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 0.136 rev/s2 and theinitial angular velocity is (a) +1.30 rev/s and(b) +2.10 rev/s.

Explanation / Answer

Initial angular speed w = 1.3 rev / s Angular deceleration = -0.136 rev / s ^2 Final angular speed w ' = 0 rev / s from the relation w ' ^ 2 - w ^ 2 = 2 angular displacement = [ w ' ^ 2 - w ^ 2 ] /2 pulg the values = 6.2132 rev                           = 6.2132 * 360 degrees                           = That is it completes 6 revolutions and trun extra (0.2132 * 360 )                           = complete 6 revolutions + 76.764 degrees                           = 76.764 is in label 3 So, answer is label 3 similarly you do next one

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