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 0.280 rev/s . The magnitude of the angular acceleration is 0.914 rev/s^2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.700m. A. Compute the fan's angular velocity magnitude after time 0.194s has passed. B. Through how many revolutions has the blade turned in the time interval 0.194s from Part A? C. What is the tangential speed of a point on the tip of the blade at time t = 0.194s? D. What is the magnitude of the resultant acceleration of a point on the tip of the blade at time t= 0.194s ?

Explanation / Answer

a)=o+t

=0.28+0.914*0.194 =0.4573 rev/s or 2.87 rad/s

b) =ot+(1/2)t2

=0.28*0.194+(1/2)*0.914*0.1942 =0.0715 rev or 0.45 rad

c)r=d/2 =0.35m

V=r=0.35*2.87 1m/s

d)resultant acceleration

a=(arad2+atan2)

a=[(2r)2+(r)2]

a=[(2.872*0.35)2+(0.914*0.35)2]

a=2.91m/s2

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