Calculating time period in vertical circular motion

AI Thread Summary
To calculate the minimum time period required for a cone filled with water to complete vertical circular motion without spilling, the equation v^2 = gR * (3 + 2 cos theta) is used, where velocity varies with the angle theta. The challenge lies in determining the time for one complete revolution given this variable velocity. Suggestions include exploring the "Elliptic Integral of the First Kind" for a solution. The discussion highlights the need for a deeper understanding of the relationship between velocity and time in this context. Further insights are encouraged to resolve the problem effectively.
taninamdar
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1. 1. Homework Statement :
How to calculate minimum time period 't' required to complete a vertical circular motion by a cone filled with water, so that the water doesn't fall?2. Homework Equations :
v^2 = gR * [ 3 + 2 cos (theta) ] obtained by applying law of conservation of energy.

3. 3. The Attempt at a Solution :
I have found that v^2 = gR * (3 + 2 cos theta ). But the velocity varies with theta. So, how to calculate the time required to complete one revolution using variable velocity?

Thanks!
 
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Hello Taninamdar,

Welcome to Physics Forums!

You might want to research "Elliptic Integral of the First Kind," perhaps. Good luck!
 

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