The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Math Topics » alt.math.undergrad

Topic: Section 19 intro johnreed March 30, 2011
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  

Posts: 61
Registered: 11/21/09
Section 19 intro johnreed March 30, 2011
Posted: Mar 30, 2011 1:30 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Section 19

Recall that we have linear momentum and spin angular momentum from
Newton?s first law. The angular velocity of a spinning disk, sphere,
or solid object, is an artifact of the uniformly spinning disk,
sphere, or solid object. The angular momentum of a spinning solid
object also follows from the first law.

We don?t have orbital angular momentum from that law. We acquire
orbital angular momentum from Newton?s mathematical derivation for
orbital centripetal force, where he used a perfect circle and perfect
motion to argue for orbital centripetal acceleration. In other words
Newton used the artifacts of spin angular momentum, ie. a perfect
circle and perfect motion, to argue the mathematical case for orbital
centripetal force and angular momentum. Here the only change in
velocity is direction.

The spinning perfect circle angular velocity is an artifact of the
uniformly spinning circle itself. So we have least action consistent,
single object, spin angular velocity in all cases..

He then associated planet surface object mass [m] with celestial
centripetal acceleration [v^2/r] by multiplying both sides of a least
action consistent equation involving [v^2/r] by planet surface object
mass [m]. The product is [mv^2/r] and voila spin angular momentum
became orbital angular momentum.

Newton then used the least action consistent angular velocity from
Kepler?s empirical, time controlled law of areas, describing 2 body
planet orbital motion, to mathematically carry his perfectly circular
2 body uniform motion, spin angular momentum analog, to the planet?s
non-uniform 2 body orbital motion.

The generalization is based on least action consistent time-space
parameters where the emergent conserved cumulative resistance of
planet and moon surface atoms is either designated as the cause of the
least action consistent celestial motion (Newton?s gravity), or as the
consequence of the least action consistent 4D space-time curvature
caused, continuum motion (Einstein and peers). Regurgitation of
original error..

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.