Homework help on Moments of inertia of system

[Dr_bug]

Homework Statement

Four masses are held in position at the corners of a rectangle by light rods.Find the moment of inertia of the system about the x axis.Find the moment of inertia of the system about the y axis.Find the moment of inertia of the system about an axis through O and perpendicular to the page. M1 (kg) M2 (kg) M3 (kg) M4 (kg) the picture is attached.
2.70 1.70 3.70 2.10

Homework Equations

I=mR2

The Attempt at a Solution

I wasn't really sure how to start. Should I first figure out the center of mass and then use that value to find the inertia?

 

[kuruman]

The center of mass has nothing to do with this. Just multiply each mass by the square of its distance from the appropriate axis and add all the terms together.

 

[kerimek]

As a scientist, my response would be:

To find the moment of inertia of a system, we need to use the formula I=mR^2, where m is the mass and R is the distance from the axis of rotation to the mass. In this case, we have four masses, each with its own distance from the axis of rotation. To find the moment of inertia about the x and y axes, we can use the parallel axis theorem, which states that the moment of inertia about an axis is equal to the moment of inertia about the center of mass plus the mass of the system times the distance between the two axes squared.

To start, we can find the center of mass of the system by using the formula x_cm=(m1x1+m2x2+m3x3+m4x4)/(m1+m2+m3+m4), where x1, x2, x3, and x4 are the x-coordinates of the four masses and m1, m2, m3, and m4 are their respective masses. Similarly, we can find the y-coordinate of the center of mass using the formula y_cm=(m1y1+m2y2+m3y3+m4y4)/(m1+m2+m3+m4).

Once we have the center of mass, we can use the parallel axis theorem to find the moment of inertia about the x and y axes. For the moment of inertia about an axis through O and perpendicular to the page, we can use the formula I=mx^2+my^2, where mx and my are the moment of inertia about the x and y axes, respectively.

I hope this helps in solving the problem. Remember to always double check your calculations and units to ensure accuracy.