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