Lect20 - Physics 211 Lecture 20 Today's Concepts: Angular...

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Unformatted text preview: Physics 211 Lecture 20 Today's Concepts: Angular Momentum Precession Physics 211 Lecture 20, Slide 1 Physics preflight explains very well. preflight I’m really confused need an explanation for everything. How does angular momentum stay constant if we apply an external torque to How have precession? I do not understand why the torque provided by the weight of a top in a do gyroscope does not point in the direction of gravity. I don't understand how you figure out the direction of procession. don't very confused about all of this external torques stuff. difficult to grasp, probably very need to see some examples, maybe watch the prelecture again. will this be on again. the test? (it probably will be, since i don't get it) I don't believe the example with the student, top, and stool. There is no way the don't top will make the stool rotate unless they touch or you prove it as a demo in as class. The physics department should give every physics student a gyroscope to play with. What is precession? And are you for serious about the test Thursday? What the direction of the Torque. I dont understand why we have to use the right understand hand rule to know the direction of the torque. there's this girl in my building, and i really want to get her to notice me. I feel like this is my last chance. She ALWAYS sits on the right side of the room and room today's the day i'm going to make my move. I REALLY need this as an going icebreaker. PLEASE put this comment up. PLEASE. I started out the semester loving Physics and understanding it all. But somehow I cannot comprehend angular anything. Maybe it's the right-hand rule; I still don't understand quite how it works. I am losing hope. Please send Bruce. Physics 211 Lecture 20, Slide 3 Physics Student on Stool There are no external torques acting on the student-stool system, so angular momentum will be conserved. Initially: Li = Iiωi ω f Ii Finally: Lf = If ωf = ωi ωf ωi If Ii Li If Lf Physics 211 Lecture 20, Slide 4 Act A student sits on a freely turning stool and rotates with constant angular velocity ω1. She pulls her arms in and her angular velocity increases to ω2. In doing this her kinetic energy: A) increases B) decreases ωf ωi If Ii L C) stays the same L Physics 211 Lecture 20, Slide 5 1 2 L2 K = Iω = (using L = Iω) 2 2I L is conserved: K f > Ki Ii < If ωf ωi If Ii L K increases! L Physics 211 Lecture 20, Slide 6 Since the student has to force her arms to move toward her body, she must be doing positive work! The work/kinetic energy theorem states that this will increase the kinetic energy of the system! ωf ωi If Ii L L Physics 211 Lecture 20, Slide 7 Act A puck slides in a circular path on a horizontal frictionless table. It is held at a constant radius by a string threaded through a frictionless hole at the center of the table. If you pull on the string such that the radius decreases by a factor of 2, by what factor does the angular velocity of the puck increase? A) 2 B) 4 C) 8 ω Physics 211 Lecture 20, Slide 8 Since the string is pulled through a hole at the center of rotation, there is no torque: Angular momentum is conserved. 2 ⎛R⎞ L1 = I1ω1 = mR ω1 = L2 = I 2ω2 = m ⎜ ⎟ ω2 ⎝2⎠ 12 2 mR ω1 = m R ω2 4 1 ω2 = 4ω1 ω1 = ω2 4 2 m R ω1 m R/2 ω2 Physics 211 Lecture 20, Slide 9 Food for thought (not on any test) m R ω1 We just used m ω2 R/2 τ ext = 0 to find ω2 = 4ω1 α ≠0 But τ = Iα So how do we get an α without a τ ?? dL d ( Iω ) dI dω τ= = = ω+I dt dt dt dt usually 0, but not now Iα Physics 211 Lecture 20, Slide 10 Food for thought (not on any test) τ EX T = I α + ω dI dt Now suppose τEXT = 0: dI Iα +ω =0 dt α=− ωdI I dt So in this case we can have an α without an external torque! Physics 211 Lecture 20, Slide 11 Precession Precession The magnitude of the torque about the pivot is τ = mgd. The direction of this torque at the instant shown is out of the page (using the right hand rule). The change in angular momentum at the instant shown must also be out of the page! τ ext dL = dt d L ω pivot mg Physics 211 Lecture 20, Slide 12 Physics torque Precession top view L(t) dL = Ltop dφ dL dφ ( pivot L(t+dt) dL dφ = Ltop = Ltop Ω dt dt Ω τext Ω= τ ext Ltop Physics 211 Lecture 20, Slide 13 Precession τ ext dL = dt In this example: Ω= τ ext = mgd τ ext Ltop mgd Ω= Iω Ltop = I ω d Direction: The tip of L moves in the direction of τ. L ω pivot mg Physics 211 Lecture 20, Slide 14 Preflight A disk is spinning with angular velocity ω on a pivoted horizontal axle as shown. Gravity acts down. In which direction does precession cause the disk to move? A) Out of the page B) Into the page C) Up D) Down disk axle ω pivot Torque is out of the page 24% got this right Physics 211 Lecture 20, Slide 15 In which direction does L point? ω ω A B Physics 211 Lecture 20, Slide 16 In which direction does precession cause the disk to move? A) Into the page B) Out of the page C) Up D) Down ω Torque is out of the page L A) The torque provided by gravity is going out of the page. Therefore, L must change out of the page. However, L since L is in the opposite direction of the axel when drawn from the pivot, precession must make the disk go into the page B) weight is down, torque must be perpendicular to angular momentum thus procession is out of the page D) the torque of weight will be in the downward direction Physics 211 Lecture 20, Slide 17 Preflight A disk is spinning with angular velocity ω on a pivoted horizontal axle as shown. Gravity acts down and the disk has a precession frequency Ω. If the mass of the disk were doubled but its radius and angular velocity were kept the same, the precession frequency would A) Increase B) Decrease ω C) Stay the same Ω M 44% got this right Physics 211 Lecture 20, Slide 18 If the mass of the disk were doubled but its radius and angular velocity were kept the same, the precession frequency would A) Increase B) Decrease C) Stay the same Ω= τ ext Ltop ω Ω M A) The weight of the disc increases, so the torque increases. B) Increasing the mass, means that angular momentum is bigger and torque is kept the same. So a bigger denominator means the precession frequency will decrease. C) Mass is a factor in both the torque and the angular momentum, so any contribution it would make to one is canceled out by its contribution to the other. Physics 211 Lecture 20, Slide 19 Preflight A disk is spinning with angular velocity ω on a pivoted horizontal axle as shown. Gravity acts down and the disk has a precession frequency Ω. If the radius of the disk were doubled but its mass and angular velocity were kept the same, the precession frequency would A) Increase B) Decrease ω C) Stay the same Ω M 60% got this right Physics 211 Lecture 20, Slide 20 If the radius of the disk were doubled but its mass and angular velocity were kept the same, the precession frequency would A) Increase B) Decrease C) Stay the same Ω= τ ext Ltop ω Ω M A) The torgue increases so the procession frequency increases. B) because as the radius increases the moment of inertia of the disk increases, therefore increasing the angular momentum and decreasing the precession frequency. C) Since the radius changes the moment of inertia, which is a factor of both the angular momentum and the torque, the precession frequency should remain the same. Physics 211 Lecture 20, Slide 21 ...
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