Rotaional Inertia of a Thin Rod

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SUMMARY

The discussion focuses on calculating the rotational inertia of a meter stick with a mass of 0.68 kg about an axis located at the 21 cm mark. The relevant equation for this calculation is I = ∫ r² dm, where r is the distance from the axis of rotation and dm is the mass differential. Participants emphasize the importance of treating the stick as a thin rod and maintaining constant density throughout the calculation. The approach involves expressing the mass as a function of distance from the axis and manipulating the integral accordingly.

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Homework Statement


Calculate the rotational inertia of a meter stick, with mass 0.68 kg, about an axis perpendicular to the stick and located at the 21 cm mark. (Treat the stick as a thin rod.)


Homework Equations


I = integral of r squared with respect to mass


The Attempt at a Solution


?
 
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Oijl said:

Homework Statement


Calculate the rotational inertia of a meter stick, with mass 0.68 kg, about an axis perpendicular to the stick and located at the 21 cm mark. (Treat the stick as a thin rod.)


Homework Equations


I = integral of r squared with respect to mass


The Attempt at a Solution


?

so you want to find the mass of the object as a function of the distance from the axis. We can assume the the density is constant, so we could write:

dm = pdV

where dm is the mass differential from the integral, p the density (a constant) and dV the volume.

But some parts of the volume are constant, so you can further manipulate this equation. Can you see where to go from here?
 

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