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 0.431 rev/s2 and theinitial angular velocity is (a) +1.53 rev/s and(b) +2.44 rev/s.

Explanation / Answer

           Given that the angular accelaration is = -0.431rev/s2 = -0.431*2 rad/s2             Theangle of each section is =300 ----------------------------------------------------------------------- (a) If the initial angular velcoity is 1 =1.53*2 rad/s                finalangular velcoity is 2 = 0 rad/s              Then theangular displacement is = (22-12 )/2                                                              = (0 -12)/2                                                                        =17.05 rad                                                                   =(17.05 rad )(3600/2rad )                                                                   =977.40          so haltat number 4        (b)  If the initial angular velcoity is1 = 2.44*2 rad/s                finalangular velcoity is 2 = 0 rad/s              Then theangular displacement is = (22-12 )/2                                                              = (0 -12)/2                                                                        =(43.37 rad )(3600/2rad )                                                                   =2486.50            sohalt at number 11                Theangle of each section is =300 ----------------------------------------------------------------------- (a) If the initial angular velcoity is 1 =1.53*2 rad/s                finalangular velcoity is 2 = 0 rad/s              Then theangular displacement is = (22-12 )/2                                                              = (0 -12)/2                                                                        =17.05 rad                                                                   =(17.05 rad )(3600/2rad )                                                                   =977.40          so haltat number 4        (b)  If the initial angular velcoity is1 = 2.44*2 rad/s                finalangular velcoity is 2 = 0 rad/s              Then theangular displacement is = (22-12 )/2                                                              = (0 -12)/2                                                                        =(43.37 rad )(3600/2rad )                                                                   =2486.50            sohalt at number 11                   finalangular velcoity is 2 = 0 rad/s              Then theangular displacement is = (22-12 )/2                                                              = (0 -12)/2                                                                        =(43.37 rad )(3600/2rad )                                                                   =2486.50

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