chp. 9.1-9.5 #9 An electric ceiling fan is rotating about a fixed axis with an i

Question

chp. 9.1-9.5 #9

An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.210 rev/s . The magnitude of the angular acceleration is 0.900 rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.760 m .

The fan's angular velocity magnitude after time 0.197s had passed was 0.387 Rev/s

Part B) Through how many revolutions has the blade turned in the time interval 0.197 s from Part A? Express the number of revolutions numerically. (answer's are NOT: .0604 rev, .0603 rev, or 6.04x10^-2 rev

Part D) What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.197 s ? Express the acceleration numerically in meters per second squared.

Explanation / Answer

wi = 0.210 rev/sec = 1.319 rad/sec

angular acceleration = 0.900 rev/sec^2 = 0.9*3*pi = 5.65 rad/sec^2

radius = 0.760/2 = 0.380 m

t = 0.197 sec

wf = 0.387 rev/sec = 2.431 rad/sec

B.

wf = wi + alpha*t

wf = 0.210 + 0.900*0.197 = 0.387 rad/sec

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

theta = 0.210*0.197 + 0.5*0.9*0.197^2

theta = 0.0588 rev

D.

tangential acceleration

at = alpha*r = 5.65*0.38 = 2.147 m/sec^2

ac = v^2/r = w^2*r = 2.431*2.431*0.38 = 2.245 m/sec^2

a = sqrt(at^2 + ac^2) = sqrt (2.147^2 + 2.245^2)

a = 3.106 m/sec^2

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