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 0.290 rev/s . The magnitude of the angular acceleration is 0.897 rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.780 m .

1.

What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.205 s ?

Express your answer numerically in meters per second.

2.

What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.205 s ?

Express the acceleration numerically in meters per second squared.

Explanation / Answer

1)  2 = 1 + t = 0.29rev/s + 0.897rev/s² * 0.205s = 0.473 rev/s = 2.97 rad/s

v(0.205s) = 2 * r = 2.97 rad/s * (0.78m)/2 = 1.15 m/s

2) tangential acceleration = * r = 0.897rad/s² * (0.78m)/2 = 0.349 m/s²
centripetal acceleration = (2)² * r = (2.97rad/s)² * 0.39m = 3.44 m/s²
resultant acceleration = sqrt(0.349² + 3.44²) m/s² = 3.45 m/s²

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