Question

5) 8 points A point mass of 12 kg is mounted to the end of a massless bar that is R = 0.6 m in length. It rotates at 6 revis around a vertical axis and is placed onto a surface for which p = 0.25. Eventually, it comes to rest. a) 5pt Find the time it takes to come to a stop. b) 3pt How many rotations did it take to come to a stop?

Answer 1

1. mg Frictional torque, e= -lugh e Angulair Aatardating, «= I : - -Mmgr =-ug MR з Initial angular velocity, W. = 20 No = 20 (6) - Wo=127 radls final angular velocity, wf = 0 radls By equation of motion in angular variables, as We = Wotat 0 = 126 - Mq + - R t= 12TR - 12 x A x 0.6 = 2.887s 1. ug 0.25x10 = 9.0478 b) By equation of motion, we - wo² = 240 0-(1217)* = 27-MG) A= 144 A²R = 54.286a radians = 144 x²x0.6 2x0.25 x 10 2 мя Noocf rotations, N= B 27 = 54.2867 = 27.14 “ 28 rotations 25

Bob makes approximately 28 rotations.