Moment of inertia problem

[Mcat35]

Experiement 1:

One student sits on a stool that rotates freely. He holds a 5-kg mass in each hand. Initially, the student has a angular velocity of 5 radians/sec with his arms in his lap.

Question:

In exp 1, with his arms outstretched, the student drops the weights. This will cause the angular velocity of the student to:

answer is remain the same...

can someone explain to me why "moment of inertia would not change for the system when the student drops the weight" since Inertia is proportional to mass x r^2 wouldn't a decrease in mass after the weight drop decrease the moment of inertia?

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[kupa]

I believe this concerns the distribution of mass. Moment of inertia of the system is the sum of the individual moments of inertias. If you set your torso as the y-axis, where would your right hand and left hand be on the x-axis?

 

[Mcat35]

I believe this concerns the distribution of mass. Moment of inertia of the system is the sum of the individual moments of inertias. If you set your torso as the y-axis, where would your right hand and left hand be on the x-axis?

so moment of inertia has nothing to do with the masses your holding?

 

[zoner]

It does. However, when the experimenter outstretched her arms, the moment of inertia went up while at the same time the MOI went down by dropping the weight. So maybe two changes cancelled out any differences? What question was that? I vaguely remember doing it.

 

[Mcat35]

It does. However, when the experimenter outstretched her arms, the moment of inertia went up while at the same time the MOI went down by dropping the weight. So maybe two changes cancelled out any differences? What question was that? I vaguely remember doing it.

In my book it was passage 8 entitled Torque. in the equalibirum and momentum chapter.

thanks for all your help

 

[Mcat35]

anyone?

 

[MalibuPreMD]

I had concerning this exact problem a few weeks ago - never resolved it.

 

[sleeve318]

Experiement 1:

One student sits on a stool that rotates freely. He holds a 5-kg mass in each hand. Initially, the student has a angular velocity of 5 radians/sec with his arms in his lap.

Question:

In exp 1, with his arms outstretched, the student drops the weights. This will cause the angular velocity of the student to:

answer is remain the same...

can someone explain to me why "moment of inertia would not change for the system when the student drops the weight" since Inertia is proportional to mass x r^2 wouldn't a decrease in mass after the weight drop decrease the moment of inertia?

when the student has the weights on his lap his inertia is low, his velocity is 5 radians per second. when he extends his arms, his inertia goes up and his velocity goes down. however when he drops the weights his inertia goes back down and his velocity goes back up and is equal to when the weights were in his lap which is 5 radians per second.

 

[sibitrum]

Experiement 1:
Question:

In exp 1, with his arms outstretched, the student drops the weights. This will cause the angular velocity of the student to:

answer is remain the same...

can someone explain to me why "moment of inertia would not change for the system when the student drops the weight" since Inertia is proportional to mass x r^2 wouldn't a decrease in mass after the weight drop decrease the moment of inertia?

I think moment of intertia does change but angular momentum does not. Intuitively, it is because the masses continue to spin in a circle. Therefore, they "take" some of the momentum with them. I hope that's correct anyway :x

 

[SN1]

Experiement 1:

 

[whiteshadodw]

is this in TBR? i'm having the same problem. the answer explanation really doesn't help that much either.

 

[MT Headed]

This is such a beautiful question, though I have my doubts it would show up on the MCAT.

So somebody has their weighted arms outstretched, and they are spinning at some speed below 5rad/s, and they drop the weights. What happens? There are many approaches to the answer, but my favorite is to simply define my "system" as the person. I think the book defines the system the same way for this problem. The weights, the chair, etc are not part of the system. When the person drops the weights, no external torque is applied to my system, so there is no change in my system's angular momentum. My system also had no change in moment of inertia (the weights are not in my system, remember?) therefore there was no change in my system's angular velocity either. My system will continue to rotate at whatever value it was, below 5rad/s.

For completeness' sake you could also analyze the system of only the weights. First, they are spinning at some rotational velocity less than 5rad/s. Then they are dropped. Was an external torque applied? No. Therefore the angular momentum cannot change. In this case, however, the moment of inertia of the weights is increasing, because the same mass is getting further and further from the axis as it travels at a constant velocity away from the axis. Therefore, the angular velocity of the weights must be going down. In fact, the angular velocity approaches zero (the weights will never complete another revolution after all) and the moment of inertia approaches infinity. But angular velocity times moment of inertia, which is angular momentum, will always remain a constant because no external torque has been applied to the system.

 

[whiteshadodw]

i finally figured this out after much heated deliberation with my partner. so let's say the student has moment of inertia with arms outstretched of 2 kg*m^2 and the dumbbells outstretched has moment of inertia 10 kg*m^2. together that's 12 kg*m^2 multiplied by angular velocity.

after you drop the dumbbells the student doesn't change angular velocity because of conservation of angular momentum. the most important part to note is that conservation of angular momentum is for a SYSTEM. thus:

Linitial = L final ; I(student + dumbbells)a(student + dumbells) = I(student)*a(student + dumbbells same as initial) + I(dumbbells)*a(student + dumbbells same as initial. that's why the student has the same angular velocity because the angular momentum for the SYSTEM is conserved.