An electric ceiling fan is rotating about a fixed axis with an initial angular v

Question

An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.210 rev/s . The magnitude of the angular acceleration is 0.881 rev/s^2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.750 m. A) Compute the fan's angular velocity magnitude after time 0.205 s has passed. B) Through how many revolutions has the blade turned in the time interval 0.205 s from Part A? 0.391 rev/ C) What is the tangential speed vtan (t) of a point on the tip of the blade at time = 0.205 s ? 0.065 rev D) What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time = 0.205 ?

Explanation / Answer

A) w = w0+at =>w = 0.210+0.881*0.205 = 0.39 rev/sec = 0.39*2*pi = 2.45 rad/sec B) theta = 0.210*0.205 + 0.5*0.881*0.205*0.205 = 0.061 rev C) tangential velocity = w*r = 2.45*0.75*0.5 = 0.91 m/s D) an = V^2/r = 2.25 m/s^2 at = r*a = 0.30 m/s^2 ares = sqrt(an^2+at^2) = 2.27 m/s^2

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