Momentum 动量

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: Greek letter gamma 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 c. γ = 7500! Large Hadron Collider, in Switzerland

As long as v << c:

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 (Assumes force is constant during time Δt.)

Newton’s Second Law of Motion Force causes change in momentum.

Newton’s Second Law of Motion Sometimes this is called the momentum principle.

Newton’s Second Law of Motion But it is probably not the version of the law you have seen before…

First, let’s re-arrange: Assuming v << c, we can use :

Newton’s Second Law of Motion (alternative version) 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.