A ceiling fan is rotating at 1.0 rev/s. When turned off, itslows uniformly to a

Question

A ceiling fan is rotating at 1.0 rev/s. When turned off, itslows uniformly to a stop in 2.0 min. Part A: How many revolutions does the fan make in thistime? Part B: Using the result from part A, find the number ofrevolutions the fan must make for its speed to decrease from 1.0rev/s to 0.5 rev/s. A ceiling fan is rotating at 1.0 rev/s. When turned off, itslows uniformly to a stop in 2.0 min. Part A: How many revolutions does the fan make in thistime? Part B: Using the result from part A, find the number ofrevolutions the fan must make for its speed to decrease from 1.0rev/s to 0.5 rev/s.

Explanation / Answer

      Given that the initial angularvelocity is 1 = 1.0 rev/s = 2 rad/s       Final angular velocity is 2 = 0       Time taken is t = 2.0 min = 120s   -------------------------------------------------------------------------    From the equation of motion angular accelerationis = ( 2 - 1 ) / t                                                                              =-0.052 rad/s2           From the equation of motion angulardisplacement is = (22 -12 ) / 2                                                                                = 379.2 rad (b) from given data final angular velocity is 2 = 0.5 rev/s = rad/s From the equation of motion angulardisplacement is = (22 -12 ) / 2                                                                                =284.7 rad                                 But one rev =2 rad                                                                                    = 45.33 rev

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