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Hello.
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In this problem, we have a centrifuge, which is some laboratory equipment of a rotating wheel.
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And we have some information that it has an initial angler speed of 3 ,850 revolutions per minute before it was switched off.
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And it continued to rotate before it comes to rest for a period of 10 .2 seconds.
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We know that the final angular velocity now is zero because it came to rest.
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And the question is to get the angular deceleration in revolution per minute square and radiance per second square.
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Okay.
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So we have this formula here that the final angular velocity is equal to the initial angular velocity plus alpha, which is the angular acceleration, multiply by t.
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Substituting numbers here the final velocity is zero and the initial velocity is 3 ,850 plus alpha and then t.
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And we need the answer to be in revolutions per minute squared.
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So in that case, what we will do is to substitute our time but converting it to minutes by dividing by 60 here.
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And in that case we have that our alpha is equal to 3 ,850 negative sign of course multiplied by 60 divided by 10 .2 and this gives us an answer of 22 ,647 revolutions per minute squared.
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So that's it for the first part...