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 0.200 rev/s . The magnitude of the angular acceleration is 0.891 rev/ s 2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.750 m .

Compute the fan's angular velocity magnitude after time 0.201 s has passed. Express your answer numerically in revolutions per second.

Through how many revolutions has the blade turned in the time interval 0.201 s from Part A?

Express the number of revolutions numerically.

What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.201 s ?

Express your answer numerically in meters per second.

What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.201 s ?

Express the acceleration numerically in meters per second squared.

Explanation / Answer

part a )

wf = wi + alpha*t

wf = 0.200 rev/s + 0.891 * 0.201

wf = 0.379091 rev/s = 0.38 rev/s

part b )

wf^2 = wi^2 + 2*alpha*theta

theta = (wf^2 - wi^2) / 2*alpha

theta = 0.058 rev

part c )

radius of the fan = 0.375 m

c = 2pi*r = 2.356 m

blade is moving at 0.38 rev/s

v = w*r

v = 0.89528 m/s

part d )

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

a_cen = v^2/r = 2.137 m/s^2

a_tan = alpha*2pir = 2.356 * 0.891 = 2.099 m/s^2

a = 2.995 m/s^2

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