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PHYS16 – Lecture 24 Ch. 10 & 11 Rotation

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Announcements Final Exam and Midterm Exam test times – No consensus on midterm – didnt 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

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

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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.) A)Angular speed increases B)Angular speed decreases C)Angular speed stays constant

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Angular Momentum & Collisions

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

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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?

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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

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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.) r vivi

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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 α and ω ? A)Both increase as the spool unwinds B)Both decrease as the spool unwinds C)α increases and ω decreases D)α decreases and ω increases E)α stays constant and ω increases

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

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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.) A)Angular speed increases B)Angular speed decreases C)Angular speed stays constant

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Application: Gears

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Gears: What are they good for? 1)Transfer rotational motion 2)Adjust the direction of motion 3)Change the torque…. 4)Change the angular velocity…

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

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Gear Ratio Gears with Teeth Belts or Smooth disks

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

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How can we use this property? Lets assume we apply a force to rotate one gear = driver gear, and it rotates another gear = driven gear

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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!

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

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Conclusions

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