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 magnitude of 0.300 rev/s . The magnitude of the angular acceleration is 0.889 rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.700 m .1)

1)What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.201 s ?

Express your answer numerically in meters per second.

2)What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.201 s ?

Express the acceleration numerically in meters per second squared.

Explanation / Answer

2 = 1 + t = 0.3rev/s + 0.889rev/s² * 0.201s = 0.4786 rev/s = 2.97 rad/s



a) v(0.889s) = 2 * r = 2.97rad/s * 0.350 = 1.04m/s

d) tangential acceleration = * r = 0.889rad/s² * 0.350 =0.3111m/s²
centripetal acceleration = (2)² * r = (2.97rad/s)² * 0.35m = 3.08 m/s²
resultant acceleration = sqrt(0.3111² +3.08 ²) m/s² = 3.01m/s²

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