The moment of inertia, $I$, is, of course, given by 

$$I = \sum m_i r_i^2$$

where the sum is over every bit, $i$, of the object with mass, $m_i$, and at a distance, $r_i$, from the axis of rotation.

You might need to calculate this by integration. 

$$I = \int_x ~r(x)^2 \rho dx$$

where

$$m = \int_x \rho dx$$

You integrate along the pendulum in infinitessimal steps of $dx$ and $r(x)$ is the function that determines $r$ as a function of $x$  and $\rho$ is density so $\rho dx = dm$, where $dm$ is the infinitessimal bit of mass at $dx$.

From my point of this this approach looks fine.

Period of swinging incomplete hula-hoop
I'm writing an article about the family and how it can change a person's life in the future. 

I need a word that tells the readers about a family in which the parents have not been good enough to teach their kids social skills and generally those things they will need in the future to be able to live well. 


The word must be formal (and polite).


I searched the dictionary for some words, but I'm not sure if they are the right words to be used with family. I found the following:


  Inefficiency, incompetence, inadequacy, ineptitude, inefficacy


None of the dictionaries I checked (Longman and Oxford) mention whether or not this is the right word to be used with family. Ineptitude of family?
