Is there a way to calculate the moment of inertia of a hanging mass (3.1 kg) without length & width dimensions?

not of the mass itself, but about some other point.

For example for a point mass hanging from a nail on a string it is m L^2 about the attachment point at the ceiling where L is the length of the string.

To calculate the moment of inertia of a hanging mass, you typically need the length and width dimensions of the object. The moment of inertia measures an object's resistance to changes in rotational motion, and it depends on the mass distribution and shape of the object.

Without the length and width dimensions, it is challenging to calculate the moment of inertia accurately. However, if you have additional information about the hanging mass, such as its shape or an approximation of its dimensions, you may be able to estimate or calculate the moment of inertia using specific formulas or equations related to that particular shape.

For example, if the hanging mass is a simple geometric shape like a rectangular plate, you can calculate its moment of inertia using the formula:

I = (1/12) * m * (a^2 + b^2)

Where:
I is the moment of inertia
m is the mass of the object
a and b are the dimensions of the object (length and width)

If you do not have any information about the dimensions or shape of the hanging mass, it becomes challenging to calculate the moment of inertia accurately. In such cases, it is recommended to measure or obtain the necessary dimensions to obtain a more precise calculation.