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

Question

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 0.413 rev/s2 and the initial angularvelocity is (a) +1.77 rev/s and(b) +2.42 rev/s.

Explanation / Answer

a) revolution acceleration = a = -0.413 revolution velocity = = -0.413t + 1.77 = 0 when t = 1.77/0.413 revolution = -0.413t2/2 +1.77t =-1.77*1.77/(2*0,413) +1.77*1.77/0.413 = 3.792857...revolutions 3.792857...* 360o = 1365.42857o =285o which will be in the number 9 on the wheel (270 to300 is in the ninth) b) same as a, only with 1.77 switched with 2.42 everywhere: revolution = -0.413t2/2 +2.42t =-2.42*2.42/(2*0.413) + 2.42*2.42/0.413 = 7.09007... revolutions 0.09007 * 360o = 32,426o which will be in thenumber 2 on the wheel (30 to 60)

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