A stirring Rod in a hemispherical bowl

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SUMMARY

The discussion focuses on the dynamics of a stirring rod placed in a frictionless hemispherical bowl, specifically deriving the angle θ0 at which the rod comes to rest. The rod, with a uniform density and length of 2R, experiences forces that can be analyzed through free body diagrams. The key to solving for θ0 involves establishing a root equation f(θ)=0 that incorporates the radial forces acting on the rod and the torque equations derived from its position in the bowl.

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[. Homework Statement
Once you place a stirring rod (uniform density) of length 2R in a frictionless hemispherical bowl of radius R, it always comes to rest after one of its ends makes an angle of θ0 with respect to the vertical
(diagram attached)

a) derive a root equation for f(θ)=0 that can be used to solve for θ0]
b) what is the numerical value of θ0?


2. Homework Equations

none

3. The Attempt at a Solution

sorry but I don't know the concepts that can be used to solve such problem. please help me. Thank you very much
we are currently taking up oscillations and i tried to relate it but i end up totally messed up.
 

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The rod is touched by the bowl at two points where there is a radial force on the rod. Draw a free body diagram and wrilte the force and torque equations.
Include mg at the center of the rod.
 

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