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Momentum
动量
50 km/hr
50 km/hr
Velocity by itself is not a good “measure of motion”.
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:
vmp
Greek letter gamma
2
2
1
1
cv
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.
Protons are accelerated to 0.999999991 c.
γ = 7500!
Large Hadron Collider, in Switzerland
As long as v << c:
vmp
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
tFp net
(Assumes force is constant during time Δt.)
Newton’s Second Law of Motion
tFp net
Force causes change in momentum.
Newton’s Second Law of Motion
tFp net
Sometimes this is called the momentum principle.
Newton’s Second Law of Motion
tFp net
But it is probably not the version of the law you have seen before…
First, let’s re-arrange:
)by (divided net
net
tFt
p
tFp
Assuming v << c, we can use :vmp
) of definition (using
constant) is (because
) with (replaced
net
net
net
aFam
mFt
vm
vmpFt
vm
Newton’s Second Law of Motion (alternative version)
amF
net
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.
m104.6 6R