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Your Comments Will we be expected to reproduce the derivation of the equations? Exams are M/C Talk about precession pretty pretty please!!! It's such a raw, awesome, and difficult concept. Lecture 20 I'm looking forward to seeing everyone stick on their hands and curl the fingers on the exam Not on exam 2 When it comes to the right hand rule, I understand the rule but why would the acceleration, and therefore torque, point in the same direction as the axis of rotation? For example, in the "torque and the cross product" slide, the acceleration is out of the screen. Nothing is coming towards us, correct? Today’s topic In the prelecture's exmaple for calculating moment of intertia for the dumbell, I still don't understand from where did the 1/12 come... Slide 8 on PL 14 Goodness knows physics isn't my favorite subject, but at least I never fall asleep during physics lectures! Let's replicate Felix Baumgartner's awesome space jump and turn it into a fantastic kinematics demonstration! I volunteer myself to jump. Better not… I apologize for the lack of time spent on the pre-lecture. As others have said Relax before, I ran out of time tonight, and so hurriedly completed both the pre-lecture and checkpoint. I hope my grade does not reflect the abysmal lapse in memory. Is there anyway that you could have high schools use this prelecture method? It helps to watch the derivation of the formulas and it definitely beats reading a book. A few do Mechanics Lecture 15, Slide 1 I really try so hard to pay attention during these prelectures because I love it when they teach crazy stuff, but I can only ever think about stupid things while I watch them... Try doing them at a different time of day… Mechanics Lecture 15, Slide 2 Physics 211 Lecture 15 Today’s Concepts: a) Parallel Axis Theorem b) Torque & Angular Acceleration Mechanics Lecture 15, Slide 3 Parallel Axis Theorem I don't understand what the parallel thingy really was or why it is useful I don't understand what the parallel thingy really was or why it is useful Smallest when D = 0 Big Idea is simple: I is bigger when stuff is further from the rotation axis. Mechanics Lecture 15, Slide 4 The parallel axis theorem always confuses me when it comes to rotating multiple three dimensional objects around an axis that is not the center of any three dimensional object. Can you talk a little more about that during lecture? F axis Mechanics Lecture 15, Slide 5 Clicker Question A solid ball of mass M and radius is connected to a thin rod of mass m and length L as shown. What is the moment of inertia of this system about an axis perpendicular to the other end of the rod? 2 1 2 2 2 A) I = MR ML mL 5 3 2 1 2 2 B) I = MR mL ML2 5 3 2 1 2 2 C) I = MR mL 5 3 1 D) I = ML2 mL2 3 R M m L axis Mechanics Lecture 15, Slide 6 CheckPoint A ball of mass 3M at x = 0 is connected to a ball of mass M at x = L by a massless rod. Consider the three rotation axes A, B, and C as shown, all parallel to the y 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 3M M L since the center of mass is at L/4, the smallest moment of inertia will be when this object is rotated about L/4 0 L/4 L/2 Mechanics Lecture 15, Slide 7 Right Hand Rule for finding Directions Big Idea is simple: The axis is the only thing that defines the direction of rotation Professor Selen, I almost stuck my head in a bucket of acid with this prelecture. …The right hand rule showed that the angular velocity was perpendicular to the rotation! How is that even possible if ω=dθ/dt? And the same with torque, perpendicular, so coming out of the screen?!!! Thanks! Mechanics Lecture 15, Slide 8 Clicker Question 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 C) Up D) Down Mechanics Lecture 15, Slide 9 Clicker Question 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 Mechanics Lecture 15, Slide 10 Clicker Question 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 Mechanics Lecture 15, Slide 11 Torque can you go over the torque on the door. t = rF sin(q ) Mechanics Lecture 15, Slide 12 Torque and F=ma F = ma Fq = maq Fq = mr rFq = mr r F = mr 2 t = I v F q r 2 Mechanics Lecture 15, Slide 13 Look at Prelecture slide 9 again It’s all there…. Mechanics Lecture 15, Slide 14 How to think of r x F F q q F F q q q r r F = rF sinq r r =r(Fsinq) =F(rsinq) Mechanics Lecture 15, Slide 15 CheckPoint In Case 1, a force F is pushing perpendicular on an object a 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 C) Same axis axis L/2 90o Case 1 F L 30o F Case 2 Mechanics Lecture 15, Slide 16 CheckPoint In which case is the torque due to the force about the rotation axis biggest? axis A) Case 1 B) Case 2 C) Same 90o L/2 F A) Because the force is perpendicular B) the length in 2 is bigger C) sin(30)=1/2 Case 1 axis L 30o F Case 2 Mechanics Lecture 15, Slide 17 Similarity to 1D motion Mechanics Lecture 15, Slide 18 Clicker Question 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 w2 w1 B) Disk 2 C) same F F Mechanics Lecture 15, Slide 19 CheckPoint Two hoops can rotate freely about fixed axles through their centers. The hoops have the same mass, but one has twice the radius of the other. Forces F1 and F2 are applied 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 F2 F1 C) F2 = 4F1 Case 1 Case 2 Mechanics Lecture 15, Slide 20 CheckPoint How are the magnitudes of the two forces related if the angular acceleration of the two hoops is the same? F2 A) F2 = F1 F1 B) F2 = 2F1 M, R C) F2 = 4F1 Case 1 t = I M, 2R Case 2 RF = MR F = MR 2 Mechanics Lecture 15, Slide 21 t = R F s in q q q = 90 0 q = 00 q = 90 36 = 54 Mechanics Lecture 15, Slide 22 t = R F s in q Direction is perpendicular to both R and F, given by the right hand rule tx = 0 ty = 0 t z = t F1 t F2 t F3 Mechanics Lecture 15, Slide 23 (i) 1 I DISK = MR2 2 (ii) t = I 1 2 (iii) K = Iw 2 Use (i) & (ii) Use (iii) Mechanics Lecture 15, Slide 24