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 0.250rev/s . The magnitude of the angular acceleration is 0.881rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.770m .

Part A

Compute the fan's angular velocity magnitude after time 0.190s has passed.

Express your answer numerically in revolutions per second.

Part B

Through how many revolutions has the blade turned in the time interval 0.190s from Part A?

Express the number of revolutions numerically.

Part C

What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.190s ?

Express your answer numerically in meters per second.

Part D

What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.190s ?

Express the acceleration numerically in meters per second squared.

Explanation / Answer

It means that after one second, the ceiling fan will be going 0.92 revolutions per second faster, and after two seconds, it will be going 1.84 revolutions per second faster, and so on.

In other words, after some time t, the angular velocity will be:

v2 = v1 + (0.92 rev/s

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