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 0.210rev/s . The magnitude of the angular acceleration is 0.908rev/s^2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.750m . Part A Compute the fan's angular velocity magnitude after time 0.209s has passed. Express your answer numerically in revolutions per second. ___rev/s Part B Through how many revolutions has the blade turned in the time interval 0.209s from Part A? Express the number of revolutions numerically. ___ rev Part C What is the tangential speed v_tan(t) of a point on the tip of the blade at time t = 0.209s ? Express your answer numerically in meters per second. v_tan(t) = ___ m/s Part D What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t = 0.209s ? Express the acceleration numerically in meters per second squared. a = ______m/s^2

Explanation / Answer

a) = 0 + t

= 0.21 + 0.908*0.209 = 0.3998 rev/s

b) = 0*t + 1/2**t^2

= 0.21*0.209 + 1/2*0.908*0.209^2 = 0.0637 rev

c) v = r*2 = (0.75/2)*0.3998*2*3.14 = 0.9415 m/s

d) a_t = r*2 = (0.75/2)*0.908*2*3.14 = 2.1383 m/s^2

a_r = r(*2)^2 = (0.75/2)*(0.3998*2*3.14)^2 = 2.3639 m/s^2

a = (a_r^2 + a_t^2) = (2.1383^2 + 2.3639^2) = 3.1876 m/s^2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.