A fan rotating with an initial angular velocity of 1000 rev/min is switched off. In 2 seconds, the angular velocity decreases to 200 rev/min. Assuming the angular acceleration is constant, how many revolutions does the blade undergo during this time?
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First, we need to convert the angular velocities from revolutions per minute to revolutions per second.
1000 rev/min = 1000/60 = 16.67 rev/sec
200 rev/min = 200/60 = 3.33 rev/sec
The angular acceleration is the change in angular velocity divided by the change in time.
Angular acceleration = (final angular velocity - initial angular velocity) / time
= (3.33 rev/sec - 16.67 rev/sec) / 2 sec
= -6.67 rev/sec^2
The number of revolutions the blade undergoes during this time can be found using the equation for angular displacement:
θ = ω_initial*t + 0.5*α*t^2
where θ is the angular displacement (the number of revolutions), ω_initial is the initial angular velocity, α is the angular acceleration, and t is the time.
θ = 16.67 rev/sec * 2 sec + 0.5*(-6.67 rev/sec^2)*(2 sec)^2
= 33.34 rev - 13.34 rev
= 20 rev
So, the blade undergoes 20 revolutions during this time.
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