Pendulum rotating about an axis

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The discussion centers on the analysis of forces acting on a pendulum rotating about the z-axis. There is confusion regarding the correct application of equations for balancing forces, particularly in the resolution of forces into components. It is emphasized that while forces can be decomposed into orthogonal components, they should not be treated as additive beyond their original form. Clarity in identifying actual forces and specifying the direction of analysis for each equation is recommended. The need for a precise problem statement is highlighted to facilitate further assistance.
Apashanka das
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Homework Statement

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Homework Equations

The Attempt at a Solution


Sir if the pendulum is given an angular velocity about the -he z axis then whether eq 1 is right for balancing force and I have a contradict regarding eq 2 and eq 3[/B]
 

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I think you are marking too many forces on your diagram.
When you resolve a force into components, you are saying those components are equivalent to that original force. They don't add to it.
You can replace a force by two orthogonal components, but you can't keep taking more bits in other directions.

Identify clearly the actual forces, then in your calculations, use their components to produce balanced equations.
It might even help to say for each equation, what direction you are looking at.
 
I would love to help with this problem, but I have no idea what question you're trying to answer. What is the exact problem statement?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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