Angular momentum conservation and energy considerations

[rcgldr]

So if there is no work done, then you are suggesting that the new velocity WON'T be twice the old velocity under these circumstances? When we actually did this on an air table, the results were virtually identical to the first case.

Are you sure about this? After going through the math, it seems that the puck shouldn't have an increase in energy, but this is based on the assumption that the puck does follow an involute of circle path, and this sure looks like the proper model for anything winding around a post. Assuming the puck is attached at the side, then it's angular momentum (rotation wise) should slow things down a bit.

I do realize that the string is moving inwards with tension, but it's tension is perpendicular to the path of the puck so I'm not sure where the increase in energy would originate from. Relative to the string (which isn't an inertial frame since it's rotating), the string is being wrapped around the pole similar to the pole rotating and pulling in the string. Using this analogy, the only work done is to increase the potential energy (relative to the pole), but not the kinetic energy of the puck, similar to rasing a weight with a string (increase in potential energy, no increase in kinetic energy).

 

[TVP45]

Measurement error

Straightforward thermodynamics says that the linear velocity cannot increase when you do this. If this were not so, David could have whacked an entire army of Goliaths by simply shortening up his sling. If you have measured otherwise, the problem is in the measurement which is difficult to make for small circles. Measure omega and calculate v.

 

[rcgldr]

Regarding the post case (involute of circle), and taking into account the post experiences a torque and applies this torque to the earth, increasing the Earth's angular momentum, then angular momentum for the entire system, earth, post, and puck are conserved. In the hole case, no there no torque applied at the hole or to the earth, so there's no change in angular momentum to the earth, so the puck retains it's angular momentum.

 

[Prologue]

Wow Jeff, I've got to dig this one up to thank you big time for your explanation. Pretty much every post enlightened me at least a little bit on angular momentum, major kudos to you.