Calculating Density and R of a Compound Pendulum

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SUMMARY

The discussion focuses on calculating the density \( p(x,y) \) and the distance \( R \) from the pivot point to the center of gravity of an equilateral triangle with side length \( B \). The density is derived using the formula \( p(x,y) = \frac{m}{A} \), where the area \( A \) is calculated as \( A = \frac{\sqrt{3}}{4} B^2 \). The resulting density formula is \( p(x,y) = \frac{4\sqrt{3}m}{3B^2} \). The distance \( R \) is computed as \( R = \frac{\sqrt{3}B}{3} \), confirming the calculations are accurate.

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Akibarika
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Little help in compound pendulum

Homework Statement


there is an equilateral triangle T with sides of length B. Suspend this triangle from a pivot through on of its corners, so that it is free to swing about this corner in the plane of the tringle.

I want to ask how to compute the density p(x,y) and the R whcih from the pivot point to the center of gravity of the triangle.

In fact I found the soluation, but I don't know it is right or not.
Could anyone check it with me?

Homework Equations


p(x,y)=m/A


The Attempt at a Solution


A=sqrt(3)/4 * B^2
therefore p(x,y)=(4*sqrt(3)*m)/(3*B^2)

about the R:
GRAPH.jpg

cos 30 = sqrt(3)/2
R = (B/2)*(2/sqrt(3)) = (sqrt(3)*B)/3

did I make any mistake??

Thanks a lot
 
Last edited:
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You did not.
 

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