# Polar moment of inertia in a rod?

1. Jan 6, 2015

### smr101

How is the polar moment of inertia in a rod calculated?

Thanks.

2. Jan 6, 2015

### BvU

No idea what it is. This link something ?

3. Jan 6, 2015

### smr101

Yeah, I've had a look at that. Formula doesn't quite make sense to me. I know what moment of inertia is but the 'polar' bit has thrown me off. Thanks anyway.

4. Jan 7, 2015

### BvU

Since there is no context whatsoever in the original posting, it's difficult to assist any further here.

5. Jan 7, 2015

### smr101

Here's the problem., 4. (b) (i) is the one I'm looking at.

6. Jan 7, 2015

### BvU

Well, at least now I can understand your confusion. However, it doesn't literally ask for the polar moment of inertia (a.k.a area moment of inertia), but for the polar mass moment of inertia. I see that used for the rotational moment of inertia, so with the context of b (ii) and b(iii) that seems the most logical choice.

7. Jan 7, 2015

### smr101

What is the formula for rotational moment of inertia?

8. Jan 7, 2015

### BvU

Can't imagine you haven't seen it before ! What did you use for 4a ?

$I=\int dI = {\displaystyle \int_0^M r^2 \; dm}$

9. Jan 7, 2015

### smr101

I'm on 4. (a) (ii) currently. Where should it be used in (a)?

Ok, thanks, I have seen it but haven't used it previously.

10. Jan 7, 2015

### smr101

I've found this... http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html#irod3

Looking at the bottom set of equations, so dm = (M/L) x dr...

So essentially, the equation is r^2 x (M/L) x dr...

Using these number that would be 0.075^2 x (20/2) x 0.15 x 0.075...

Is that correct?

11. Jan 7, 2015

### BvU

Tempting indeed (*), but I think this time the rod is turning around its length axis. I.e. it's a solid cylinder !

And you will need a moment of inertia in 4a (ii) as well: you don't just have to accelerate the cart, but also the drum.
However, in 4a (ii) they give you a radius of gyration, so you use that to calculate the moment of inertia..

(*) well, not really. did you really think dr stands for diameter x radius (because I see a 0.15 x 0.075, and then a few dots, indicating justified doubt, I hope) ?

12. Jan 7, 2015

### smr101

Ok, I am familiar with the equation for mass moment of inertia for a cylinder, which fits with this.

So are you saying the equation you gave me wouldn't work with this? I find it odd they say it's a rod and expect a cylinder equation to be used.

And yes I knew it wasn't the correct answer as I have the solutions and it didn't match...I see that dr is used in the integration equation now.

So what is the formula?
dm = elemental mass =
(M/L) x dr so the whole equation is r^2 x (M/L) x dr
And then?

13. Jan 7, 2015

### BvU

It's a drilling rod. Look here

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