Why am I getting "extra alignment tab has been changed to \cr" error?

Question

I'm trying to align an equation in two points, my code is the following:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
    \begin{cases}
    \omega_W \geq \omega_{W0} \hspace{2mm} &\Leftrightarrow \hspace{2mm} S_x \rightarrow \infty & \longrightarrow \text{Wheel is spinning} \\
    \omega_W > \omega_{W0} \hspace{2mm} &\Leftrightarrow \hspace{2mm} S_x > 0 & \longrightarrow \text{Tire driving force} (F_x >0) \\
    \omega_W = \omega_{W0} \hspace{2mm} &\Leftrightarrow \hspace{2mm} S_x =0 & \longrightarrow \text{Free-rolling tire} (F_x=0) \\
    \omega_W \leq \omega_{W0} \hspace{2mm} &\Leftrightarrow \hspace{2mm} S_x < 0 & \longrightarrow \text{Tire braking force} (F_x <0) \\
    \omega_W =0 \hspace{2mm} &\Leftrightarrow \hspace{2mm} S_x= -1 & \longrightarrow \text{Wheel lock-up} \\
    \end{cases}
\end{equation}
\end{document}

The thing is that I want an alignment in "Leftrightarrow" and in "longrightarrow". However, the output I'm getting is the following (and of course the error of "extra alignment tab has been changed to \cr"):

Any idea about why it's not working, or how can I fix it? I wrote all the \\ and also I added the & in the points I want to get an alignment.

Answer 1

cases only accepts one & per row. You can easily emulate it with array. The r>{{}}l trick is for obtaining the correct spacing around the relation symbols. I removed the long arrows, which I find redundant.

\documentclass{article}
\usepackage{amsmath,array}

\begin{document}

\begin{equation}
\left\{
  \renewcommand{\arraystretch}{1.2}% like cases
  \setlength{\arraycolsep}{0pt}%
  \begin{array}{ r>{{}}l @{\quad} c @{\quad} r>{{}}l @{\quad} l }
  \omega_W &\geq \omega_{W0} &\Leftrightarrow & S_x &\to \infty & \text{Wheel is spinning} \\
  \omega_W &>    \omega_{W0} &\Leftrightarrow & S_x &>   0      & \text{Tire driving force ($F_x>0$)} \\
  \omega_W &=    \omega_{W0} &\Leftrightarrow & S_x &=   0      & \text{Free-rolling tire ($F_x=0$)} \\
  \omega_W &\leq \omega_{W0} &\Leftrightarrow & S_x &<   0      & \text{Tire braking force ($F_x<0$)} \\
  \omega_W &=    0           &\Leftrightarrow & S_x &=  -1      & \text{Wheel lock-up}
  \end{array}
\right.
\end{equation}

\end{document}

Answer 2

A simple code with empheq and an alignedat environment:

\documentclass{article}

\usepackage{empheq}

\begin{document}

\begin{empheq}[left =\empheqlbrace\,]{equation}
    \begin{alignedat}{3}
        & \omega_W \geq \omega_{W0} & \: &\Leftrightarrow\: S_x \rightarrow \infty &\: & \longrightarrow \text{Wheel is spinning} \\
        & \omega_W > \omega_{W0} & &\Leftrightarrow \: S_x > 0 & & \longrightarrow \text{Tire driving force} (F_x >0) \\
        & \omega_W = \omega_{W0} & &\Leftrightarrow \: S_x =0 & & \longrightarrow \text{Free-rolling tire} (F_x=0) \\
        & \omega_W \leq \omega_{W0} & &\Leftrightarrow \: S_x < 0 & & \longrightarrow \text{Tire braking force} (F_x <0) \\
        & \omega_W =0 & &\Leftrightarrow \: S_x= -1 & & \longrightarrow \text{Wheel lock-up} \\
    \end{alignedat}
\end{empheq}

\end{document} 

Answer 3

You can use only one & per line in the cases environment:

\documentclass{article}

\usepackage{amsmath,eqparbox}

\begin{document}

\begin{equation}
  \begin{cases}
    \omega_W \geq \omega_{W0} &\Leftrightarrow \quad S_x \rightarrow \infty \longrightarrow \text{Wheel is spinning} \\
    \omega_W > \omega_{W0}    &\Leftrightarrow \quad S_x >  0               \longrightarrow \text{Tire driving force ($F_x > 0$)} \\
    \omega_W = \omega_{W0}    &\Leftrightarrow \quad S_x =  0               \longrightarrow \text{Free-rolling tire ($F_x = 0$)} \\
    \omega_W \leq \omega_{W0} &\Leftrightarrow \quad S_x <  0               \longrightarrow \text{Tire braking force ($F_x < 0$)} \\
    \omega_W = 0              &\Leftrightarrow \quad S_x = -1               \longrightarrow \text{Wheel lock-up}
  \end{cases}
\end{equation}

\newcommand{\Scond}[1]{\eqmakebox[Scond][l]{$#1$}}

\begin{equation}
  \begin{cases}
    \omega_W \geq \omega_{W0} &\Leftrightarrow \quad \Scond{S_x \rightarrow \infty} \longrightarrow \text{Wheel is spinning} \\
    \omega_W > \omega_{W0}    &\Leftrightarrow \quad \Scond{S_x >  0}               \longrightarrow \text{Tire driving force ($F_x > 0$)} \\
    \omega_W = \omega_{W0}    &\Leftrightarrow \quad \Scond{S_x =  0}               \longrightarrow \text{Free-rolling tire ($F_x = 0$)} \\
    \omega_W \leq \omega_{W0} &\Leftrightarrow \quad \Scond{S_x <  0}               \longrightarrow \text{Tire braking force ($F_x < 0$)} \\
    \omega_W = 0              &\Leftrightarrow \quad \Scond{S_x = -1}               \longrightarrow \text{Wheel lock-up}
  \end{cases}
\end{equation}

\end{document}

The above provides two options, depending on your alignment requirements.

Answer 4

Cases can only handle one &.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
\left\{
    \begin{array}{lll@{}}
    \omega_W \geq \omega_{W0} &\Leftrightarrow S_x \rightarrow \infty &\longrightarrow \text{Wheel is spinning} \\
    \omega_W > \omega_{W0} &\Leftrightarrow S_x > 0  &\longrightarrow \text{Tire driving force} (F_x >0) \\
    \omega_W = \omega_{W0} &\Leftrightarrow S_x =0 &\longrightarrow \text{Free-rolling tire} (F_x=0) \\
    \omega_W \leq \omega_{W0} &\Leftrightarrow S_x < 0 &\longrightarrow \text{Tire braking force} (F_x <0) \\
    \omega_W = 0 &\Leftrightarrow S_x= -1 &\longrightarrow \text{Wheel lock-up} \\
    \end{array}
\right.
\end{equation*}
\end{document}