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A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s. It is then turned off and coasts to a stop in an additional 40 s. The ratio of the average angular acceleration for the first 20 s to that for the last 40 s is which of the following?

a.2
b.-0.5
c.0.5
d.-2

Respuesta :

Answer:

option D

Explanation:

given,

angular speed of the fan = 120 rev/min

time = 20 sec

After 40 s fan comes to rest

ration angular acceleration of the first 20 s to last 40 s.

angular acceleration for first 20 s

[tex]\alpha_1= \dfrac{\Delta \omega}{t}[/tex]

[tex]\alpha_1= \dfrac{120}{20}[/tex]

[tex]\alpha_1=6 rev/s^2[/tex]

for last 40 s

[tex]\alpha_2= \dfrac{\Delta \omega}{t}[/tex]

[tex]\alpha_2= \dfrac{0-120}{40}[/tex]

[tex]\alpha_2= -3 rev/s^2[/tex]

now, ratio

[tex]\dfrac{\alpha_1}{\alpha_2}=\dfrac{6}{-3}[/tex]

[tex]\dfrac{\alpha_1}{\alpha_2}=-2[/tex]

hence, the correct answer is option D

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