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 0.220 rev/s . The angular acceleration is 0.916 rev/s2 . Its blades form a circle of diameter 0.800 m .

partC:

What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.210 s ? Express your answer numerically in meters per second.

Part D:

Part D

What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.210 s ?

Express the acceleration numerically in meters per second squared.

Explanation / Answer

o = 0.220rev/s * 2rads/rev = 1.38 rad/s

a) = o + t = 1.38rad/s + 0.916rad/s² * 0.210s =1.572 rad/s

b) = o*t + ½t² = 1.38rad/s * 0.210s + ½ * 0.916rad/s² * (0.210s)² =0.310 rads
or = 0.0493 revs

c) v = t = 1.572rad/s * 0.80m / 2 = 0.629 m/s

d) tangential at = r = 0.916rad/s² * 0.80m/2 = 0.3664 m/s²
centripetal ac = ²r = (1.50rad/s)² * 0.80m/2 = 0.6 m/s²
a = (at² + ar²) = 0.7030 m/s²

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