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Announcements Thurs, 23 Oct Exam 2 starts Oct 30, a week from today. a. Late fee on Monday Nov 3, after 2 pm b. Closes on Tuesday Nov 4, 2 pm c. Jerika exam reviews, both in room C295 ESC: i. Wed

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Announcements Thurs, 23 Oct Exam 2 starts Oct 30, a week from today. a. Late fee on Monday Nov 3, after 2 pm b. Closes on Tuesday Nov 4, 2 pm c. Jerika exam reviews, both in room C295 ESC: i. Wed Oct :30 pm ii. Thurs Oct 30 5:30-7 pm d. Exam covers through today's lecture i. Ch. 5, 6, , 8 ii. HW Equations from last time: Energy: KEtrans Force: F ma 1 mv 2 2 KErot I 1 I Equation from today: Momentum: p mv ang. momentum =?? Colton - Lecture 16 - pg 1 Which of the problems from last night's HW assignment would you most like me to discuss in class today? Colton - Lecture 16 - pg 2 Worked problem from last time: A falling mass starts a cylinder rotating (not a massless pulley ). What is the acceleration of m? Draw FBDs R M Write equations, plug in = a/r Cylinder Pail m TR p I a R MR F ma mg T ma Solve simultaneous equations for a (and T, if desired) Answer: m a m M g 2 Colton - Lecture 16 - pg 3 What if you just want to know v f (given a distance d)? mgd m M Answer: v f Colton - Lecture 16 - pg 4 Worked Problem A bicycle tire (r = 0.4 m, I = 0.8 kg m 2 ) is hanging from a string from the ceiling, not moving. You push tangentially on the edge with a 30 N force for 0.3 seconds. What is f? (Hint: because time is given, might be simplest to do it with N2, not energy.) 30 N Answer: 4.5 rad/s Colton - Lecture 16 - pg 5 Clicker quiz x x The left disk has a rope wrapped around its edge and the rope passes over a second disk. The two disks are identical and their mass is significant. As the system accelerates there is no slipping of the rope on either wheel; both wheels accelerate at the same rate. The tension in the rope is a. Largest between the disks (red arrows) b. Largest above the mass (blue arrows) c. The same in both places. (What s the difference with our old massless pulleys?) Colton - Lecture 16 - pg 6 Angular momentum Imagine a mass m on a thin rod moving in a circle, with constant speed v. It has linear momentum p =. r p Is p constant? Is magnitude of p constant? What do we need in order to affect magnitude of p? Colton - Lecture 16 - pg 7 Derivation of Angular Momentum Force-momentum relationship Start with Newton 2: F ma Torque-ang. mom. relationship I Define L = I units of L? Momentum is conserved if no net external force Angular momentum is conserved if no net external torque Colton - Lecture 16 - pg 8 Conservation of Angular momentum blueprint L bef L aft if and only if no net external torque Colton - Lecture 16 - pg 9 Problem Two space stations are connected by a cable. They are rotating about their center of mass. Someone in the blue station pulls the cable in so they are each closer to the center of rotation. What happens? Demo: Hoberman sphere Colton - Lecture 16 - pg 10 Clicker quiz Is rotational kinetic energy conserved in the Hoberman sphere? The final KE is as the initial KE: a. more b. less c. the same Hint: is there any non-conservative work done? Colton - Lecture 16 - pg 11 From warmup Rotating stool, student with weights. What happens to her moment of inertia as she pulls in the weights? a. increases b. decreases c. remains the same What happens to her rotational speed as she pulls in the weights? a. increases b. decreases c. remains the same What happens to her rotational kinetic energy as she pulls in the weights? a. increases b. decreases c. remains the same Colton - Lecture 16 - pg 12 Demo: Spinning chair Colton - Lecture 16 - pg 13 Worked Problem A skater has an initial of 2 rad/s and I = 30 kg m 2. When she brings in her arms, I = 10 kg m 2. What is her final? How much work did it take to do this? Answers: 6 rad/s, 120 J Colton - Lecture 16 - pg 14 Videos marbles and funnel train on circular track pocket watch Colton - Lecture 16 - pg 15 Food for thought: two skaters joining hands Before After Any L? Any L? Angular momentum conserved No external torque (system=both skaters) Clicker quiz: Is there an external torque here? I.e. was angular momentum conserved? a. Yes external torque/ang. mom. not conserved b. No external torque/ang. mom. is conserved Colton - Lecture 16 - pg 16 Hidden angular momentum L = r p ( = r p = r p sin ) Derivation: rf p r t rp t But remember also = L/ t! Colton - Lecture 16 - pg 17 Worked Problem The skaters have 0.7 m arms and are each 62 kg. They come together at 3.5 m/s. How fast (rad/s) are they turning afterwards? Answer: 5 rad/s Colton - Lecture 16 - pg 18 L is a vector With no external torques both and of L stay the same Demo: gyroscope With external torques? Colton - Lecture 16 - pg 19 From warmup: Ralph watched the video with the bicycle wheel, but became very confused. He had learned that angular momentum is conserved, but in this case isn t the angular momentum of the wheel constantly changing in direction as the wheel spins around. What s up? Think-pair-share Think about it for a bit Talk to your neighbor, find out if he/she thinks the same as you Be prepared to share your answer with the class if called on Clicker: I am now ready to share my answer if randomly selected. a. Yes Note: you are allowed to pass if you would really not answer. Colton - Lecture 16 - pg 20 Demo Bicycle wheel Colton - Lecture 16 - pg 21 Demo: Angular momentum with external torque (wacky briefcase) Demo: briefcase To fully describe what happens to angular momentum with external torque takes more math than we have just understand that strange things can happen. Colton - Lecture 16 - pg 22 Clicker quiz José sits still on frictionless ice, holding a bicycle wheel that s already spinning. Viewed from above it is going clockwise (CW). If he grabs on to the wheel edge firmly and stops it from spinning he will: a. Start to turn CW (viewed from the top) b. Start to turn CCW c. Remain sitting without turning Colton - Lecture 16 - pg 23 Clicker quiz José still on frictionless ice holding this spinning wheel. Viewed from above it is going clockwise (CW). If, instead of stopping the wheel, he carefully turns it over so it is going CCW (viewed from the top), he will start to: a. Turn CW, but slower than in the previous problem b. Turn CCW, but slower than in the previous problem c. Turn CW, but faster than in the previous problem d. Turn CCW, but faster than in the previous problem e. Remain sitting without turning Demos: rotating platform, bicycle wheel Demo: double bicycle wheels Colton - Lecture 16 - pg 24 Clicker quiz What will happen to the rotational speed of the merrygo-round if the girl walks towards the center? a. it slows down b. it stays same speed c. it speeds up Colton - Lecture 16 - pg 25 Clicker quiz starts running opposite to the spinning so she is at rest vs the ground? a. it slows down b. it stays same speed c. it speeds up HINT: Sometimes it s easier to think of the forces (torques) she puts on the merry-go-round to change, rather than conservation of L. Colton - Lecture 16 - pg 26 Clicker quiz slips off when she steps on a frictionless icy part? a. it slows down b. it stays same speed c. it speeds up Colton - Lecture 16 - pg 27 Clicker quiz throws her shoe off tangentially in the direction she s moving? a. it slows down b. it stays same speed c. it speeds up Colton - Lecture 16 - pg 28

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