THE PROBLEM On a hot day, you have started a fan blowing air directly on you at

Question

THE PROBLEM On a hot day, you have started a fan blowing air directly on you at 43 rpm j. After f-13 seconds you increase the angular speed and turn the fan by 90 degrees, giving ,-59 rpm . Calculate the average angular acceleration (magnitude and direction). PAPER SOLUTION Solve the problem on paper first, including all four IDEA steps. You will become a better physicist that way! Have you finished your paper solution already? yes o no NTERPRET DEVELOP In your answers below, type wi and wf to representw and w Derive an algebraic expression for the magnitude of the average acceleration. Deive an algebraic expression for the direction of the average acceleration (counterclockwise from as usual) 0-

Explanation / Answer

initial angylar speed Wi = 43 rpm

1rpm = 2pi/6o rad/s

so Wi = 43* 2pi/60 = 4.5 rad/s

final angular speed Wf =59 rpm = 59 * 2pi/60 = 6.18 rad/s i

time = 13 secs

use the identity

Wf = Wi + A t

here A is alpha = angular acceleration = ?

so

A = (Wf- Wi)/t

A =   (6.18/13) i -(4.5/13) j

A = 0.475 i - 0.35 j

magnitude of Alpha A^2 = 0.475^2 + 0.35^2

A = 0.59 rad/s^2

for direction, use tan theta   = 0.35/0.475

theta = 323.6 deg CCW from +axis.
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