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A centrifuge in a medical laboratory is rotating at an angular velocity, [tex]w[/tex], of 3600 revolutions per minute. When switched off, it takes the centrifuge 9.0 seconds to come to rest. What is the angular acceleration, [tex]a[/tex], of the centrifuge in [tex]\text{rad/s}^2[/tex]?

Answer :

Final answer:

The angular acceleration of the centrifuge is -40π rad/s^2.

Explanation:

The angular acceleration of the centrifuge can be determined by converting the given angular velocity from revolutions per minute (rev/min) to radians per second (rad/s). To do this, we can use the formula ω = 2πN/60, where ω is the angular velocity in rad/s and N is the angular velocity in rev/min. Once we have the angular velocity, we can calculate the angular acceleration using the formula α = ∆ω/∆t.

First, let's convert the given angular velocity of 3600 rev/min to radians per second: ω = 2π(3600)/60 = 120π rad/s.

Next, we can calculate the angular acceleration using the time taken to come to rest: α = ∆ω/∆t = (0 - 120π)/9.0 = -40π rad/s^2. Therefore, the angular acceleration of the centrifuge is -40π rad/s^2.

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