Determine the moment of inertia of a bar and disk assembly

  • #1
TheBigDig
65
2
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.
 
Last edited:

Answers and Replies

  • #3
haruspex
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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.
 
  • #4
TheBigDig
65
2
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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