Solve Centrifuge Problem with Calculus & Angular Velocity

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The discussion revolves around solving a physics problem involving a centrifuge tube filled with liquid, requiring calculus and knowledge of angular velocity. The problem states that the resultant pressure of the liquid at a distance r from the axis of rotation can be expressed as delta p/delta r = prw^2. To derive this result, it is suggested to analyze the net force on a small slice of the liquid using Newton's second law, focusing on the centripetal acceleration involved in the rotation. The user seeks guidance on how to approach this calculation step-by-step. Understanding the relationship between pressure, density, and angular velocity is crucial for solving the problem effectively.
Omar.Castillo
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I have a problem with a small physics problem. It requires some knowledge of calculus which I don't yet posses I am looking here for ideas. The problem states that there is a centrifuge tube with a length 12cm that is caused to spin by a rotating arm with lengt 8 cm. The tube is filled with 10 cm of a homogenous liquid with density p. It is rotating at a full angular velocity w and its traveling fast enough to be almost horizontal.

The question requires me to show that the resultant pressure of the liquied at a distance r from the axis of rotation is delta p/ delta r= prw^2

any suggetions on how to get this result?
 
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Start by writing the net force on a small slice (thickness delta r) of the liquid. Use Newton's 2nd law to find that force. The acceleration is centripetal.
 

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