Help with internal moments = external moments

[urbano]

Homework Statement

Internal moments need to equal external moments, work out the total of the internal moments. The object has a mass of 2 kg

Homework Equations

I have obtained

the moment about I (labelled as MI) + Iα

The Attempt at a Solution

the moment about I (MI)

Force in y direction = 2 kg x 12m/s^2 = 24 N.m
Force in x direction = 2 kg x 30m/s^2 = 60 N.m

(Force y x moment arm x) = 24N.m x 5m = 120 N
(Force x x moment arm y) = 60 N.m x 10m = 600N

120N - 600N = -480 N

Iα = 3kg.m^2 x 10 rad/s^2 = 30 N

sorry I know I may have the units all jumbled

So the total internal moments = 600N + 30N = 630 N

the crunch for me is I don't actually get why the internal moment consists of Iα and the moment about point I.

What is Iα actually telling me ? I interpret it to mean that an object offers I resistance to being moved and it is moving at α, therefore it's force is Iα.

But if that is telling me the torque about that point why do we need to calculate the moment about the point as well to get the internal moment ?

thanks

 

[David Lewis]

Force in x direction = 2 kg x 30m/s^2 = 60 N.m

I came up with -60 N because inertial reaction force is to the left, and force is expressed in Newtons.
What do diagonal red line and orange horiz. and vert. lines represent?