Re: Question about Kepler's second law

On Apr 11, 3:16 pm, "Peter" <Poakfi...@xxxxxxx> wrote:
On Apr 11, 1:52 pm, "PD" <TheDraperFam...@xxxxxxxxx> wrote:





On Apr 11, 12:24 pm, "Peter" <Poakfi...@xxxxxxx> wrote:

On Apr 11, 12:27 pm, "Greg Neill" <gneill...@xxxxxxxxxxxxxx> wrote:

"Peter" <Poakfi...@xxxxxxx> wrote in message

news:1176308435.240966.89420@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

According to Newton'ssecondlawFnet = dp/dt, only a net force causes
the acceleration of an object. If a net torque also produces the
acceleration of an object, doesn't this contradict Newton'ssecond
law?

Torque applies to angular momentum and thus
angular acceleration. dp/dt refers to the
change in linear momentum.

A torque applied to a point mass can produce a change in its linear
(tangential) momentum about some point of reference. If the point of
reference is far away, the acceleration of the point mass would be
almost linear.No?

A particle traveling in a *straight line* has both linear momentum and
angular momentum with respect to an axis through a point not on the
line. It is not a case of "either linear or angular momentum but not
both."

PD- Hide quoted text -

- Show quoted text -

The rotational variables were developed to facilitate the use of
Newton's laws to rotation? But they are not indispensable, and
rotation can be handled with Newton's laws directly. It does not make
sense to me that the angular momentum of a point particle depends on,
and varies with, the point one arbitrarily chooses as the point of
reference.

Well, that's unfortunate that it doesn't make sense to you. Perhaps it
doesn't make sense to you that gravitational potential energy depends
on, and varies with, the point one arbitrarily chooses as the point of
reference. Perhaps it doesn't make sense to you that kinetic energy
depends on, and varies with, the reference frame one arbitrarily
chooses.

In contrast, linear momentum is the same anywhere in a
given frame of reference.

And there's a reason for that. (See Noether.) Linear momentum
conservation is directly related to position translation invariance of
the laws of physics. You might ask yourself what angular momentum
conservation is directly related to. (It's not position translation
invariance.)

Since all extended objects are made up of
point particles, it is just a matter of summation, and one could deal
with any kind of motion of any object, but the results could be
different from those obtained using the rotational variables. This
means something is awfully wrong with some of the rotational
variables, like torque. Do you agree?

No, I don't. Just because there is a relationship between linear
momentum and angular momentum through the connection you just
mentioned, this does NOT mean that when one changes, the other has to
change. I've already explained why and given you several examples of
where this is not the case. You are simply making an assumption that
should not be made.

PD


Peter

Peter
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