Why can't I treat the disk as a point mass?

[cory21]

Homework Statement

A grandfather’s clock consists of a disk of mass, 𝑴 attached to the end of rod of negligible mass and length, 𝑳. The grandfather’s clock is hanging vertically initially from a hinge at point 𝑨.
A lump of clay mass, 𝒎 moving horizontally at speed, 𝒗 collides with and sticks to the center of the disk, causing the grandfather’s clock to rise to a maximum angle 𝜽𝒎𝒂𝒙.

Which of the following is an expression for the angular speed angular speed, 𝝎 of the grandfather's clock (with a lump of clay sticking to center of disk) just after the collision? [Note: Assume that the clay is a point mass. Moment of inertia of disk about axis through center of disk I_disk=1/2MR^2]

Relevant Equations

𝐿𝑡𝑜𝑡,𝑃 = 𝐿𝑟𝑜𝑡𝐶𝑀,𝑟𝑜𝑑 + 𝐿𝑟𝑜𝑡𝐶𝑀,𝑑𝑖𝑠𝑘 + 𝐿𝑡𝑟𝑎𝑛𝑠,𝑃,𝑟𝑜𝑑 + 𝐿𝑡𝑟𝑎𝑛𝑠,𝑃,𝑑𝑖𝑠𝑘

Since the question made no indication of the disk rotating about its center, I just straight up assumed that the disk did not rotate about its center, and instead treated it as a point mass. However, to my surprise my calculations did not bear me any fruit. Below is my first attempt at the solution, where you could clearly see that my calculations did not yield me an answer that's even remotely close as to what was offered in the MCQ.

If I treated the disk to have rotated around its center however, I would get D as an answer. Below is my second attempt at the solution

So, am I to assume that the disk experienced some translational motion along with rotational motion about the disk's center of mass, because the question along with the diagram isn't very clear.

 

[TSny]

So, am I to assume that the disk experienced some translational motion along with rotational motion about the disk's center of mass, because the question along with the diagram isn't very clear.

Yes. I think you are supposed to assume that the disk is attached to the rod so that the disk doesn't rotate relative to the rod.

Suppose you paint an orange line on the disk.

You can see how the disk rotates through some angle $\phi$ as the rod swings through an angle $\theta$. What is the relation between $\theta$ and $\phi$?

 

[kuruman]

Here is a figure that I posted in another thread where the same issue arose. The Moon showing the same side to the Earth is an illustration of this idea of one spin revolution per orbit revolution.

 

[haruspex]

What surprised me about this scenario is that having the bob attached rigidly to the shaft, rather than on a free axle, increases the energy loss in the impact.