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 0.230rev/s . The magnitude of the angular acceleration is 0.890rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.750m .

Part A

Compute the fan's angular velocity magnitude after time 0.192s has passed.

Express your answer numerically in revolutions per second.

Part B

Through how many revolutions has the blade turned in the time interval 0.192s 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 = 0.192s ?

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 = 0.192s ?

Express the acceleration numerically in meters per second squared.

Explanation / Answer

A) Apply, w = wo + alfa*t

= 0.23 + 0.89*0.192

= 0.401 rev/sec

B) Apply, theta = wo*t + 0.5*alfa*t^2

= 0.23*0.192 + 0.5*0.89*0.192^2

= 0.06 revolutions

C) v = R*w

= (d/2)*w

= (0.75/2)*0.401*2*pi

= 0.945 m/s

d) a_rad = v^2/r

= 0.945^2/(0.75/2)

= 2.38 m/s^2

a_tan = r*alfa

= (0.75/2)*0.89*2*pi

= 2.097 m/s^2

a = sqrt(a_rad^2 + a_tan^2)

= sqrt(2.38^2 + 2.097^2)

= 3.17 m/s^2

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