A cooling fan is turned off when it is running at 840 rev/min . It turns...

A cooling fan is turned off when it is running at 840 rev/min . It turns 1400 revolutions before it comes to a stop. Part A:What was the fan's angular acceleration, assumed constant? Part B: How long did it take the fan to come to a complete stop? Please show step by step

Solutions

Expert Solution

Initial rotational speed of the cooling fan = N₁ = 840 rev/min

Initial angular speed of the cooling fan = ₁

₁ = 87.96 rad/s

Final angular speed of the cooling fan = ₂ = 0 rad/s

Number of revolutions made by the cooling fan = n = 1400 rev

Angle through which the fan has rotated =

= 2n

= 2(1400)

= 8796.46 rad

Angular acceleration of the fan =

₂² = ₁² + 2

(0)² = (87.96)² + 2(8796.46)

= -0.44 rad/s²

Negative as the fan is slowing down.

Time taken by the fan to come to a stop = T

₂ = ₁ + T

0 = 87.96 + (-0.44)T

T = 200 sec

A) Angular acceleration of the fan = -0.44 rad/s²

B) Time taken by the fan to come to a stop = 200 sec

genius_generous answered 1 year ago

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