A centrifuge in a medical laboratory rotates at an angular speed of 3500 rev/min. When switched off, it rotates through 54.0 revolutions before coming to rest. Find the constant angular acceleration of the centrifuge in rad/s^2.
3500 rev/min = 366.5 rad/s
Time to stop = 54 rev/(average rpm) = 0.0309 min = 1.851 seconds
angular deceleration rate
= (366.5 rad/s)/(1.851s)
= ____ rad/s^2
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To find the constant angular acceleration of the centrifuge, we can use the equation that relates angular acceleration (α), angular speed (ω), and time (t):
ωf = ωi + αt
where:
ωf is the final angular speed (0 rad/s),
ωi is the initial angular speed (3500 rev/min),
t is the time it takes for the centrifuge to come to a stop (unknown), and
α is the angular acceleration (unknown).
We also know that the centrifuge rotates through 54.0 revolutions before coming to rest. One revolution is equal to 2π radians. Therefore, the initial angular speed can be converted to radians per second (rad/s) as follows:
ωi = 3500 rev/min × (2π rad/1 rev) × (1 min/60 s) = 366.519 rad/s.
Substituting the values into the equation, we have:
0 = 366.519 rad/s + αt.
Since the centrifuge rotates through 54.0 revolutions before coming to rest, we can also express the time (t) in terms of revolutions:
t = 54.0 rev × (1 min/3500 rev) × (1 s/60 min) = 0.0276 s.
Solving the equation for α, we get:
α = (0 - 366.519 rad/s) / 0.0276 s = -13,306.677 rad/s^2.
Thus, the constant angular acceleration of the centrifuge is approximately -13,306.677 rad/s^2.
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