# Additive moments of inertia?

#### chattkis3

Hi! Im working on this problem:

A solid circular disk has a mass of 1.2 kg and a radius of 0.17 m. Each of three identical thin rods has a mass of 0.16 kg. The rods are attached perpendicularly to the plane of the disk at its outer edge to form a three-legged stool. Find the moment of inertia of the stool with respect to an axis that is perpendicular to the plane of the disk at its center. (Hint: When considering the moment of inertia of each rod, note that all of the mass of each rod is located at the same perpendicular distance from the axis.)
Here is my thinking so far (but im stumped!):
-Moment of Inertia's are additive
- The moment of inertia for the circular disk is (1/2)M*R^2
- I don't know how to get the moment of inertia for the three legs because they dont give me a mass. Im pretty sure the formula is 1/3M*L^2 but I dont know L ??

Thanks for the help.

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#### NateTG

Science Advisor
Homework Helper
Re-read the problem - the mass of the rods is stated explicitly. The length of the rods should be unimportant - perhaps you can figure out why.

#### chattkis3

Oh whoops, I didn't mean to put that the mass was not known. So it's been a couple of days and Im still stumped on why the length would not matter.
Is this close to the right track?

(1/2*M*R^2)+(1/3m)+(1/3m)+(1/3m) = I

M= mass of stool top
m = mass of one leg

#### NateTG

Science Advisor
Homework Helper
The legs are parralel to the axis of rotation right? So, in the plane of rotation (perpendicular to the axis of rotation) they're essentially point masses. (Does this make sense to you?)

I get:
$$\frac{1}{2}MR^2 + 3 \times (\frac{R}{3})^2m$$

#### teclo

NateTG said:
The legs are parralel to the axis of rotation right? So, in the plane of rotation (perpendicular to the axis of rotation) they're essentially point masses. (Does this make sense to you?)

I get:
$$\frac{1}{2}MR^2 + 3 \times (\frac{R}{3})^2m$$
could you please explain that for me? it would seem like the legs would matter, since there is a r (distance between them and the axis of rotation). we just covered angular momentum and i have yet to work through the homework.

thanks, if you've the time!

#### CartoonKid

NateTG, why you put R/3? Since the rods can be considered as point masses on the solid disc, I think it should be mR^2 for each, right?

#### teclo

CartoonKid said:
NateTG, why you put R/3? Since the rods can be considered as point masses on the solid disc, I think it should be mR^2 for each, right?
well from the lab on angular momentum that we did, two point particles rotating on a bar -- the moment of intertia can be calculated as

2mr^2

now that i see what he's talking about with that r/3 part, he's doing the same thing. it's like there are 3 of them adding to the moment of inertia. i don't understand what the 1/3 of R is for. it seems to me like it should be 3mR^2.

#### NateTG

Science Advisor
Homework Helper
That was a brain fart. I thought the rods were $$\frac{1}{3}$$ of the radius out rather than at the edge.

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