Re: When Physical Intuition Fails

[Brian Whatcott <betwys@DIRECTVINTERNET.COM>]

Bob, having read your reasoned development, can I ask:
does this treatment copied below lead to maximal translation
velocity in the case where there is no initial slippage at the
interface of the cylinder and substrate?

I am taken with the suggestive comparison with the transfer of charge
 between capacitors that your result indicates: where if spark
discharge (analogy:friction)  is avoided, em radiation (analogy: ??)
becomes significant.

Brian W

At 02:33 AM 10/30/02, Bob Sciamanda, you wrote:
> In the "collision" (better, interaction) between the linear and rotational
> modes, the changes in linear and angular momentum are correlated because the
> same force f effects both changes:
> fR = -(d/dt) (Iw) and f = (d/dt) (mv)
>
> As v increases from zero, w decreases from w_o and
>
> mv = -(Iw)/R + (Iw_o)/R
> This correlation plays the same mathematical role as the conservation of
> linear momentum in the two particle collision.
>
> If you require v = Rw   =>
>
> w =  w_o / (1 + [R/k]^2 ), where k=rad of gyration.
>
> For the simplest case, take R=k (the analog equivalent of equal particle
> masses) and get w = w_o/2, the analog of the halving of the particle
> velocity in a totally inelastic particle collision of equal masses.
>
> Just as in the particle collision, this forces a dissipation of kinetic
> energy.  As in the equal mass particle case, in the k=R case exactly 1/2 of
> the original energy is dissipated.
>
>
> Bob Sciamanda (W3NLV)
> Physics, Edinboro Univ of PA (em)
> trebor@velocity.net
> http://www.velocity.net/~trebor
> ----- Original Message -----
> From: "Brian Whatcott" <betwys@DIRECTVINTERNET.COM>
> To: <PHYS-L@lists.nau.edu>
> Sent: Tuesday, October 29, 2002 11:14 PM
> Subject: Re: When Physical Intuition Fails
>
>
> | I find it easy to visualize a spur wheel spinning at 1 rpm suddenly
> engaging
> | a fixed rack with no friction, in a fully elastic way.
> | Is this a limitation of my imagination, or of yours, Bob?  :-)
> | . . .
> | Brian W

Brian Whatcott
  Altus OK                      Eureka!

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.