Does principle of moment always depend on mass density?

[yetar]

Homework Statement

Does the prinicple of moment always depend on the mass density of the rigid body?
I have an example in my book with a pully and the principal of moment in there is calculated depending only on the pully's geometry and the pully mass is not considered in the calculation.
Is that possible?
Thank you.

Homework Equations

The Attempt at a Solution

 

[Meir Achuz]

For a pulley, considered as a solid disk, the moment of inertia is
(1/2)MR^2. The mass has to be included to get the proper units.
It could be in your particular problem, the mass cancels in finding acceleration.