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

Question

At a county fair there is a betting game that involves a spinning wheel. As the drawing shows, the wheel is set into rotational motion with the beginning of the angular section labeled "1" at the marker at the top of the wheel. The wheel then decelerates and eventually comes to a halt on one of the numbered sections. The wheel in the drawing is divided into twelve sections, each of which is an angle of 30°. Determine the numbered section on which the wheel comes to a halt when the deceleration of the wheel has a magnitude of 0.429 rev/s2 and the initial angular velocity is (a) +0.940 rev/s and (b) +3.18 rev/s.

Explanation / Answer

(a)initial angular velocity , u =.940 rev/s deceleration = -a =.429 rev/s2 final velocity = v = 0. let angle through which the wheel moves be s by equation of motion,v^2 - u^2 = 2as =>-u^2/2a = s = 1.029836 rev => 1 complete rotation and .029836 revolution the numbered section on which the wheel stops = 12.029836*12 = 12.3580 hence the wheel stops on number 1. (b)v=0 ; u=3.18 , -a=.429 s = -u^2/2a = 11.7860 => 11 complete rotation and .786 revolution the numbered section on which the wheel stops = 12*.786 = 9.432 hence the wheel stops on number 10.

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