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 0.270rev/s . The magnitude of the angular acceleration is 0.891rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.710m .
Part A

Compute the fan's angular velocity magnitude after time 0.190s has passed.

Express your answer numerically in revolutions per second.

Part B

Through how many revolutions has the blade turned in the time interval 0.190s 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 = 0.190s ?

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 = 0.190s ?

Express the acceleration numerically in meters per second squared.

Explanation / Answer

A vf=vi+a*t= 0.27 + 0.891 * 0.19 = 0.43929

B rev=v*t+a*t*t/2= 0.27*0.19 + 0.5*0.891*0.19*0.19 = 0.0513 +0.01608255 = 0.06738255 revolutions

C tangetioal speed: v=(ang velocity)*2*pi*(diameter/2)= 0.27*2*3.14*(0.71/2) = 0.601938 m/s

D acceleration is sqrt((a(tangetial))^2+a(centripetal)^2)=
a(tangetial)=(ang acceleration)*2*pi*(diameter/2)= 0.891*2*3.14*(0.71/2) = 1.9863954m/s^2...
a(centripetal)=(diameter/2)*((ang velocity)*2*pi)^2=(0.71/2)*((0.27)*2*3.14)^2 = 1.021 m/s2
resultant acceleration is= sqrt(1.042441+3.94576685) = 2.2334 m/s2

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