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 0.290 rev/s2 and the initial angular velocity is (a) +1.37 rev/s and (b) +2.06 rev/s.

Explanation / Answer

given

alfa = -0.29 rev/s^2

a) angular displacement, theta = (wf^2 - wi^2)/(2*alfa)

= (0^2 - 1.37^2)/(2*(-0.29))

= 3.236 rev

= 3 revolutions + 0.236 rev

= 3 revolutions + 0.236*360

= 3 revolutions + 85 degrees

4th section on which the wheel comes to a halt

b) angular displacement, theta = (wf^2 - wi^2)/(2*alfa)

= (0^2 - 2.06^2)/(2*(-0.29))

= 7.316 rev

= 7 revolutions + 0.316 rev

= 7 revolutions + 0.316*360

= 7 revolutions + 114 degrees

5th section on which the wheel comes to a halt

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