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Understanding Angular Motion and Momentum in Physics

This lecture provides an overview of chapters 10 and 11, focusing on rotational motion, angular displacement, velocity, and acceleration. Key concepts include angular inertia, kinetic energy, and momentum, especially regarding collisions and practical applications of gears in machinery. The lecture also features various pre-questions and problems such as the dynamics of ponies on a disk and the effects of pulling in arms while spinning. Students are reminded of exam schedules and collaborative decision-making issues with previous tests.

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Understanding Angular Motion and Momentum in Physics

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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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