Announcements Thurs 22 Oct 2009 1 From last time CAUTION Starting with HW 14 due Tuesday some of your HW answers will need to be written in scientific notation Do this with e notation not with x signs For example if the answer range says 5 00 1033 9 00 1033 kg m2 s x x and you get 6 57 1033 kg m2 s as your answer then you should type in the answer as 6 57E33 No spaces no x s If you put any spaces or x s in your answer the computer will mark it wrong 2 TA led Exam Review session results of doodle com voting a Day Time b Place 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 and both wheels accelerate the same The tension in the rope is a Largest between the disks b Largest above the mass c The same in both places Hint apply N2 for torques to the right hand disk What s different with our old massless pulleys Colton Lecture 16 pg 1 Another review problem A bicycle tire r 0 4 m I 0 8 kg m2 is hanging from a string from the ceiling not moving You push on the edge with a 30 N force for 0 3 seconds What is f Hint because time is given do it with N2 not energy Colton Lecture 16 pg 2 Angular Correspondences Review Kinematics Distance x Velocity v Acceleration a 1 x x0 v0t at 2 2 Angle Angular velocity Angular acceleration 1 0 0t t 2 2 v v0 at 0 t 2 2 2 0 2 2 0 v v0 2a x x0 30 N Mass Mass m Moment of inertia I Force Newton s 2nd Law Force F Torque r r F ma I Energy KEtrans 1 2 mv 2 KErot Momentum Momentum p mv Angular momentum Answer 4 5 rad s Colton Lecture 16 pg 3 1 2 I 2 Colton Lecture 16 pg 4 Angular momentum Imagine a mass m on a thin rod moving in a circle with constant speed v It r hasrlinear momentum p Is prconstant Is p constant p r Conservation of Angular momentum Lbef Laft if and only if no net external torques magnitude r What do we need in order to affect p Force momentum relationship Start with Newton 2 Torque ang mom relationship F ma I r r 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 Define If no net external force no change in momentum L I If no net external torque no change in angular momentum Clicker quiz Is rotational kinetic energy conserved The total energy afterwards is a more b less c the same Hint is there any non conservative work done Colton Lecture 16 pg 5 Spinning From warmup Rotating stool student with weights Her arms are extended holding the weights as far from her body as possible She then pulls the weights in close to her body she will rotate faster What happens to her moment of inertia as she pulls in the weights a increases b decreases c remains the same From warmup What happens to her rotational speed as she pulls in the weights a increases b decreases c remains the same Colton Lecture 16 pg 6 Worked Problem A skater has an initial of 2 rad s and I 30 kg m2 When she brings in her arms I 10 kg m2 What is her final How much work did it take to do this Application to skaters frictionless ice Demo spinning chair From warmup What happens to her rotational kinetic energy as she pulls in the weights a increases b decreases c remains the same Answers 6 rad s 120 J Colton Lecture 16 pg 7 Colton Lecture 16 pg 8 Food for thought two skaters joining hands Is L conserved in these cases frictionless ice Teacups central post is connected to the platform floor Before Train on circular track Any L After Any L Yo yo Pocket watch with internal spring Was angular momentum conserved system both skaters It must be if there is no net external torque Videos train on circular track pocket watch Clicker quiz Is there an external torque here I e was angular momentum conserved a Yes external torque not conserved b No external torque yes conserved Colton Lecture 16 pg 9 Comment on vectors aka L has a direction Another expression for L Start with r F Colton Lecture 16 pg 10 Remember Fnet p t net L t Does have a direction Therefore Thus with no external torques Result L r p r p r p sin Worked Problem Skaters on previous page 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 Demos gyroscope With external torque 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 Answer 5 rad s Colton Lecture 16 pg 11 Colton Lecture 16 pg 12 From warmup http science howstuffworks com gyroscope1 htm 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 Jos sits still on frictionless ice holding a bicycle wheel that s already spinning View from above it is going clockwise CW Clicker quiz 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 Answer from the class Clicker quiz 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 Demo bicycle wheel Colton Lecture 16 pg 13 A girl is on a spinning merry go round What will happen to the rotational speed of the merry go round if she HINT Sometimes it s easier to think of the forces torques she put on the merry go round to change rather than conservation of L Clicker quiz 1 Walks towards the center a it slows down b it stays same speed c it speeds up Clicker quiz 2 Starts running opposite to the …