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 0.918 rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.710 m .

Compute the fan's angular velocity magnitude after time 0.200 s has passed. Express your answer numerically in revolutions per second.

Through how many revolutions has the blade turned in the time interval 0.200 s from Part A? Express the number of revolutions numerically.

What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.200 s ? Express your answer numerically in meters per second.

What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.200 s ? Express the acceleration numerically in meters per second squared.

Explanation / Answer

A)

Radius of fan blade=r=0.355 m

The initial angular velocity of fan=wi=0.280

rev/s=0.280*2pi radian/s.

The angular acceleration = a! = 0.918 rev/s^2.=0.918*2pi radian/s^2

time 't'=0.200 s

angular velocity after 0.200 s

wf=wi+a!t

wf = 0.280*2pi +.0.918*2pi *0.2

wf= 2.9128 rad/s

wf=0.4636 rev./s  

B)

number of revolutions=N=angular displacement O/2pi

angular displacement O=[(wf+wi)/2 ]t=[0.3718]*2pi*0.2=0.07436*2pi radian

number of revolutions=N=O/2pi=0.07436

C)

tangential speed v=r*wf =0.355*2.9128=1.034044 m/s  

D)

resultant acceleration is vector sum of centripetal acceleration and tangential acceleration

centripetal acceleration= Ac =r(wf)^2= 3.01196 m/s^2

tangential acceleration= At=r*a = 0.355*5.7679=2.0476 m/s^2

resultant acceleration = sq rt [Ac^2+At^2] = 3.6420 m/s^2

resultant acceleration of a point on the tip at 0.200 s is 3.6420 m/s^2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.