Determine the moment of inertia of a bar and disk assembly

AI Thread Summary
The discussion focuses on calculating the moment of inertia for a bar and disk assembly, with a target answer of 0.430 kg·m². The user initially attempts to use formulas for the moment of inertia of a compound pendulum but arrives at an incorrect value of 2.61 kg·m². Corrections are suggested regarding the application of the parallel axis theorem and the proper definitions of variables, particularly the length of the rod versus the pendulum. The importance of correctly identifying the mass center and applying the parallel axis theorem in reverse is emphasized. The user acknowledges the corrections and plans to adjust their calculations accordingly.
TheBigDig
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Homework Statement
A homogeneous 3kg rod is welded to a homogeneous 2kg disc. Determine it's moment of inertia about the axis L which passes through the object's centre of mass. L is perpendicular to the bar and the disk.
Relevant Equations
## I_x = \int y^2\mathrm{d}A ##
## I_y = \int x^2\mathrm{d}A ##
Q.PNG

I have been given an answer for this but I am struggling to get to that point
$$ANS = 0.430\, kg \cdot m^2$$

So I thought using the moment of inertia of a compound pendulum might work where ##I_{rod} = \frac{ml^2}{12}## and ##I_{disc} = \frac{mR^2}{2}## (##l## is the length of the rod and ##R## is the radius of the disc)
$$ I_P = I_{rod} + M_{rod} \bigg( \frac{S}{2} \bigg)^2 + I_{disc} + M_{disc} (S+R)^2$$
where S is the length of the pendulum

$$ I_P = 0.09 + 1.2 + 0.04 + 2 = 2.61\, kg \cdot m^2$$
Much too large for my purposes.
Not really sure where to go after this. Any help is appreciated.
 
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It looks like you are defining P as the free end of the rod and applying the parallel axis theorem. You forgot to square the L/2, but maybe that's just a typo in writing the thread. And you wrote that your L is the length of "the pendulum', but you mean the length of the rod. It is rather confusing that you switched from the given "l" to "L", when L was already defined as an axis.

Anyway, you are asked for the moment about the mass centre. To get that you need to find where that is and apply the parallel axis theorem in reverse.
 
haruspex said:
It looks like you are defining P as the free end of the rod and applying the parallel axis theorem. You forgot to square the L/2, but maybe that's just a typo in writing the thread. And you wrote that your L is the length of "the pendulum', but you mean the length of the rod. It is rather confusing that you switched from the given "l" to "L", when L was already defined as an axis.

Anyway, you are asked for the moment about the mass centre. To get that you need to find where that is and apply the parallel axis theorem in reverse.
Sorry about that, I changed the post to reflect your corrections. ##l## is for the length of the rod and S is the length of the pendulum now. Thanks for the advice. I'll try giving that a go
 
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