How Do You Calculate Moment of Inertia for CD and FE in a Multi-Rod System?

[PhyAmateur]

If we have five identical rigid rods, each of length l and mass m, are connected together to form the system shown in the figure. The system may rotate about an axis passing through AB.

The question is to find the moment of inertia of the system with respect to axis AB.

I managed to find the MOI of BC and DE using parallel axis theorem. My question is more about CD and FE. How to find the MOI wrt CD and FE?

 

[BiGyElLoWhAt]

I'm not sure if there's a way to do this other than starting from the integral definition of a moment of inertia. $I=\int_a^b r^2dm$ So you need to find a relation between the density and radius for the rods.

 

[PeroK]

If we have five identical rigid rods, each of length l and mass m, are connected together to form the system shown in the figure. The system may rotate about an axis passing through AB.

The question is to find the moment of inertia of the system with respect to axis AB.

I managed to find the MOI of BC and DE using parallel axis theorem. My question is more about CD and FE. How to find the MOI wrt CD and FE?

CD and EF are parallel to the axis of rotation. Doesn't that make their MoI quite straightforward to calculate?

 

[brainpushups]

Indeed. Treat the rods as point masses at their respective distances from the axis AB.