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 0.920 rev/s^2. Both the angular velocity and the angular acceleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.720 m.

A) Compute the fan's angular velocity magnitude after time 0.198 s has passed. ANSWER: 0.483 rev/s

HELP WITH:

B) Through how many revolutions has the blade turned in the time intercval 0.198 s from Part A?

C) What is the tangential speed vtan(t) of a point on the tip of the blade at time t=0.198 s ?

D) What is the magnitude (alpha) of the resultant acceleration of a point on the tip of the blade at time t=0.198 s ?

Explanation / Answer

a) ?2 = ?1 + ?t = 0.3rev/s + 0.92rev/s * 0.199s = 0.483 rev/s = 3.04 rad/s

b) ? = ?1 * t + ?t = 0.3rev/s * 0.199s + * 0.92rev/s * (0.199s) = 0.0779 rev = 0.490 rad

c) v(0.199s) = ?2 * r = 3.04rad/s * 0.76m/2 = 1.16 m/s

d) tangential acceleration = ? * r = 0.92rad/s * 0.76m/2 = 0.35 m/s
centripetal acceleration = (?2) * r = (3.04rad/s) * 0.38m = 3.51 m/s
resultant acceleration = sqrt(0.35 + 3.51) m/s = 3.53 m/s

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