1.4
Single Particle Conservation theorems
Where do conservation theorems come from? They cannot be proven
per se
, but are conse
quences of Newton’s laws of dynamics. The conservations theorems must be put to the test
of experiment, and if found not to be violated, give a measure of confidence in the original
dynamical laws. That these conservation theorems have been found to be valid in a wide
range of circumstances is an important part of the “proof” of the correctness of Newton’s
laws, at least in classical and nonrelativistic physics.
1.
The total energy of a particle in a conservative force field is constant in time
. Discussed
above: see section below.
2.
Conservation of linear momentum
:
The total linear momentum
p
of a particle is
conserved when the total force applied to it is zero.
The vector equation ˙
p
= 0 is
satisfied for each component of linear momentum.
3.
Conservation of angular momentum
: If we define the the angular momentum
L
≡
r
×
p
(34)
and the torque
→
τ
≡
r
×
F
(35)
This can be written:
→
τ
=
r
×
m
˙
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 Spring '10
 RogerMelko
 Energy, Force, Kinetic Energy, DT DT DT

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