An electric ceiling fan with blades of diameter 0.800m is rotating about a fixed

Question

An electric ceiling fan with blades of diameter 0.800m is rotating about a fixed axis with an initial angular velocity of 0.230 rev/s . The angular acceleration is 0.887 rev/s^2. A) Compute the angular velocity after a time of 0.199s 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 = 0.199s ? D) What is the magnitude of the resultant acceleration of a point on the tip of the blade at time t= 0.199s ? All answers have to be to 4 sig figs.

Explanation / Answer

A) W = R1 * a*t = .23 + .887*0.199 = .4866 rev/sec B) T = R1*t + ½a*t² = .23*0.199 + ½*0.887*.0.199² = .0802 rev C) Vt = r*W = (.75/2)*(.4866 r/s)*(2prad/r) = 1.147 m/s D) At = a*r = (.3*2p)*(.75/2) = .70686 m/s²; Ac = Vt²/r = 1.147²/.375 = 3.5083 m/s²; Ar = v(At² + Ar²) = 3.5788 m/s²

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