Versions Compared

Key

  • This line was added.
  • This line was removed.
  • Formatting was changed.
Comment: Migration of unmigrated content due to installation of a new plugin

Definition and Law of Change     Image Added

...

Although Newton is famous for the law

F = ma,

...

he

...

actually

...

stated

...

his

...

Second

...

Law

...

in

...

terms

...

of

...

momentum

...

and

...

its

...

change

...

due

...

to

...

impressed

...

forces

...

or

...

impulses

...

(the

...

time

...

integral

...

of

...

the

...

force).   He defined Momentum as

The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjointly. - DEFINITION II, Principia (Motte and Cajori).  

In modern terminology, this definion becomes:

Latex
   He defined Momentum as
_The [quantity of motion] is the measure of the same, arising from the [velocity] and quantity of matter conjointly_. - DEFINITION II, Principia (Motte and Cajori).  

In modern terminology, this definion becomes:

{latex}\begin{large}\[ \vec{p} = m\vec{v} \]\end{large}{latex}

and [

Newton's

...

Second

...

Law

...

can

...

be written in terms of momentum, and represents the fundamental law of change for the Momentum and External Force model:

Latex
 written:

{latex}\begin{large}\[ \sum_{\rm ext} \vec{F} = \frac{d\vec{p}}{dt}\]\end{large}{latex}

This

...

form

...

is

...

totally

...

equivalent

...

to

...

F

...

=

...

ma

...

,

...

provided

...

that

...

the

...

system

...

under

...

consideration

...

has

...

constant

...

mass

...

.

...

Unlike

...

the

...

traditional

...

F

...

=

...

ma

...

formulation,

...

however,

...

the

...

formulation

...

of

...

Newton's

...

Second

...

Law

...

in

...

terms

...

of

...

momentum

...

is

...

accurate

...

even

...

for

...

systems

...

whose

...

mass

...

is

...

variable.

...