Review of Quiz 4Problem 1Problem 2Problem 3Problem 4Problem 5Problem 6Slide 8Problem 7Slide 10A Narrative: Where We’ve BeenFinalComputing GradesGrade ScaleFinal Exam Topics & ProblemsSlide 1601/14/1901/14/19 Physics 253Physics 25311Review of Quiz 4Review of Quiz 4•Total: 50Total: 50•Average: 28.4Average: 28.4•High: 47High: 47•Low: 5Low: 501/14/1901/14/19 Physics 253Physics 25322Problem 1Problem 1•Problem 1 (5 points): Suppose a 7.5kg mass is rotating Problem 1 (5 points): Suppose a 7.5kg mass is rotating about an axis at a distance of 5 m. What is the object’s about an axis at a distance of 5 m. What is the object’s moment of inertia about the axis?moment of inertia about the axis?a) 38 kg-ma) 38 kg-m22b)190 kg-mb)190 kg-m22 c)280 kg-mc)280 kg-m22 d)400 kg-md)400 kg-m22•Answer:Answer:22221905.187)5)(5.7(kgmkgmmkgmRI01/14/1901/14/19 Physics 253Physics 25333Problem 2Problem 2•Problem 2 (5 points): What is the vector product of Problem 2 (5 points): What is the vector product of AAxxBB if if A=3A=3ii and and BB=4=4jj? ? a) 3a) 3ii + 4 + 4jjb) 0b) 0c) 0.7c) 0.7iid) 12d) 12kk•Answer:Answer:  kjiABBAkkjiBAkBABAjBABAiBABABAxyyxzxxzyzzyˆˆ RHR by the and12)90sin()4)(3(sinor4)043(ˆ00ˆ)00()(ˆˆ)(01/14/1901/14/19 Physics 253Physics 25344Problem 3Problem 3•Problem 3 (5 points): A post is driven perpendicularly into Problem 3 (5 points): A post is driven perpendicularly into the ground and serves as the axis about which a gate the ground and serves as the axis about which a gate rotates. A force of 12N is applied perpendicular to the gate rotates. A force of 12N is applied perpendicular to the gate and acts parallel to the ground. How far from the post and acts parallel to the ground. How far from the post should the force be applied to produce a torque of 3.0 Nm?should the force be applied to produce a torque of 3.0 Nm?a) 0.25ma) 0.25mb) 4.0mb) 4.0m c) 36m c) 36md) 12 d) 12 mm•Answer:Answer:mNNmFRRFRF25.0120.3sin01/14/1901/14/19 Physics 253Physics 25355Problem 4Problem 4•Problem 4 (5 points): A constant torque of 30Nm is applied Problem 4 (5 points): A constant torque of 30Nm is applied to a merry-go-round for 10 seconds. Neglecting friction to a merry-go-round for 10 seconds. Neglecting friction what is the magnitude of the change of the merry-go-what is the magnitude of the change of the merry-go-round’s angular momentum?round’s angular momentum?a)3kg-ma)3kg-m22/s/sb)0.3kg-mb)0.3kg-m22/s /s c) 300kg-mc) 300kg-m22/s /s d) 3kg-md) 3kg-m22/s/s•Answer:Answer:skgmsNmtLdtLd/3001030201/14/1901/14/19 Physics 253Physics 25366Problem 5Problem 5•Problem 5 (5 points): A disk of 4.0 kg and 0.20 m is rotating Problem 5 (5 points): A disk of 4.0 kg and 0.20 m is rotating about its axis of symmetry at about its axis of symmetry at  =10 rads/sec. What is the =10 rads/sec. What is the rotational kinetic energy? rotational kinetic energy? •AnswerAnswerJsradmkgMRIKE1)/10()10.0)(0.4(21212121212222201/14/1901/14/19 Physics 253Physics 25377Problem 6Problem 6•Problem 6 (10 points): Starting from rest a 5.0kg cylinder of Problem 6 (10 points): Starting from rest a 5.0kg cylinder of radius 0.5m rolls down an inclined plane without slipping or radius 0.5m rolls down an inclined plane without slipping or sliding. How much will the height of the cylinder have sliding. How much will the height of the cylinder have decreased when the velocity is 10m/s?decreased when the velocity is 10m/s?.2121 :so zero arelocity angular ve and velocity initial First the velocity.final thegiven hieght final for the solve tohave weNow .21212121result As 10m/s. of velocity a toscorrespond second theand hill theof top at the isposition first the where, is,That energy. mechanical ofon conservati is thereveconservati is field nalgravitatio searth' theSince222221222222211221121ImvmgymgyImvmgyImvmgyPEKEPEKEEE+5pts01/14/1901/14/19 Physics 253Physics 25388mmsmsmgvhvghmvmvmvRvMRmvmgh mRIRvImvmgh87.7)/8.9(4)/10(343434341 21 )/(212121 ng,substituti,21 and /cylinder aFor .2121height of change in the interested are weSecond2222222222222+5pts01/14/1901/14/19 Physics 253Physics 25399Problem 7Problem 7Problem 7(15points): As Problem 7(15points): As shown in the figure, a shown in the figure, a diver of weight 530 N is diver of weight 530 N is poised at the right end of a poised at the right end of a diving board. The board diving board. The board has length 3.90 m. The has length 3.90 m. The board has negligible board has negligible weight and is bolted down weight and is bolted down at the left end while at the left end while supported 1.4 m away by a supported 1.4 m away by a fulcrum. Draw the fulcrum. Draw the equilibrium diagram with equilibrium diagram with all three forces involved. all three forces involved. Find the forces F1 and F2 Find the forces F1 and F2 that the bolt and fulcrum that the bolt and fulcrum exert on the board.exert on the board. +5pts01/14/1901/14/19 Physics 253Physics 2531010NFNmNmFNmFmWlFlFNFFNFFWFFFWy950 have eequation wfirst theinto ngSubstituti1480)4.1()530)(9.3()530)(9.3()4.1()0(05305300122221212121+5pts+5pts01/14/1901/14/19 Physics 253Physics 2531111A Narrative: Where We’ve BeenA Narrative: Where We’ve Been•Started by describing linear motion with constant Started by describing linear motion with constant acceleration, free fall, and projectile motion.acceleration, free fall, and projectile motion.•Studied Newton’s 2Studied Newton’s 2ndnd Laws and Law of Gravitation Laws and Law of Gravitation and saw how these can be quantitatively applied to and saw how these can be quantitatively applied to many systems.many systems.•Laws naturally lead to concepts of work, energy, Laws naturally lead to concepts of work, energy, and conservation of energy and momentum.and conservation of energy and momentum.•Finally applied these to find complete analog to Finally applied these to find complete analog to rotational motion.rotational motion.•We can now describe the mechanical universe