Center Gravity and Moment of Inertia

ymehuuh

1. The problem statement, all variables and given/known data
Four objects are held in position at the corners of a rectangle by light rods as shown in the figure below. The mass values are given below.
M1 (kg) M2 (kg) M3 (kg) M4 (kg)
3.50 1.50 3.90 1.70

(a) Find the moment of inertia of the system about the x axis.

(b) Find the moment of inertia of the system about the y axis.

(c) Find the moment of inertia of the system about an axis through O and perpendicular to the page.

2. Relevant equations

Center of Gravity: sumM1*X1+M1*X2.../M1+M2...

3. The attempt at a solution

I found the center of gravity for the x axis to be .037736...how do I find the moment of inertia with that information?

LowlyPion

You need to find the x and y CoM.

Knowing that then the moment I about the CoM is Σmr².

The axes are simpler in that for

I_x = Σm_i*y_i²

I_y = Σm_i*x_i²

ymehuuh

Oh, I reversed the two and that's why I got it wrong. Thanks.
What would I use for part c?

LowlyPion

What are the distances to each corner from O to each mass?

I_o = Σmr²

It's made a little easier by Pythagoras, so be sure and thank him.

ymehuuh

perfect! Thanks!!