Download Momentum

Momentum
动量
50 km/hr
Velocity by itself is not a good
“measure of motion”.
50 km/hr
The “measure of motion” (momentum)
must involve the mass…
What about
mass x velocity ?
This is almost right, but not
exactly!
质量
Thanks to Einstein, we now
know the correct definition
of momentum:


p   mv
Greek letter gamma

1
2
v
1 2
c
depends on how close the velocity
is to the speed of light c.
The value of γ is very close
to 1, unless the velocity is
extremely close to the
speed of light.
Large Hadron Collider, in Switzerland
Protons are
accelerated to
0.999999991 c.
γ = 7500!
As long as v << c:


p  mv
Newton’s Second Law of Motion
The change in momentum
of a body is equal to the
net force acting on the
body times the duration of
the interaction.
Newton’s Second Law of Motion


p  Fnet t
(Assumes force is constant during time Δt.)
Newton’s Second Law of Motion


p  Fnet t
Force causes change in
momentum.
Newton’s Second Law of Motion


p  Fnet t
Sometimes this is called the
momentum principle.
Newton’s Second Law of Motion


p  Fnet t
But it is probably not the version
of the law you have seen before…
First, let’s re-arrange:
 
p  Fnet t
 
p
 Fnet (divided by t )
t


Assuming v << c, we can use p  mv :



mv  
 Fnet (replaced p with mv )
t
 
v
m
 Fnet (because m is constant)
t
 

ma  Fnet (using definition of a )
Newton’s Second Law of Motion
(alternative version)


Fnet  ma
This version is less fundamental
than the first one.
It is only true for v << c.
Force has units of Newtons (N).
1 N is roughly the
gravitational force on
a small apple.
Example: Swinging my keys
Newton’s laws only hold in an
inertial reference frame:
one that is not accelerating.
惯性参考系
Is our classroom an inertial
reference frame?
Not exactly, but close enough.
R  6.4 10 6 m