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 0.230 rev/s . The magnitude of the angular acceleration is 0.913 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 .

Compute the fan's angular velocity magnitude after time 0.204 s has passed.

Through how many revolutions has the blade turned in the time interval 0.204 s from Part A?

What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.204 s ?

Explanation / Answer

Part A.

Given that

initial angular velocity = wi = 0.230 rev/sec = 1.445 rad/sec

angular acceleration = alpha = 0.913 rev/sec^2 = 5.736 rad/sec^2

final angular velocity = wf = ?

t = 0.204 sec

Using equation

wf = wi + alpha*t

wf = 1.445 + 5.736*0.204 = 2.615 rad/sec = 0.416 rev/sec

Check the unit in which you need your answer.

Part B.

theta = wi*t + 0.5*alpha*t^2

Using know values

theta = 1.445*0.204 + 0.5*5.736*0.204^2 = 0.414 rad = 0.066 rev

Part C.

Tangential speed is given by:

Vt = wf*r

r = radius = 0.700/2 = 0.350

wf = 0.416 rev/sec

So,

Vt = 0.416*0.350 = 0.146 m/sec

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