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 0.300rev/s . The magnitude of the angular acceleration is 0.883rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.770m .

1- Compute the fan's angular velocity magnitude after time 0.202s has passed.

2- Through how many revolutions has the blade turned in the time interval 0.202s from Part A?

3-What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.202s ?

4-What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.202s ?

Explanation / Answer

1. wf = wi + alpha*t

wf = 0.300 + (0.883x 0.202) = 0.478 rev/s

wf = 0.478 x 2pi rad/s = 3 rad/s

2. wf^2 -wi^2 = 2 x alpha x @

0.478^2 - 0.300^2 = 2 x 0.883 x @

@ =0.0784rev

3. V_tan = w.r = 3 x (0.770/2) = 1.16 m/s

4. a_t = alpha x r = (0.883 x 2pi rad/s2) x (0.770/2) = 2.14 m/s2

a_c = w^2.r = 3^2 * (0.770/2) =3.47 m/s2

resultant = sqrt(a_t^2 + a_c^2) = 4.07 m/s2

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