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 0.220 rev/s . The magnitude of the angular acceleration is 0.900 rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.700 m . What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.204 s ? What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.204 s ?

Explanation / Answer

(omega = w), wo = 1.38 rad/s, alpha = 5.65 rad/s^2

w = wo + alpha t

w = 1.38 + (5.65 x .204) = 1.15 rad/s

Vtan = r x w = (.7/2) x 1.15

Vtan = .4 m/s

Atan = r x alpha = (.7/2) x 5.65 = 1.97 m/s^2

Acentripetal = V^2 / r = (.4)^2 / .35 = .45 m/s^2

net acceleration = sqrt (Atan^2 + Ac^2)

Anet = sqrt ((1.97)^2 + (.45)^2)

Anet = 2.02 m/s^2

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