<p>An electric ceiling fan is rotating about a fixed axis with an initial angula

Question

<p>An electric ceiling fan is rotating about a fixed axis with an initial angular velocity of 0.210 rev/s . The angular acceleration is 0.903 rev/s^2 . Its blades form a circle of diameter 0.800 m .<br />a) Compute the angular velocity of the fan after time 0.209 s has passed.<br />Express your answer numerically in revolutions per second.<br />b) Through how many revolutions has the blade turned in the time interval 0.209 s from Part A?<br />Express the number of revolutions numerically.<br />c) What is the tangential speed of a point on the tip of the blade at time = 0.209 s ? <br />Express your answer numerically in meters per second.</p>
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Explanation / Answer

An electric ceiling fan is rotating about a fixed axis with an initial angular velocity of 0.210 rev/s . The angular acceleration is 0.903 rev/s^2. Its blades form a circle of diameter 0.800 m. a) Compute the angular velocity of the fan after time 0.209s has passed. 0.21+0.903*0.209=0.4(rev/s)=2.5(rad/s) b)Through how many revolutions has the blade turned in the time interval 0.209s from Part A? 0.21*0.209+0.903*0.209^2/2=0.064(rev) c) What is the tangential speed of a point on the tip of the blade at time = 0.209s ? v=R*w=2.5*0.4=1(m/s) d) What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time = 0.209s ? a_centripetal=v^2/r=2.5(m/s2). a_tangental=0.903*2*pi*0.4=2.3(m/s2) so a_re=sqrt(a1^2+a2^2)=3.4(m/s2)

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