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 0.290 rev/s . The magnitude of the angular acceleration is 0.919 rev/s2 . Both the the angular velocity and angular accleration are directed clockwise. The electric ceiling fan blades form a circle of diameter 0.790 m .

Part A

Compute the fan's angular velocity magnitude after time 0.210 s has passed.

Express your answer numerically in revolutions per second.

Part B

Through how many revolutions has the blade turned in the time interval 0.210 s from Part A?

Express the number of revolutions numerically.

Part C

What is the tangential speed vtan(t) of a point on the tip of the blade at time t = 0.210 s ?

Express your answer numerically in meters per second.

Part D

What is the magnitude a of the resultant acceleration of a point on the tip of the blade at time t= 0.210 s ?

Express the acceleration numerically in meters per second squared.

Explanation / Answer

A) Apply,

w2 = w1 + alfa*t

= 2.9 + 0.919*0.21

= 3.093 rev/s

B) angular dispalcement, theta = w1*t + 0.5*alfa*t^2

= 2.9*0.21 + 0.5*0.919*0.21^2

= 0.63 revolutions

C) r = d/2 = 0.79/2 = 0.395 m

V_tan = r*w2

= 0.395*3.093

= 1.22 m/s

d) a_rad = v^2/r

= 1.22^2/0.395

= 3.77 m/s^2

a_tan = r*alfa

= 0.395*0.919

= 0.363 m/s^2

a_total = sqrt(a_rad^2 + a)tan^2)

= sqrt(3.77^2 + 0.363^2)

= 3.79 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.