Moment of Inertia of Rod w/ Masses M, m1, & m2

[roman15]

Homework Statement

Find the moment of inertia of a rod with mass M, that has a mass m1, L/2 to the left of the axis of rotation and a mass m2, L/4 to the right of the axis of rotation. L is the length of the entire rod?

Not sure what to do. My professor said that I had to use the parallel axis theorem, but I am having trouble appling it to this problem, any help would be great!

Homework Equations

I = Icm + mr^2

The Attempt at a Solution

 

[vela]

You're not providing enough information, like where the axis of rotation is relative to the center of mass of the rod and how the rod is oriented.

 

[roman15]

Oh sorry about that. Well the rod is horizontal and I wasn't given the centre of mass. But the axis of rotation is at the middle of the rod.

 

[vela]

If the rod is of uniform density, its center of mass will be in the middle, and the axis of rotation passes through this point.

From how you've described the problem, you don't need to use the parallel-axis theorem. You just need to sum the moments of inertia of the rod and the two masses.

 

[roman15]

oh ok so then the moment of inertia would just be

I = Icm +m1r1^2 +m2r2^2

 

[vela]

Yup, you just need to find I_cm in terms of the mass and length of the rod and express r₁ and r₂ in terms of L.