The accents package defines command that are not robust: for instance we find
\newcommand\underaccent[2]{%
\begingroup
\def\cc@a{#2}% Stores the nucleous...
\cc@palette\cc@underaccent{#1}% ...and the accent is passed
#2%
\endgroup}
A command like this will not survive being found in a “moving argument” (the argument to \caption, \chapter, \section and similar commands). Defining \ubar in terms of \underaccent makes \ubar share the same fragility.
The package really ought to do
\DeclareRobustCommand\underaccent[2]{%
\begingroup
\def\cc@a{#2}% Stores the nucleous...
\cc@palette\cc@underaccent{#1}% ...and the accent is passed
#2%
\endgroup}
so the problem would disappear.
There are various fixes. The first is putting \protect in front of the command when it appears in a moving argument:
\caption{$\protect\ubar{\pi}$}
A better fix would be providing the protection to your command
\DeclareRobustCommand{\ubar}[1]{\underaccent{\bar}{#1}}
instead of using \newcommand.
An even better fix would be to remedy to the glitch in accents:
\documentclass{article}
\usepackage{fixltx2e}
\usepackage{accents}
\MakeRobust{\underaccent} % make \underaccent not fragile in moving arguments
\newcommand{\ubar}[1]{\underaccent{\bar}{#1}}
\begin{document}
\begin{figure}
\caption{$\ubar{\pi}$}
\end{figure}
\end{document}
Instead of fixltx2e you can use etoolbox:
\usepackage{etoolbox}
\usepackage{accents}
\robustify{\underaccent}
would do the same (in a different way).
In the following part of your input,
então deduz que os ângulos $\widehat{\left (OA,AA' \right )}$ e ̂$\widehat{\left ( AA,A'O \right )}$ são iguais
specifically this part:
)}$ e ̂$\widehat
the sequence of Unicode characters between the dollar signs (inclusive) is:
U+0024 DOLLAR SIGN
U+0020 SPACE
U+0065 LATIN SMALL LETTER E
U+0020 SPACE
U+0302 COMBINING CIRCUMFLEX ACCENT
U+0024 DOLLAR SIGN
You may not be able to see it in your editor or here, but if you copy and paste it into a Unicode character viewer like this one, you will be able to see it.
That U+0302 COMBINING CIRCUMFLEX ACCENT is meaningless there, and you probably don't want it. What you want there between (strictly) the dollar signs is probably just e. With just this change to your input, it works:
\documentclass{article}
\usepackage[utf8]{inputenc}
\begin{document}
Sendo que as tensões de entrada $U_{OA}$ e a de saída $U_{OA'}$ são constantes e iguais e o ângulo projetado entre essas tensões é igual a $7,5^{\circ}$, então deduz que os ângulos $\widehat{\left (OA,AA' \right )}$ e $\widehat{\left ( AA,A'O \right )}$ são iguais a $86,25^{\circ}$, mostrado na figura \ref{diagramafasauto}. Note-se que Co representa a extensão de C (fase c) e OCo a bissetriz do ângulo $\widehat{\left ( OA,AB \right )}$, então o valor do ângulo $\widehat{\left ( OA,OCo \right )}$ é igual a $60^{\circ}$. Deduz-se então o ângulo $\widehat{\left ( OA',OCo \right )}$.
\end{document}
producing:
That solves the problem, but note that without the fix, TeX actually tells you everything you need to know, pointing out the exact character at which there is a problem:
l.5 ...los $\widehat{\left (OA,AA' \right )}$ e ̂
$\widehat{\left ( AA,A'O \...
— the top line is everything that was read before the error happened, and the bottom line is what is not yet read.
A word of advice: you can avoid such super-long lines in your input. TeX (by default) treats a single newline character as equivalent to a space, so you may have an easier time debugging errors (if you don't take time to learn the error-line format) if you have shorter lines. (Of course, long lines are not a problem if you know how to deal with them.)
Best Answer
How about using
{\"u}instead of\"{u}?