/mech_demos/Rotating%20Stool%20&%20Bicycle%20Wheel.jpg

  9. Problem • A 50 g ball of clay is thrown at 10 m/s tangent to the edge of a 2 kg 30-cm-diameter disk that can turn. The clay hits the edge of disk and sticks. If disk initially at rest, what is angular speed after? (Ignore friction.) vi r

  10. Rotation pre-question • You are unwinding a large spool of cable. As you pull on the cable with a constant tension and at a constant radius, what happens to αand ω? • Both increase as the spool unwinds • Both decrease as the spool unwinds • αincreases and ω decreases • αdecreases and ω increases • αstays constant and ω increases

  11. Rotation pre-question • An ice skater spins with his arms extended and then pulls his arms in and spins faster. Which statement is correct? • His kinetic energy of rotation does not change because energy is conserved • His kinetic energy of rotation increases because angular velocity increases • His kinetic energy of rotation decreases because rotational inertia is decreasing

  12. Rotation pre-question • Two ponies of equal mass are initially at diametrically opposite points on the rim of a large horizontal turning disk at a fair. The ponies both simultaneously start walking toward the center of the disk. As they walk what happens to the angular speed of the disk? (Ignore friction.) • Angular speed increases • Angular speed decreases • Angular speed stays constant

  13. Application: Gears

  14. Gears: What are they good for? • Transfer rotational motion • Adjust the direction of motion • Change the torque…. • Change the angular velocity…

  15. Simple Machine = Gears and Belts • Gears are machines that transfer rotational motion • Gear/belt system linear velocity is equal Trade radius for rot. speed

  16. Gear Ratio • Gears with Teeth • Belts or Smooth disks

  17. How can we use this property? • Angular speed decreases with increasing radius • Torque (rotational equivalent of force) changes with radius • Power depends on τandω, stays constant Trade torque for ang. speed

  18. How can we use this property? • Let’s assume we apply a force to rotate one gear = driver gear, and it rotates another gear = driven gear

  19. Example Question: Bicycle • A bike is set such that it has 44 teeth on the front pedalling gear and 11 teeth on the rear gear attached to the wheel • What is the use of this setting? • Then in a “Granny” setting it has 15 teeth on the front gear and 30 teeth on the rear gear • What is the use of this setting? Gear ratio = 1/4, back wheel 4 times ang. speed of pedals and ¼ times the torque -> Going downhill or on road! Gear ratio = 2, back wheel 1/2 times ang. speed of pedals and 2 times the torque -> Going uphill or on sand!

  20. Example Question: Gears • Which way does Gear C turn? • What is the ang. velocity of Gear C in rev/min?

  21. Conclusions

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