Rack and Pinions

Inertia of the shaft is generally negligible

Kinetic Energy

$KE=\frac{1}{2}m{x}^{{}^{\prime }2}+\frac{1}{2}I{\theta }^{{}^{\prime }2}$
Using Equivalent Mass and Inertia we can see what inertia the shaft feels:
$KE=\frac{1}{2}\left[m{R}^2+I\right]{\omega }^2$
where x’^2 is (R)theta’

Modelling the System Dynamics

$T=I_e{\theta }^{{}^{\prime \prime }2}$
Where T is torque. You can also put it in terms of x”