Why are there no negative signs in this solution?

[Benjamin_harsh]

Homework Statement

Calculating moment of inertia for 4 bodies by parallel axis theorem.

Relevant Equations

$I_{CM} = 2kg (1m)^{2} + 2kg (1m)^{2} + 2kg (1m)^{2} + 2kg (1m)^{2} = 8kgm^{2}$

$\sum {I} = Md^{2}$

$I_{CM} = 2kg (1m)^{2} + 2kg (1m)^{2} + 2kg (1m)^{2} + 2kg (1m)^{2} = 8kgm^{2}$

$I_{P} = I_{CM} + Md^{2}$ ($M$ is total mass of all 4 bodies)

$I_{P} = 8 + 8(1) = 16kgm^{2}$

 

[jbriggs444]

As I understand the drawing, you have four masses arranged in a rectangle. You compute the moment of inertia about a vertical center-of-mass axis that is embedded in the plane of the drawing. The goal is to compute the moment of inertia about a parallel axis at a distance "d" away from the center-of-mass axis.

You apply the parallel axis theorem and add the moment of inertia of the assembly about its center of mass axis to the moment of inertia that a point mass at that center would have about the chosen axis.

Apparently d = 1 meter.

The thread title asks why there are no negative signs in the calculation. Why would you expect negative signs in the calculation?

 

[Benjamin_harsh]

Why would you expect negative signs in the calculation?

If two moments are positive side and other two will be obviously negative because axis is located at the center.

 

[jbriggs444]

If two moments are positive side and other two will be obviously negative because axis is located at the center.

I am having trouble following this reasoning.

Moment of inertia is the sum of $mr^2$. The r term is squared. Its sign is irrelevant.