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 0.200 rev/s . The magnitude of the angular acceleration is 0.918 m/s^2 . 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 0.206 s has passed Through how many revolutions has the blade turned in the time interval 0.206 s from Part A? What is the tangential speed of a point on the tip of the blade at time = 0.206 s ? What is the magnitude (a) of the resultant acceleration of a point on the tip of the blade at time = 0.206 s ?

Explanation / Answer

A )vf=vi+a*t=0.389 rev/s B )rev=v*t+a*t*t/2=0.0607revolutions C tangetioal speed: v=(ang velocity)*2*pi*(diameter/2)= 0.869 m/s D acceleration is sqrt((a(tangetial))^2+a(centripetal)^2)= a(tangetial)=(ang acceleration)*2*pi*(diameter/2)=2.05 m/s2 a(centripetal)=(diameter/2)*((ang velocity)*2*pi)^2=2.12 m/s2 resultant acceleration is 4.17 m/s2

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