Announcements
•
Reading for Wednesday: 3.13.6
•
First Midterm is next week (Feb. 9
th
,
7:30pm). It will cover Chapters 1&2.
•
Support Haiti:
On Facebook: CU Stands with Haiti
Momentum
The classical definition of the momentum
p
of a
particle with mass m is:
p
=m
u
.
In absence of external forces the total momentum is
conserved (Law of conservation of momentum):
n
.
1
const
i
i
=
∑
=
p
Due to the velocity addition formula, the definition
p
=m
u
is not
suitable to obtain conservation of momentum in special
relativity!!
Need new definition for relativistic momentum!
Review: Transformation rules and
conservation of momentum
y
u
1
u
2
m
m
y'
u
'
1
u
'
2
m
u
u
1y
v = u
1x
x
S
x'
m
S'
1x
2
/
1
'
c
v
u
v
u
u
x
x
x


=
(
29
2
/
1
'
c
v
u
u
u
x
y
y

=
γ
Relativistic:
Classical:
u'
x
= u
x
– v
u'
y
= u
y
Conservation of momentum
is extremely
useful in classical physics.
For the new
definition of relativistic momentum we want:
1. At low velocities the new definition of
p
should match the classical definition of
momentum.
2. We want that the total momentum
(
Σ
p
)
of
an isolated system of bodies is conserved
in all inertial frames.
Relativistic momentum
Classical definition:
dt
d
m
r
p
=
Say we measure the mass 'm' in its restframe ('
proper
mass'
or '
rest mass'
). Since we measure 'm' it's rest
frame we agree on the same value for 'm' in all frames.
Relativistic definition:
proper
dt
d
m
r
p
≡
Assume we take the derivative with respect to the
proper
time t
proper
, which has the same meaning in all frames.
This definition fulfills the conservation of momentum in SR!
To prove it you can apply the relativistic velocity transformation.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 staff
 Physics, Energy, Kinetic Energy, Mass, Momentum, Special Relativity, dr dt

Click to edit the document details