Conservation of Angular Momentum: angular speed

mickellowery

1. The problem statement, all variables and given/known data
A student sits on a freely rotating stool holding 2 3.00kg dumbbells. When the students arms are extended horizontally the dumbbells are 1.00m from the axis of rotation and the student rotates with an angular speed of 0.750 rad/sec. The moment of inertia of the student and the stool is 3.00 kgm² and it is assumed to be constant. The student pulls the dumbbells in to a position 0.300m from the rotation axis. What is the new angular speed?


2. Relevant equations
I was going to try I_i[tex]\omega[/tex]_i=I_f[tex]\omega[/tex]_f but the problem with this is that the problem says I is constant at 3.00 kgm². I assume that I need to factor in the radius somehow but I'm not sure how to do it.


3. The attempt at a solution

rock.freak667

When the dumbells are at 1m, what is the moment of inertia of them?

Add that to the inertia of the stool and you have the initial moment of inertia.

initial angular momentum = I_initialω_initial.


When the dumbells are at 0.3m, what is the moment of inertia then? (Add this to get inertia of the stool to get the final moment of inertia)

mickellowery

So can I model the dumbbells as a rod and use 1/12 ML² as the moment of inertia or do I have to integrate [tex]\int[/tex][tex]\rho[/tex]dV? I am facing problems with both ways, I don't know what the volume would be if I integrate, and it seems like modeling as a rod would not be correct.

rock.freak667

No need to do all of that. Just treat them as point masses such that I=mr²