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 0.917 rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.760 m .

A)compute the fan's angular velocity magnitude after time 0.192 s has passed.

Part B

Through how many revolutions has the blade turned in the time interval 0.192 s from Part A?

Part C

What is the tangential speed vtan(t) of a point on the tip of the blade at timet = 0.192 s ?

Part D

What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.192 s ?

Explanation / Answer

a) ?2 = ?1 + ?t = 0.290rev/s + 0.917rev/s² * 0.192s = 0.466rev/s = 2.92 rad/s

b) ? = ?1 * t + ½?t² = 0.290rev/s * 0.192s + ½ * 0.917rev/s² * (0.192s)² = 0.07168 rev = 0.450 rad

c) v(0.192s) = ?2 * r = 2.92rad/s * 0.76m/2 = 1.10 m/s

d) tangential acceleration = ? * r = 0.917rad/s² * 0.76m/2 = 0.3484m/s²
centripetal acceleration = (?2)² * r = (2.92rad/s)² * 0.38m = 3.24 m/s²
resultant acceleration = sqrt(0.3484² + 3.24²) m/s² = 3.2586m/s²

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