An electric ceiling fan is rotating about a fixed axis with aninitial angular ve

Question

An electric ceiling fan is rotating about a fixed axis with aninitial angular velocity of 0.260 rev/s. The angular accelerationis 0.917 rev/s^2. Its blades form a circle of diameter 0.770m.

Part A. Compute the Angular Velocity of the fan after time 0.195shas passed.

Part B. Through how many revolutions has the blade turned inthe time interval 0.195s from part A?

Part C. What is the tangential speed v_tan9t) of a point on the tipof the blade at time t=0.195s?

Part D. What is the magnitude of a of the resultant acceleration ofa point on the tip of the blade at time t=0.195s?

Explanation / Answer

Given that the initial angular velocity is 1 = 0.260rev/s The angular acceleration is = 0.917 rev/s2    The diameter is d = 0.770m    Then the radius is r = d/2 = 0.385 m ------------------------------------------------------------------------- (a) Time taken is t = 0.195s    The angular velocity after time t is     2 = 1 + t             = ----------rev/s (b) The angular displacement is = 1*t +(1/2)t2                                                     = ------- rev    (c) The tangential speed is v = r*2                                              = --------- m/s    (d) The radial acceleration is ac =v2/ r                                                        = -------- m/s2          tangentialacceleration is at = r                                                   = ----------- m/s2       The resultant acceleration is a = (ac2 + at2 )1/2                                                                    = ---------- m/s2

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