Lect15 - Physics 211 Lecture 15 Today's Concepts: Parallel...

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Unformatted text preview: Physics 211 Lecture 15 Today's Concepts: Parallel Axis Theorem Torque & Angular Acceleration Physics 211 Lecture 15, Slide 1 Physics everything Nothing 42 42 Inertia that has several components. I really wish I had watched this before finishing the homework...that way there wouldn't be a head shaped dent in my wall. the comparison between the angular and linear equations Right hand rule and the vectors and equations associated with it. parallel axis theorem, and I love how the wrench used in the prelecture said said physics on it! Need more Bruce. Through lecture 13 topics that will be on second midterm Why exactly is the direction of torque parallel to the axis of rotation? It kinda makes sense when you think about how other directions would make even less makes even sense, but it still seems sort of arbitrary. What is up with that thumb rule? Is that really going to help me or is it just going or to make me look like an idiot when i'm in Grainger doing this week's in homework? I'd like further explanation about how torque is related to forces and moment of inertia. Also, that upside down right hand was disturbing. all of them! then we can go over how the bears=illini=suck! What is full when it is half empty? A: A skilift Rene Descartes walked into a bar. The bartender asked him if he wanted a Physics drink. Descartes said "I think not" and then disappeared.Physics 211 Lecture 15, Slide 2 Everything. I'm going to fail this class now. This stuff is so complicated. Everything. Please have mercy on us with the exams. I beg you on behalf of 700 students of the class. Think of this way, you'll be sure to go to heaven if you help 700 people. God would surely love that. Also, you never know.. know.. you just might just get a box of chocolates after class everyday. Just think about it. :) Speaking of exams… We have one Thursday night -Sign up for the conflict if you have to -We will review the Spring/09 exam during Wednesdays lecture I tell you that I tried everything to get posted- jokes, interesting comments, jokes, bribes- and you post THAT comment? My humor and personality aren't and powerpointworthy, only my patheticness. And now I am making up words. Today's treat (for doing well on clicker questions) Today's Will delay HW-9 until next week Right Hand Rule for finding Directions Physics 211 Lecture 15, Slide 5 Physics Act Act A ball rolls across the floor, and then starts up a ramp as shown below. In what direction does the angular velocity vector point when the ball is rolling up the ramp? A) into the page B) out of the page Physics 211 Lecture 15, Slide 6 Act Act A ball rolls across the floor, and then starts up a ramp as shown below. In what direction does the angular acceleration vector point when the ball is rolling up the ramp? A) into the page B) out of the page Physics 211 Lecture 15, Slide 7 Act Act A ball rolls across the floor, and then starts up a ramp as shown below. In what direction does the angular acceleration vector point when the ball is rolling back down the ramp? A) into the page B) out of the page Physics 211 Lecture 15, Slide 8 Parallel Axis Theorem Smallest when D=0 Physics 211 Lecture 15, Slide 9 Physics Act A solid ball of mass M and radius is connected to a rod solid and of mass m and length L as shown. What is the moment and as of inertia of this system about an axis perpendicular to the other end of the rod? 2 12 2 2 A) I = MR + ML + mL 5 3 2 1 2 2 B) I = MR + mL + ML2 5 3 C) I = 2 1 MR 2 + mL2 5 3 12 D) I = ML + mL 3 2 R M m L axis Physics 211 Lecture 15, Slide 10 Prelecture A ball of mass 3M at x=0 is connected to a ball of mass ball 3M at x=0 is M at x=L by a massless rod. Consider the three rotation at x=L by axes A, B and C as shown, all parallel to the y axis. and as axis. For which rotation axis is the moment of inertia of the object smallest? (It may help you to figure out where the center of mass of the object is.) A C B y x M 3M L 70% got this right 0 L/4 L/2 Physics 211 Lecture 15, Slide 11 For which rotation axis is the moment of inertia of the For object smallest? A) Most of the mass is nearest to this axis, therefore the moment of rotational inertia is not as large. A y B) The axis at the center of the mass has the smallest moment of inertia for the object. C) The center of mass will have the smallest amount of inertia. C B x M 3M L 0 L/4 L/2 Physics 211 Lecture 15, Slide 12 τ = rFsin(θ) rFsin( Physics 211 Lecture 15, Slide 13 Physics Prelecture In Case 1, a force F is pushing perpendicular on an object a In distance L/2 from the rotation axis. In Case 2 the same force is pushing at an angle of 30 degrees a distance L from the axis. In which case is the torque due to the force about the rotation axis biggest? A) Case 1 B) Case 2 B) axis axis L/2 90o Case 1 68% got this right C) Same C) F L 30o F Case 2 Physics 211 Lecture 15, Slide 14 In which case is the torque due to the force about the In rotation axis biggest? A) Case 1 B) Case 2 C) Same B) axis A) The biggest torque is produced when the force remains perpendicular to the object. B) Even though in case 2 the force is not perpendicular to the object, it acts at a longer distance so that the torque is higher in the second case. C) In the first case torque is FL/2 in the second case torque is FLsin30=FL/2 thus both have the same torque 90o L/2 F Case 1 axis L 30o F Case 2 Physics 211 Lecture 15, Slide 15 Similarity to 1D motion Physics 211 Lecture 15, Slide 16 Physics ACT Strings are wrapped around the circumference of two solid disks and pulled with identical forces. Disk 1 has a bigger radius, but both have the same moment of inertia. Which disk has the biggest angular acceleration? (a) disk 1 ω2 ω1 (b) disk 2 (c) same F F Physics 211 Lecture 15, Slide 17 Prelecture Two hoops can rotate freely about fixed axles through their centers. The hoops have the same mass, but one has same twice the radius of the other. Forces F1 and F2 are applied twice of and are as shown. How are the magnitudes of the two forces related if the angular acceleration of the two hoops is the same? A) F2 = F1 B) F2 = 2F1 2F F1 F2 C) F2 = 4F1 4F 59% got this right Case 1 Case 2 Physics 211 Lecture 15, Slide 18 Physics How are the magnitudes of the two forces related if the angular acceleration of the two hoops is the same? A) F2 = F1 B) F2 = 2F1 2F F1 F2 C) F2 = 4F1 4F M, R Case 1 M, 2R Case 2 A) The angle of the applied force is the same in both cases, as well as the angular acceleration. Therefore, the forces must be equal. B) rF = Ia, rF = mr^2a, F = mra. Therefore, if the radius is doubled, the Ia mr^2a, perpendicular force must be doubled to prevent angular acceleration from changing. C) wheel 2 has a bigger moment of inertia and will requie a biiger biiger force to spin at the same ang accel. The third answer is right because force accel I depends on the square of the radius Physics 211 Lecture 15, Slide 19 Physics ACT Two identical hoops can rotate freely about fixed axles through their centers. The a force having the same magnitude but different direction is applied to the hoops as shown. How does the angular acceleration in the two cases compare? F Α) α1 = α2 60o F Β) α1 = 2α2 C) α1 = 4α2 α1 α2 Case 1 Case 2 Physics 211 Lecture 15, Slide 20 Physics ACT A solid disk of mass M and radius R has a force F acting tangent and has acting to its outer edge as shown. If the disk is free to rotate about an axis through its center, what is its angular acceleration? F Α) α = 2F/MR Β) α = 2FR/M Β) C) α = 2F/MR2 R M α Physics 211 Lecture 15, Slide 21 Physics ...
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This note was uploaded on 09/22/2011 for the course PHYSICS 211 taught by Professor Selig during the Fall '10 term at University of Illinois, Urbana Champaign.

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