Is My Calculation of Moment of Inertia Using the Parallel Axis Theorem Correct?

[Romain Nzebele]

Homework Statement

If M=0.50Kg, L=1.2 m, and the mass of each connecting rod shown is negligible, what is the moment of inertia about an axis perpendicular to the paper through the center of mass? Treat the mass as particles.

Relevant Equations

Xcm=total mx/ total m

The picture of the problem and my attempt to solve it are below. Please let me know if my resolution is correct. Thank you in advance.

 

[PeroK]

Yes, it looks right. Personally, I would have kept $M$ and $L$ until you had a single expression for the MoI. In this case $3.2ML^2$.

 

[Romain Nzebele]

Yes, it looks right. Personally, I would have kept $M$ and $L$ until you had a single expression for the MoI. In this case $3.2ML^2$.

Great, thank you so very much.

 

[haruspex]

A slightly easier way is to use the parallel axis theorem 'in reverse'.
Find the MoI about the central mass M and subtract (Σm)x², where x is the displacement to the common mass centre.