momentum 动量. 50 km/hr velocity by itself is not a good “measure of motion”
TRANSCRIPT
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Momentum
动量
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50 km/hr
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50 km/hr
Velocity by itself is not a good “measure of motion”.
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The “measure of motion” (momentum) must involve the mass…
What about
mass x velocity ?
This is almost right, but not exactly!
质量
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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.
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The value of γ is very close to 1, unless the velocity is extremely close to the speed of light.
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Protons are accelerated to 0.999999991 c.
γ = 7500!
Large Hadron Collider, in Switzerland
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As long as v << c:
vmp
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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.
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Newton’s Second Law of Motion
tFp net
(Assumes force is constant during time Δt.)
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Newton’s Second Law of Motion
tFp net
Force causes change in momentum.
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Newton’s Second Law of Motion
tFp net
Sometimes this is called the momentum principle.
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Newton’s Second Law of Motion
tFp net
But it is probably not the version of the law you have seen before…
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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
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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.
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Force has units of Newtons (N).
1 N is roughly the gravitational force on a small apple.
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Example: Swinging my keys
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Newton’s laws only hold in an inertial reference frame:
one that is not accelerating.
惯性参考系
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Is our classroom an inertial reference frame?
Not exactly, but close enough.
m104.6 6R