Why Is Steiner's Law Applied Differently in These Physics Problems?

[transgalactic]

http://www.freeimagehosting.net/uploads/th.c0292675ee.gif

here they colculate the new center of mass
and do the sum of mvr before equals the sum of mvr after

but here
http://www.freeimagehosting.net/uploads/th.f7428bf535.gif

they are doing the shtiner law I=I+mr^2
but why arent they shtiner law in the first question too
??

 

[HallsofIvy]

I= I+ mr^2 makes no sense. It is equivalent to mr^2= 0.

 

[tiny-tim]

Hi transgalactic!

{rod with 2 or 3 masses}
here they colculate the new center of mass
and do the sum of mvr before equals the sum of mvr after

but here {dancer with outstretched arms}

they are doing the shtiner law I=I+mr^2
but why arent they shtiner law in the first question too
??

First, it's Steiner's law … and nearly everyone calls it the Parallel Axis theorem anyway

Second, it's I = I_C + mr², where I_C is the moment of inertia about a parallel axis through the centre of mass

In the second question, the centre of mass doesn't change, so I don't see how they can be using Steiner's law