A student holding weights angular momentum problem

[BrainMan]

Homework Statement

A student sits on a rotating stool holding two weights, each of mass 10 kg. When his arms are extended horizontally, the weights are 1 m from the axis of rotation and he rotates with an angular speed of 3 rad/s. The moment of inertia of the student plus the stool is 8 kg*m^2 and is assumed to be constant. If the student pulls the weights horizontally to 0.3 m on the rotation axis calculate (a) the final angular speed of the system and (b) the change in the mechanical energy of the system.

Homework Equations

The Attempt at a Solution

I am not sure how to attempt this problem because I am confused by the statement "The moment of inertia plus the stool is assumed to be constant. " I thought that if the student brings its arms in it will change its moment of inertia so it can't be constant?

 

[Nathanael]

I am not sure how to attempt this problem because I am confused by the statement "The moment of inertia plus the stool is assumed to be constant. " I thought that if the student brings its arms in it will change its moment of inertia so it can't be constant?

I think what it means is that the stool and student (NOT including the weights) have a constant moment of inertia.

Yes, the moment of inertia will change when the student extends his arms, even without weights, but the problem is basically telling you to ignore that.

 

[Orodruin]

It is an approximation (assume student's arms are massless).

 

[rcgldr]

Note - the student performs internal work when pulling in the weights, and this internal work is the source of the increase in mechanical energy of the system. It's possible to calculate the work performed using calculus, but the math is simpler if the problem is approached based on the fact that angular momentum is conserved.

 

[BrainMan]

I think what it means is that the stool and student (NOT including the weights) have a constant moment of inertia.

Yes, the moment of inertia will change when the student extends his arms, even without weights, but the problem is basically telling you to ignore that.

So how should I approach this problem?

 

[Nathanael]

So how should I approach this problem?

You need to find the moment of inertia of the weights at a distance of 1m, then add it to the moment of inertia of the student+stool (which is said to be 8) then use that to find the angular momentum

Then use conservation of angular momentum (you'll need to also find the new moment of inertia when the weights are at a distance of 0.3m)