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 0.904 rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.750 m .

Part A

Compute the fan's angular velocity magnitude after time 0.209 s has passed.

Part B

Through how many revolutions has the blade turned in the time interval 0.209 s from Part A?

Part C

What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.209 s ?

Part D

What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.209 s ?

Explanation / Answer

  a) 2 = 1 + t = 0.2rev/s + 0.92rev/s² * 0.209s = 0.392 rev/s = 2.463 rad/s

b) = 1 * t + ½t² = 0.2rev/s * 0.209s + ½ * 0.92rev/s² * (0.209s)² = 0.0619 rev = 0.490 rad

c) v(0.209s) = 2 * r = 2.463rad/s * 0.375m/2 = .8479 m/s

d) tangential acceleration = * r = 0.92rad/s² * 0.375m/2 = 0.345 m/s²
centripetal acceleration = (2)² * r = (2.463rad/s)² * 0.375m = 2.27 m/s²
resultant acceleration = sqrt(0.345² + 2.27²) m/s² = 2.296 m/s²

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