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Answer to Question #7558 in Mechanics | Relativity for brawlf

Question #7558
A fan blade is initially rotating an angular speed of 4.6 rpm. It slows down and eventually comes to rest in a time of 32 seconds after turning through a total of 8.8 revolutions. Find (a) the angular speed in rad/s, (b) the average angular velocity and (c) the average angular acceleration of the fan blade.
Expert's answer
A fan blade is initially rotating an angular speed of 4.6 rpm. It slows down and eventually comes to rest in a time of 32 seconds after turning through a total of 8.8 revolutions. Find (a) the angular speed in rad/s

4.6 r/m = 4.6/60 r/s = 4.6*2π/60 rad/s = 23/150 rad/s (=0.15(3) rad/s).

(b) the average angular velocity

Va = 8.8 r / 32 s = 0.275 r/s.

(c) the average angular acceleration of the fan blade

V(t) = at + V0,

where V0 = 4.6 r/m = 23/300 r/s and a is a the average angular acceleration. We know that

V(32) = 0 ==> 32a + 23/300 = 0 ==> a = -23*32/300 = -184/75 r/s².

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