  We investigate the influence of Toomre's $Q$ parameter on the bar-forming
dynamics of Maclaurin disk using $N$-body simulations. According to the
Toomre's criterion, local velocity dispersion parametrized by $Q\geq 1$ is
required to suppress the local axisymmetric instability but, in turn, it
deviates particle orbits from nearly circular limit in which particle natural
frequencies are calculated. We resolve this by including the effect of velocity
dispersion, as the pressure potential, into the effective potential with the
gravitational potential. With this formulation, circular orbit approximation is
retrieved. The effective potential hypothesis can describe the $Q$-dependences
of angular and epicyclic motions of the bar-forming processes and the
established bars reasonably well provided that $Q\geq 1$. This indicates the
influence of initial $Q$ that is imprinted in the entire disk dynamics, not
only that $Q$ serves as the stability indicator. In addition, we perform the
stability test for the disk-in-halo systems. With the presence of halo, disks
are more susceptible to the bar formation as seen by the elevated critical $Q$
than that for the isolated disk. This is attributed to the differential
rotation that builds the unstable non-axisymmetric spiral modes more
efficiently which are the ingredients of bar instability.
