How would you do this problem? At a county fair there is a betting game that inv
ID: 1674413 • Letter: H
Question
How would you do this problem?At a county fair there is a betting game that involves a spinningwheel. As the drawing shows, the wheel is set into rotationalmotion with the beginning of the angular section labeled "1" at themarker at the top of the wheel. The wheel then decelerates andeventually comes to a halt on one of the numbered sections. Thewheel in the drawing is divided into twelve sections, each of whichis an angle of 30°. Determine the numbered section on which thewheel comes to a halt when the deceleration of the wheel has amagnitude of 0.246 rev/s2and the initial angular velocity is (a) +0.790 rev/s and (b)+2.62rev/s. (a) Numbered section = (b) Numbered section =
Explanation / Answer
a) angular displacement, =[ 2 - (o)2 ] / 2 = (0 - 0.79 2 ) / (2 * - 0.246 ) = 1.268rot
= (1+ 0.268) rot = 0.268 rot ( from marker)
= 0.268 * 360 o
= 96.48 o
Itcomes to rest in the range of 90 o to 120 oi.e., in the number 9
(b) angular displacement, = [ 2 - (o)2 ] /2 = (0 -2.62 2 ) / (2 * - 0.246 ) =13.952 rot
= (13 + 0.952 ) rot = 0.952 rot ( from marker )
= 0.952 * 360 o
= 342.73o
Itcomes to rest in the range of 330 o to 360 oi.e., in the number 1
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