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 0.750 m . Part A Compute the fan's angular velocity magnitude after time 0.191 s has passed. Express your answer numerically in revolutions per second. Part B Through how many revolutions has the blade turned in the time interval 0.191 s from Part A? Express the number of revolutions numerically Part C What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.191 s ? Express your answer numerically in meters per second. Part D What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.191 s ? Express the acceleration numerically in meters per second squared.

Explanation / Answer

A vf=vi+a*t=0.455 rev/s

B rev=v*t+a*t*t/2=0.0702 revolutions

C tangetioal speed: v=(ang velocity)*2*pi*(diameter/2)=
1.072 m/s

D acceleration is sqrt((a(tangetial))^2+a(centripetal)^2)=
a(tangetial)=(ang acceleration)*2*pi*(diameter/2)=2.16298 m/s^2
a(centripetal)=(diameter/2)*((ang velocity)*2*pi)^2=3.06488 m/s2
resultant acceleration is 3.75 m/s2

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