t An Electric Ceiling Fan Constants Part A An electric ceiling fan is rotating a
ID: 2036685 • Letter: T
Question
t An Electric Ceiling Fan Constants Part A An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.300 ((rm rev/s)). The magnitude of the angular Compute the fan's angular velocity magnitude after time O.199 (frm sj) has passed Express your answer numerically in revolutions per second. View Available Hint(s) acceleration is 0.880 Vfrm revis 2)). Both the the angular velocity and angular accleration are directed clockwise. The electric celing fan blades form a circle of diameter 0.700 flrm m)U) (rm rev/sl) Submit Part B Through how many revolutions has the blade tuned in the time interval 0.199 (m sj) from Part A? Express the number of revolutions numerically View Availiable Hint(s irm rev) Submit
Explanation / Answer
The initial angular velocity, ?0 = 0.300 rev/s
The angular acceleration, ? = 0.880 rev/s2
The time, t = 0.199 s
The diameter of the circle, d = 0.700 m
The radius of the circle, r = d/2 = 0.700 m/2 = 0.350 m
a. Using the rotational kinematic relation, we have
? = ?0+ ?t = (0.300 rev/s)+(0.880 rev/s2 )(0.199 s) = 0.475 rev/s
b. Using the rotational kinematic relation, we have
? = ?0t + (1/2)?t2 = (0.300 rev/s)(0.199 s)+(1/2)(0.880 rev/s2 )(0.199 s)2 = 0.077 revolutions
c. The final angular velocity, ? = 0.475 rev/s
= (0.475 rev/s)(2? rad/s/1 rev/s)
= 2.985 rad/s
The tangential speed, v = r? = (0.350 m)(2.985 rad/s) = 1.04 m/s
d. The angular acceleration, ? = 0.880 rev/s2
= (0.880 rev/s2)(2? rad/s2/1 rev/s2)
= 5.529 rad/s2
The tangential acceleration, at= r? = (0.350 m)(5.529 rad/s2) = 1.935 m/s2
The radial acceleration, ac= r?2 = (0.350 m)(2.985 rad/s)2= 3.118 m/s2
The resultant acceleration, a = ?(at2+ac2) = 3.67 m/s2
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.