# Concept of Moment of Inertia and its limits of integration

1. Apr 26, 2015

### Yam

1. The problem statement, all variables and given/known data

I am trying to work the moment of inertia for

a) rotating rod, axis through the centre of the rod
http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html#irod3

b) Solid cylinder
http://hyperphysics.phy-astr.gsu.edu/hbase/icyl.html#icyl2

2. Relevant equations
I = R^2 dM

3. The attempt at a solution

I understand all of the steps, except the limits of integration in terms of R or L.

For the rod, the limit of integration is from L/2 to -L/2

Why is the limit of integration for the cylinder from R to 0?
Should it be from the end to end? R to -R?

2. Apr 26, 2015

### Orodruin

Staff Emeritus
You need to fix your integration limits such that you integrate over the entire body once. In the case of the cylinder, you integrate from zero, but you allow the angular coordinate to vary between zero and 2pi, thus covering the full lap.

3. Apr 26, 2015

### Yam

I dont quite understand this part, when did i allow the angular coordinate to vary between zero and 2pi? What is meant by the angular coordinate?

4. Apr 26, 2015

### Orodruin

Staff Emeritus
It is implicit when you multiply by 2pi in $dV = 2\pi L r dr$. The integral is really a volume integral, but the direction along the cylinder axis and the angular direction are trivial since the integrand does not depend on them, thus they are replaced by the size of their integration ranges, $L$ and $2\pi$, respectively.

5. Apr 26, 2015

### Yam

I understand now, thank you for your help! cheers.