Does Anybody agree with me?

Question

"A thin disk, mounted on a frictionless vertical shaft of negligible rotational inertia, is rotating at 636 revolutions per minute. An identical disk (that is not initially rotating) is dropped onto the first disk. The frictional force between the disks causes them to rotate at a common angular velocity. Find this common angular velocity. NOTE: Be careful with your units!"
Since it is stated that there is no moment of inertia, the common angular velocity is the same as the first velocity which is 66.6 rad/s (converted it into radian/s). If this is not correct, please explain to me. Thank you.

Answer 1

To solve this, you use conservation of angular momentum. The two discs are identical, so they have the same moment of inertia, I. The angular momentum of a rotating object is:

L = I*omega
where I is the moment of inertia, and omega is the angular velocity.

The angular momentum of the system after dropping the second disc must be the same as the first. Two identical discs have exactly twice the moment of inertia of a single disc, so to conserve L, omega must be half its former value.

1/2 * 636 RPM = 318 RPM = 33.3 rad/s

Answer 2

It is stated that the vertical shaft, not the disk that is being dropped, has negligible inertia. Thus, the disk would have a moment of inertia as it gains velocity.