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 0.260 rev/s . The magnitude of the angular acceleration is 0.909 rev/s^2 . Both the the angular velocity and angular acceleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.770m . A) Compute the fan's angular velocity magnitude after time 0.204 has passed. B) Through how many revolutions has the blade turned in the time interval 0.204 from Part A? C) What is the tangential speed of a point on the tip of the blade at time = 0.204 ? D) What is the magnitude of the resultant acceleration of a point on the tip of the blade at time = 0.204 ?

Explanation / Answer

angular speed w2=w1+w’*t = 0.26 +0.909*0.204 =0.4454 rev/s;

angular path u =w1*t +0.5w’*t^2 =
= 0.26*0.204 +0.5*0.909*0.204^2 = 0.0719544 rev;

v2=2pi*w2*r = 2pi*0.4454*(0.77/2) =1.07743 m/s;

vector a = (a1,a2), where

a1=2pi*w’*r is tang component of acceleration,

a2=(2pi*w2)^2*r is centripetal acceleration;

thus |a| = (a1^2 +a2^2)

= (0.77/2) ((2pi*0.909)^2 +(2pi*0.4454)^4) =3.73185 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.