A propeller slows from 490 rev/min to 177 rev/min in 3.50 s. What is its angular acceleration?
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Divide the angular velocity change in RADIANS/SEC (not rpm) by the time interval required (3.20 s). The answer should be negative, with dimensions of radans/s^2
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To find the angular acceleration of the propeller, we can use the formula:
Angular acceleration (α) = (final angular velocity - initial angular velocity) / time
Given:
Initial angular velocity (ω1) = 490 rev/min
Final angular velocity (ω2) = 177 rev/min
Time (t) = 3.50 s
First, let's convert the angular velocities from rev/min to rad/s. Since 1 rev = 2π radians:
ω1 = 490 rev/min * (2π rad/1 rev) * (1 min/60 s) = 51.41 rad/s
ω2 = 177 rev/min * (2π rad/1 rev) * (1 min/60 s) = 29.24 rad/s
Now we can substitute these values into the formula to calculate the angular acceleration:
α = (ω2 - ω1) / t
= (29.24 rad/s - 51.41 rad/s) / 3.50 s
= -22.17 rad/s / 3.50 s
≈ -6.34 rad/s^2
Therefore, the angular acceleration of the propeller is approximately -6.34 rad/s^2. The negative sign indicates that the propeller is slowing down.