Max Rotation Rate of a Slowing Turntable

AI Thread Summary
The discussion focuses on determining the maximum rotation rate of a slowing turntable, defined by its radius "r" and initial rate "ω." Participants are tasked with expressing the time at which the rotation rate, denoted as ωt², reaches its maximum in terms of T, the total time until the turntable stops. The conversation emphasizes the importance of understanding the slope of a curve at points of maxima and minima to solve the problem effectively. Additionally, the need to formulate an equation for the curve is highlighted as a crucial step in the analysis. The discussion aims to clarify the mathematical approach required to find the solution.
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Homework Statement



A turntable of radius "r" is spinning counterclockwise at an initial rate of ω. at t=0, its rotation rate begins to slow at a steady pace. the rotation finally stops at t=T. At what time is ωt^2 maximum. Express your answer in terms of T.
 
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As this is thehomework section the rules require you to post your attempt before asking for help. Meanwhile...

Write an equation for the curve.

What do you know about the slope of a curve at maxima and minima?
 

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