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 0.230rev/s . The magnitude of the angular acceleration is 0.903rev/s 2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.790m . Compute the fan's angular velocity magnitude after time 0.210s has passed.Through how many revolutions has the blade turned in the time interval 0.210s from Part A?What is the tangential speed v tan (t) of a point on the tip of the blade at time t = 0.210s ?What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.210s ?

Explanation / Answer

angular velocity

W =0.23 *2pi =1.445 rad/s

angular accelration

alpha -0.907*2pi =5.674 rad/s^2

r=d/2 =0.395 m

a)

V =rW =0.395*1.445

V=0.57 m/s

b)

tangential acceleration

at=r*alpha =0.395*5.674

at=2.24 m/s^2

radial acceleration

ar=rW^2=0.395*1.445^2

ar=0.8247 m/s^2

resultant acceleration

a =sqrt[at^2+ar^2]

a =2.387 m/s^2

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