Moment of inertia, verbal question

[Lorens]

I was reading this in http://en.wikipedia.org/wiki/Moment_of_inertia

This formula explains the speeding up of ice skaters when they pull in their arms. Since the ice is nearly frictionless, the kinetic energy should stay constant during their spin. When they pull in their arms, the skaters decrease their moment of inertia I (their mass is more concentrated close to the rotation axis). To keep the kinetic energy constant, the angular velocity ω must increase; hence, the skaters spin faster.

I can not understand, why would the mass become more concentrated around the rotation axis just because they move there arms, what have i missed? ...

Kindly Paul-Martin

 

[Hootenanny]

Okay, if we consider the arms as two uniform rods of length l and the body as a rod of radius r, when the arms are outstreched how far is the centre of mass of the arms away from the axis of rotation? Assuming the skater rotates about the centre of their body?

Now consider the centres of mass of the arms when they are by the skater's side.

~H

 

[Lorens]

oki thx, but what do it mean that the skater "skater spin faster" ? (i am from sweden .. )

 

[Hootenanny]

oki thx, but what do it mean that the skater "skater spin faster" ? (i am from sweden .. )

It means the angular velocity ($\omega$) increases. In otherwords, the number of rotations per time period increases.

~H

 

[Lorens]

Okay, if we consider the arms as two uniform rods of length l and the body as a rod of radius r, when the arms are outstreched how far is the centre of mass of the arms away from the axis of rotation? Assuming the skater rotates about the centre of their body?

Now consider the centres of mass of the arms when they are by the skater's side.

~H

The thing who confuse me is that the bodies center of mass don't rotate, it translate, and the arms rotate around the shoulder and create a torque ...

:grumpy:

 

[Hootenanny]

The bodies centre of mass doesn't rotate because it is on the axis of rotation, i.e. the skater is rotating about her median line. What happens to the moment of inertia if the arms are brought close to the body?

~H

 

[Lorens]

The skater is moveing forward in a straigth line the arms are rotating but not the body.

I don't blamie you if you give up ...

Kindly Paul-Martin

 

[Hootenanny]

The skater is moveing forward in a straigth line the arms are rotating but not the body.

Where are you getting this information from? I have read the website and there is no reference to this. My take is as in this picture;

~H

 

[Curious3141]

Sorry to get in the middle of your excellent instruction, Hootenanny, but I thought I should get this out of the way : Wikipedia's explanation is wrong, wrong, wrong!

This formula explains the speeding up of ice skaters when they pull in their arms. Since the ice is nearly frictionless, the kinetic energy should stay constant during their spin. When they pull in their arms, the skaters decrease their moment of inertia I (their mass is more concentrated close to the rotation axis). To keep the kinetic energy constant, the angular velocity ω must increase; hence, the skaters spin faster.

WRONG! Rotational Kinetic Energy is NOT conserved. Angular momentum IS conserved, since negligible external torque acts on the skater. When the skater draws her arms in, she gains rotational kinetic energy (which comes from the conversion of biochemical potential energy to kinetic energy). When she let's her arms go out, she loses rotational KE (this is a more stable state, under normal circumstances she has to hold her arms in while spinning to prevent them from going out as far as possible from the axis of rotation).

Sorry to interrupt, please carry on. I must go and edit Wiki when free.

 

[Lorens]

Oh a misunderstanding from my side, i thought we were talking about ice skater, they who tries to do a distance as fast as possible. anyway I got worried for awhile, and I started to believe I had misunderstood something.

Anyway thanks a million for you help and time Hootenanny.

 

[Hootenanny]

Sorry to get in the middle of your excellent instruction, Hootenanny, but I thought I should get this out of the way : Wikipedia's explanation is wrong, wrong, wrong!



WRONG! Rotational Kinetic Energy is NOT conserved. Angular momentum IS conserved, since negligible external torque acts on the skater. When the skater draws her arms in, she gains rotational kinetic energy (which comes from the conversion of biochemical potential energy to kinetic energy). When she let's her arms go out, she loses rotational KE (this is a more stable state, under normal circumstances she has to hold her arms in while spinning to prevent them from going out as far as possible from the axis of rotation).

Sorry to interrupt, please carry on. I must go and edit Wiki when free.

I must have read that paragraph tens of times and have never spotted that before! I've even re-written out it but replace rotational kinetic energy with angular momentum without even thinking about it! This is a case for multiple sourcings. That's really annoyed me now, how I could miss read something that's so obviously wrong!

Oh a misunderstanding from my side, i thought we were talking about ice skater, they who tries to do a distance as fast as possible. anyway I got worried for awhile, and I started to believe I had misunderstood something.

Anyway thanks a million for you help and time Hootenanny.

Take note of the blatent mistake Curious pointed out (and I missed ) ROTATIONAL KINETIC ENERGY IS NOT CONSERVED, however, angular momentum is.

~H

 

[Curious3141]

I must have read that paragraph tens of times and have never spotted that before! I've even re-written out it but replace rotational kinetic energy with angular momentum without even thinking about it! This is a case for multiple sourcings. That's really annoyed me now, how I could miss read something that's so obviously wrong!



Take note of the blatent mistake Curious pointed out (and I missed ) ROTATIONAL KINETIC ENERGY IS NOT CONSERVED, however, angular momentum is.

~H

I've edited it, but for some reason my annotation is not showing in the history. But the page has changed, I just removed that whole idiotic paragraph. Sheesh...:yuck:

 

[Hootenanny]

I've edited it, but for some reason my annotation is not showing in the history. But the page has changed, I just removed that whole idiotic paragraph. Sheesh...:yuck:

I'd have thought someone would have spotted it earlier, but then again I didn't .

~H

 

[Curious3141]

I'd have thought someone would have spotted it earlier, but then again I didn't .

~H

Surprising how easy it is to miss small but obvious errors (though this one was not that small!)

I also edited the classical Doppler effect page a while back - the sign convention was inconsistent (making a big difference when the formula was applied). Then some other stuff on cars regarding intercooler technology.

I'm beginning to share Zapper's reservations about the reliability of Wiki. Between well-meaning but misinformed editors and outright vandals, what chance do we have of accuracy?

 

[Hootenanny]

Surprising how easy it is to miss small but obvious errors (though this one was not that small!)

I also edited the classical Doppler effect page a while back - the sign convention was inconsistent (making a big difference when the formula was applied). Then some other stuff on cars regarding intercooler technology.

I'm beginning to share Zapper's reservations about the reliability of Wiki. Between well-meaning but misinformed editors and outright vandals, what chance do we have of accuracy?

I agree, I would never use Wikipedia as an outright source, I usually use it as a reference, just to confirm my own thoughts; even so I will use Wikipedia more reservedly in future.

~H