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 0.300rev/s . The magnitude of the angular acceleration is 0.917rev/s^2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.800m . A) Compute the fan's angular velocity magnitude after time 0.198s has passed. B) Through how many revolutions has the blade turned in the time interval 0.198s from Part A? C) What is the tangential speed v_tan(t) of a point on the tip of the blade at time t = 0.198s ? D) What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.198s ?

Explanation / Answer

1) Wf=Wi+A*t =.3 + (.917*.198) = 1.415 rev/s 2) Wf^2 - Wi^2 = 2*theta*A theta = (Wf^2 - Wi^2)/2A =(1.415^2-.3^2)/(2*.917) = 1.042 radians 1 revolution = 2*pi radian .159 revolution = 1 radian .165 revolution = 1.042 radian merely 1/8th of a revolution 3) v = 0.5d*Wf = 0.5*.8*1.415 = .566 m/s 4) a= 0.5d*A = 0.5*.8*.917 = .3668 m/s^2

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