An electric ceiling fan is rotating about a fixed axis with an initial angular v
ID: 1369933 • Letter: A
Question
An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.290 rev/s . The magnitude of the angular acceleration is 0.919 rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.790 m .
Part A
Compute the fan's angular velocity magnitude after time 0.210 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 0.210 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 = 0.210 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= 0.210 s ?
Express the acceleration numerically in meters per second squared.
Explanation / Answer
a.
Using the rotational kinematic relation, we have
= 0+ t = (0.290 rev/s)+(0.919 rev/s2)(0.210 s) = 0.483 rev/s
b.
Using the rotational kinematic relation, we have
= 0t+(1/2)t2 = (0.290 rev/s)(0.210 s)+(1/2)(0.919 rev/s2)(0.210 s)2 = 0.0811 rev
c.
The final angular velocity is
= 0.483 rev/s = (0.483 rev/s)(2 rad/s/1 rev/s) = 3.033 rad/s
The tangential speed is
v = r = (0.395 m)(3.033 rad/s) = 1.198 m/s
d.
The angular acceleration is
= 0.919 rev/s2 = (0.919 rev/s2)(2 rad/s2/1 rev/s2) = 5.77132 rad/s2
The tangential acceleration is
at= r = (0.395 m)(5.77132 rad/s2) = 2.28 m/s2
The radial acceleration is
ac= r2
= (0.395 m)(3.033 rad/s)2 = 3.633 m/s2
The resultant acceleration is
a = (at2+ac2) = (2.282m/s2+3.6332m/s2) = 4.29 m/s2 = 4.3 m/s2
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