Center of Mass/Moment of Inertia Question

[Victorzaroni]

Homework Statement

Masses M₁ and M₂ are separated by a distance L. The distance of the center of mass of the system at P from M₁ as shown above would be:
(A) (M1L)/(M2)
(B) ((M2+M1)L)/M1
(C) ((M2+M1)L)/M2
(D) (M2L)/(M1+M2)
(E) (M1L)/(M1+M2)

The moment of inertia of the system about the center of mass at P would be:
(A) (M1+M2)L^2
(B) [(M1+M2)/(M1M2)]L^2
(C) (M1M2L^2)/(M1+M2)
(D) (M1L^2)/(M1+M2)
(E) (M2L^2)/(M1+M2)

All of the 1s and 2s should be subscripts, I'm just lazy.

Homework Equations

X_com=(M1X1+M2X2)/(M1+M2)
I=ML²?

The Attempt at a Solution

I got the first part, that ended up being simple. The answer was D. I don't understand how to get the moment of inertia though. I tried doing I=mL^2=>I=(M1+M2)(Choice D)^2, but it didn't work. Help!

Kids were telling me it was C, but I don't know how to get that.

 

[ehild]

The moment of inertia of a point mass M at a distance d from a point is Md², with respect to that point. You have masses M1 and M2. What is their distances from the CM?

ehild

 

[Victorzaroni]

I have the distances to the CM from M1. I need to do the same thing for M2 then. But where do I go from there? Once I have these two distances, do I plug them both in for d separately and add?

 

[ehild]

Yes, square the distances, multiply by the masses and add.

ehild

 

[Victorzaroni]

I got it. Thanks!

 

[ehild]

You are welcome.

ehild