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 degree. Determine the numbered section on which the wheel comes to a halt when the deceleration of the wheel has a magnitude of 0.275 rev/s2 and the initial angular velocity is (a) +0.830 rev/s and (b) +2.62 rev/s. (a) Numbered section = (b) Numbered section =

Explanation / Answer

Angular Acceleration = - 0.275 rev/s^2                                       = - 2*0.275 rad/s^2                                       = - 1.727 rad/s^2 (a) Initial angular speed = 0.83 rev/s                                      = 2*0.83 rad/s                                      = 5.215 rad/s Angular displacement = - ^2/2                                       = - (5.215 rad/s)^2/(2*-1.727 rad/s^2)                                       = 7.87 rad                                       = 7.87*(180/) degree                                       = 451.14 degree Numbered section = 4 (b) Initial angular speed = 2.62 rev/s                                      = 2*2.62 rad/s                                      = 16.46 rad/s Angular displacement = - ^2/2                                       = - (16.46 rad/s)^2/(2*-1.727 rad/s^2)                                       = 78.45 rad                                       = 78.45*(180/) degree                                       = 4495.34 degree Numbered section = 6
Initial angular speed = 2.62 rev/s                                      = 2*2.62 rad/s                                      = 16.46 rad/s Angular displacement = - ^2/2                                       = - (16.46 rad/s)^2/(2*-1.727 rad/s^2)                                       = 78.45 rad                                       = 78.45*(180/) degree                                       = 4495.34 degree Numbered section = 6      

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