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 4/1/2018Explanation / 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
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