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 0.916 rev/s . Both the the angular velocity and angular accleration are directed clockwise.
The electric ceiling fan blades form a circle of diameter 0.800 m .


a. Compute the fan's angular velocity magnitude after time 0.210 has passed.

b. Through how many revolutions has the blade turned in the time interval 0.210 s from Part A?

c.What is the tangential speed of a point on the tip of the blade at time = 0.210 ?
Express your answer numerically in meters per second.

d. What is the magnitude of the resultant acceleration of a point on the tip of the blade at time = 0.210 ?
Express the acceleration numerically in meters per second squared.

Explanation / Answer

a)=0+t

=0.28+0.916*0.21=0.47236rev/s

b)=0.28*0.21+0.5*0.916*0.212=0.079revolutions

c)v=r=2*0.47236*0.4=1.187m/s

d)resultant acceleration=sqrt( (2r)2+(r)2)=2.37m/s2

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