An electric ceiling fan with blades of diameter 0.760m is rotating about a fixed

Question

An electric ceiling fan with blades of diameter 0.760m is rotating about a fixed axis with an initial angular velocity of 0.200 rev/s . The angular acceleration is 0.883 rev/s^2 .

A) Compute the angular velocity after a time of 0.202 s.

B) Through how many revolutions has the blade turned in this time interval?

C) What is the tangential speed of a point on the tip of the blade at time t = 0.202s

D) What is the magnitude of the resultant acceleration of a point on the tip of the blade at time t = 0.202s ?

Please show work so i can follow alogn and learn. thanks!

Explanation / Answer

a) w2 =w1 + alpha t = 0.2rev/s + 0.883rev/s² * 0.202s = 0.378 rev/s = 2.37 rad/s b) Theta = w1 * t + 0.5 Alphat² = 0.2rev/s * 0.202s + ½ * 0.883rev/s² * (0.202s)² = 0.0584rev = 0.367 rad c) v(0.199s) = w2 * r = 2.37rad/s * 0.76m/2 = 0.9006 m/s d) tangential acceleration = Alpha * r = 0.883rad/s² * 0.76m/2 = 0.33 m/s² centripetal acceleration = (w2)² * r = (2.37rad/s)² * 0.38m =2.13 m/s² resultant acceleration = sqrt(0.33² + 2.13²) m/s² = 2.15 m/s²

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