hi, guys

I am sure that at some time during your studies you have taken a look at the phenomenum of an ice skater doing their spins on their skates on ice.

You know, when the skater spins on the spot with arms extended and brings her arms closer to her body generating an incredible speed of rotation.

I know you will probably think of Conservation of angular momentum and I guess that probably is the answer but what is puzzling me is that they spin with out any sign of slowing down and look like they could spin for ages.

Is it all in the flick of a hand or a twist of the feet or what?

BY bringing the hands inwards what does this actually do?

Quantum Quack,

BY bringing the hands inwards what does this actually do?

As you said "Conserves Momentum - energy). Arms out stretched calculate the kenetic energy Ke = mv^2/2. If you pull the arms in without increasing rotation (spin) rates you would have a decrease in velocity and that decrease squared would be the change in energy.

Energy of the hands outstretched actually accelerates the rest of the mass to cause the hands to retain there kenetic energy (conservation of momentum). When drawn in the velocity must be maintained, at the shorter circumference that means greater angular acceleration higher rotational spin).

THanks for that

Does the energy needed to pull the hands in add to the velocity of rotational spin as well do you think?

( my first guess would be no but I have a feeling that it may)

Quantum Quack,

Does the energy needed to pull the hands in add to the velocity of rotational spin as well do you think?

( my first guess would be no but I have a feeling that it may)

Actually your first guess is right. In a theoretically perfect system the velocity remains the same. With the shorter circumference the rotational speed increases but not the disatance/time = v.

Otherwise Ke = mv^2/2 would change. In actual practice the added wind resistance causes a slight loss of momentum, so velocity will decrease slightly.

if I remember from my skating days if one is in a spin, the spin can be maintained by simply extending and retracting the arms slightly as you rotate.

The energy needed to pull the hands inwards seems to add to the spin velocity.

The reason I am asking all these questions is that I am exploring the possibility of what i would call a velocity at which minimum and maximum spins are self perpetuating.

Say you spin an object to 5000 rpm and due to harmonics achieved by slowing, speeds up going on to repeat the velocity oscilations.

But the question extends to how fast does the velocity need to be before this harmonic or resonating effect takes place.

MacM is not quite right.

The energy expended in pulling your arms in is converted to energy of rotation, and that causes your rate of rotation to speed up.

What you are actually doing by pulling your arms in is to decrease your rotational inertia. Since angular momentum is conserved in the absence of external forces, your angular speed must increase to compensate.

As to spin being "self-perpetuating", ALL rotation carries on forever unless there is some kind of external force which stops the rotation. That's why all the planets keep spinning over billions of years. A spinning ice skater spins for a long time because the friction between his or her feet and the ice is very small. However, it is still there, and the skater will eventually slow down and stop due to this friction.

James, thanks for taking the time to respond.

You may have missed another aspect that I mentioned
if I remember from my skating days if one is in a spin, the spin can be maintained by simply extending and retracting the arms slightly as you rotate.

By moving the limbs outward and inward it appears that the skater has control over the duration of their spin. Indefinite if I am not mistaken other than getting tired.

Extrapolated to a spinning top ( toy )

I have noticed that when spinning a "top" the spin speed oscilates until eventually it will slow and stop.

I am wondering if this oscilation may be more effective at considerably higher rpms.

the harmonics coming into play being more productive with regards to overcoming frictional drag.

Have you any knowledge of this area?

QQ: there is no input of energy to they system from what I can tell so the energy will evetually be lost to friction. There should be no perpetual spinning.

I know I am in the realms of abstraction again and you all know how I like abstractions ha.....well

If a top spinning at 50,000 rpm oscillates and sets up a harmonic vibration this hamonic may pull energy towards the top by bouncing it's environment. Setting up a wave or pulse within the top sustaining it's spin. As the energy travells inwards it's velocity increases ( as in the ice skater) as the spin slows the harmonic re-starts up and the energy is pull in again thus repeating the cycle......( I am sure this is not a new Idea)

Just a thought on how harmonics can possibly come to play. Not based on any real knowledge too I might add.

James R.,

The energy expended in pulling your arms in is converted to energy of rotation, and that causes your rate of rotation to speed up.

I agree. One must do work to pull the arms in and that work must be stored. But in general the increased rotation is not due to such work alone, there is a conservation of kenetic energy of the arms which will increase rotational speed in a conservation of momentum, not taking into account the added work of pulling the arms in.

Do you agree?

QQ,

If a top spinning at 50,000 rpm oscillates and sets up a harmonic vibration this hamonic may pull energy towards the top by bouncing it's environment. Setting up a wave or pulse within the top sustaining it's spin. As the energy travells inwards it's velocity increases ( as in the ice skater) as the spin slows the harmonic re-starts up and the energy is pull in again thus repeating the cycle......( I am sure this is not a new Idea)

I don't know but I think you are mistaking precessional wobble for Rpm oscillation. This wobble does not induce added energy. The Rpm of the top doesn't oscillate. The precessional velocity oscillates.

MacM:

But in general the increased rotation is not due to such work alone, there is a conservation of kenetic energy of the arms which will increase rotational speed in a conservation of momentum, not taking into account the added work of pulling the arms in.

Do you agree?

No.

Kinetic energy is not conserved.

James R.,

No.

Kinetic energy is not conserved.

Excluding minutiae, such as the work of pulling in the arms against centrifugal force, which has already been discussed here. I would be intereted to see how kenetic energy is not conserved.

Thanks.

Kinetic energy is not conserved.

This too is of interets to me.

But I guess first we need to define the terminology James is refrring to.
James, in your terms what does:
Kinetic energy means?
and conserved means?

Ok, MacM. Take an object with angular momentum 20 kg m²/s and a rotational inertia of 10 kg m². It is rotating at 2 radians per second on ice.

Now, by exerting forces only within the object system, we reduce the rotational inertia to 1 kg m². Due to conservation of angular momentum, the object now rotates at 20 radians per second.

The initial kinetic energy of this object was 20 Joules. The final kinetic energy is 200 Joules.

Kinetic energy has been gained. It is not conserved.

James R.,

Ok, MacM. Take an object with angular momentum 20 kg m2/s and a rotational inertia of 10 kg m2. It is rotating at 2 radians per second on ice.

Now, by exerting forces only within the object system, we reduce the rotational inertia to 1 kg m2. Due to conservation of angular momentum, the object now rotates at 20 radians per second.

The initial kinetic energy of this object was 20 Joules. The final kinetic energy is 200 Joules.

Kinetic energy has been gained. It is not conserved.

Perhaps you would now enlighten us as to the amount of energy expended in altering the rotation by applying forces through distance to relocate the mass in the system.

The amount of energy expended would be 180 Joules, in the example I just gave.

James R.,

The amount of energy expended would be 180 Joules, in the example I just gave.

Prior Post by MacM: "Excluding minutiae, such as the work of pulling in the arms against centrifugal force, which has already been discussed here."

Which words in my post did you not understand? 20 + 180 = 200. Energy is conserved the only difference is in the form and that was convered by my statement. You appear to want to make it look like I was in error and you simply restated my position!

You claimed that KINETIC energy was conserved. Your were wrong, and I pointed it out.

James R.,

Prior Post by MacM: "Excluding minutiae such as the work of pulling in the arms against centrifugal force, which has already been discussed here."

Reduced to playing word games are we? Your example had already been given as an offset in kenetic energy.

But in general the increased rotation is not due to such work alone, there is a conservation of kenetic energy of the arms which will increase rotational speed in a conservation of momentum, not taking into account the added work of pulling the arms in.

Your statement in bold was false, as I have pointed out. Moreover, if you ignore the work of pulling the arms in, then there is no source for the increased kinetic energy of the spin. This is not "minutiae", as you claim, but the entire source of the kinetic energy increase - all 180 Joules of it in my example.

This is not a word game. This is the truth.

James R.,,

Your statement in bold was false, as I have pointed out. Moreover, if you ignore the work of pulling the arms in, then there is no source for the increased kinetic energy of the spin. This is not "minutiae", as you claim, but the entire source of the kinetic energy increase - all 180 Joules of it in my example.

This is not a word game. This is the truth.

Sorry you are correct I made a terrible statement there. I don't recall writting that but I'm sure I must have. It is not a good description.

awwwhhh ....I dunno....I have just been watching footage of skaters and there seems to be a hell of lot more happening than what we seem to think......The velocities are inordinately high and the duration is controlled by the dancer.....also the ability to come out of the spin appears way to sudden and with little effort.

Something is happening beyond what we have discussed so far and for the life of me I can't figure it out.....

Maybe the dancer is tapping into something else.....

observation:
The dancer is spinning slowly and starts to pull her hands in. bringing them in say 90% of the way shows only a slight increase in spin but when she pulls the last 10% she gains about 400% on the spin and in two revolutions has pulled out with out falling over or looking awkward,