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need help solving Constants Part C An electric ceiling fan is rotating about a f

ID: 2034356 • Letter: N

Question

need help solving

Constants Part C 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 0.905 rev/s Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.780 m What is the tangential speed vean (t) of a point on the tip of the blade at time t 0.191s? Express your answer numerically in meters per second. View Available Hint(s) Temp Van (t) - 43 Submit Part D What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t E 0. 191 s? Express the acceleration numerically in meters per second squared. View Available Hintis) 11:17 PM 4/1/2018

Explanation / Answer

The initial angular velocity, ?0 = 0.230 rev/s

The angular acceleration, ? = 0.905 rev/s2

The time, t = 0.191 s

The diameter of the circle, d = 0.780 m

r = d/2 = 0.780/2 = 0.39 m

Using the rotational kinematic relation, we have

? = ?0+ ?t

= (0.230 rev/s) + (0.905 rev/s2 )(0.191 s)

= 0.402855 rev/s

C)

The final angular velocity is

? = 0.402855 rev/s

= (0.402855 rev/s)(2? rad/s/1 rev/s)

= 2.531 rad/s

The tangential speed is

v = r?

v = (0.39 m)(2.531 rad/s)

v = 0.987 m/s

D)

The angular acceleration is

?  = 0.905 rev/s2

= (0.905 rev/s2)(2? rad/s2/1 rev/s2)

= 5.686 rad/s2       

The tangential acceleration is

at = r?

= (0.39 m)(5.686 rad/s2)

   = 2.218 m/s2

The radial acceleration is

ac = r?2

= 0.39 x (2.218)^2

= 1.918 m/s^2

The resultant acceleration is

a = sqrt(at2+ac2)

a = sqrt(2.2182 m/s2 + 1.9182 m/s^2)

a = 2.9322 m/s2