  We have conducted mapping observations ($\sim 2'\times2'$) of the Class I
protostar L1489 IRS using the 7-m array of the Atacama Compact Array (ACA) and
the IRAM-30m telescope in the $\mathrm{C^{18}O}$ 2-1 emission to investigate
the gas kinematics on 1000-10,000 au scales. The $\mathrm{C^{18}O}$ emission
shows a velocity gradient across the protostar in a direction almost
perpendicular to the outflow. The radial profile of the peak velocity was
measured from a $\mathrm{C^{18}O}$ position-velocity diagram cut along the disk
major axis. The measured peak velocity decreases with radius at a radii of
$\sim$1400-2900 au, but increases slightly or is almost constant at radii of
$r\gtrsim$2900 au. Disk-and-envelope models were compared with the observations
to understand the nature of the radial profile of the peak velocity. The
measured peak velocities are best explained by a model where the specific
angular momentum is constant within a radius of 2900 au but increases with
radius outside 2900 au. We calculated the radial profile of the specific
angular momentum from the measured peak velocities, and compared it to analytic
models of core collapse. The analytic models reproduce well the observed radial
profile of the specific angular momentum and suggest that material within a
radius of $\sim$4000-6000 au in the initial dense core has accreted to the
central protostar. Because dense cores are typically $\sim$10,000-20,000 au in
radius, and as L1489 IRS is close to the end of mass accretion phase, our
result suggests that only a fraction of a dense core eventually forms a star.
