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 0.280rev/s . The magnitude of the angular acceleration is 0.884rev/s2 . 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 0.193s has passed.

B)Through how many revolutions has the blade turned in the time interval 0.193s from Part A?

C)What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.193s ?

D)What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t= 0.193s ?

Explanation / Answer

a)

W=Wo+alpha*t

W=0.28+0.884*0.193

W=0.4506 rev/s

b)

angular displacement

theta=Wot+(1/2)*alpha*t2=(0.28)*0.193+(1/2)*0.884*0.1932

theta=0.0705 rev

c)

radius

r=0.8/2 =0.4 m

Tangential speed

Vtan=W*r =(0.4506*2pi)*0.4

Vtan=1.13 m/s

d)

Tangential acceleration

atan=alpha*r=(0.884*2pi)*0.4 =2.22 m/s2

Centripetal accelerationa

acen=V2/r =1.132/0.4 =3.19 m/s2

So resultant acceleration

a=sqrt[acen2+atan2]=sqrt[3.192+2.222]

a=3.89 m/s =3.9 m/s (approx)

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