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 0.880 rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.800 m .

A) Compute the fan's angular velocity magnitude after time 0.209 s has passed.

B)Through how many revolutions has the blade turned in the time interval 0.209 s from Part A?

C)What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.209 s ?

D)What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.209 s ?

Explanation / Answer

from the rotational kinematic equation the final angualr velocity

wf = wi + alph t

=0.280+ 0.880)( 0.209)

=0.463 rev/s

(B) = 0t+(1/2)t2 =0.280(0.209) + 1/2 ( 0.880)( 0.209)^2 = 0.077 rev

(C)

the tangential speed

v = r w = 0.4( 0.463 rev/s( 2 pi rad) = 1.16 m/s

(D)

at= r= (0.4 m)(0.88 rev/s2)( 2 pi)=2.21 m/s^2

ac = r w^2 = 0.4( ( 0.463 rev/s( 2 pi rad)^2 = 3.38 m/s62

resultant accleration

a = root at^2 +a c^2 = root 2.21^2 + 3.38 ^2 = 4.03 m/s^2

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