At a county fair there is a betting game that involves aspinning wheel. As the d

Question

At a county fair there is a betting game that involves aspinning wheel. As the drawing shows, the wheel is set intorotational motion with the beginning of the angular section labeled"1" at the marker at the top of the wheel. The wheel thendecelerates and eventually comes to a halt on one of the numberedsections. The wheel in the drawing is divided into twelve sections,each of which is an angle of 30°. Determine the numberedsection on which the wheel comes to a halt when the deceleration ofthe wheel has a magnitude of 0.298 rev/s2 and theinitial angular velocity is (a) +1.42 rev/s and(b) +2.94 rev/s.

Explanation / Answer

(a) angular displacement, = [ 2 -(o)2 ] / 2 = (0 -1.42 2 ) / (2 * - 0.298 ) = 3.383 rot                                        = (3 + 0.383) rot = 0.383 rot ( from marker)                                                                    = 0.383 * 360 o                                                                    = 137.88 o                                 Itcomes to rest in the range of 120 o to 150 oi.e., in the number 5 (b) angular displacement, = [ 2 -(o)2 ] / 2 = (0 -2.942 ) / (2 * - 0.298 ) = 14.502rot                                        = (14 + 0.502 ) rot = 0.502 rot ( from marker )                                                                    = 0.502 * 360 o                                                                    = 180.96o                                 Itcomes to rest in the range of 180 o to 210o i.e., in the number 7 (b) angular displacement, = [ 2 -(o)2 ] / 2 = (0 -2.942 ) / (2 * - 0.298 ) = 14.502rot                                        = (14 + 0.502 ) rot = 0.502 rot ( from marker )                                                                    = 0.502 * 360 o                                                                    = 180.96o                                 Itcomes to rest in the range of 180 o to 210o i.e., in the number 7                                        = (14 + 0.502 ) rot = 0.502 rot ( from marker )                                                                    = 0.502 * 360 o                                                                    = 180.96o                                 Itcomes to rest in the range of 180 o to 210o i.e., in the number 7

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