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 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.
b)Through how many revolutions has the blade turned in the time interval 0.209s from Part A?
c) What is the tangential speed of a point on the tip of the blade at time = 0.209s ?
d) What is the magnitude of the resultant acceleration of a point on the tip of the blade at time = 0.209s ?

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*0.8=2(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=5(m/s2). a_tangental=0.903*2*pi*0.8=4.53 so a_re=sqrt(a1^2+a2^2)=6.6(m/s2)

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