I Conservation of Momentum versus Conservation of Velocity

[paulfreda]

TL;DR Summary

Inertia = Conservation of Velocity

I have often wondered why Inertia , Newton's 1st Law, is not simply called
Conservation of Velocity
Can anyone give me a reason why it should NOT be called
Conservation of Velocity ???

Conservation of Energy is valid in the absence of External Forces.
Conservation of Momentum is valid in the absence of External Forces.
Velocity is constant in the absence of External Forces too ! !

It seems so obvious to me.
What am I missing ???

Thanks for your thoughts

 

[Mark44]

Conservation of Momentum is valid in the absence of External Forces.

Conservation of velocity is equivalent to conservation of momentum (p = mv) provided that the mass doesn't change.

 

[Ibix]

Consider a very light ball striking a very massive wall initially at rest. The sum of the momenta is unchanged; the sum of the velocities is very different - very nearly minus what it started as.

Velocity is not a conserved quantity in collisions.

 

[topsquark]

TL;DR Summary: Inertia = Conservation of Velocity

I have often wondered why Inertia , Newton's 1st Law, is not simply called
Conservation of Velocity
Can anyone give me a reason why it should NOT be called
Conservation of Velocity ???

Conservation of Energy is valid in the absence of External Forces.
Conservation of Momentum is valid in the absence of External Forces.
Velocity is constant in the absence of External Forces too ! !

It seems so obvious to me.
What am I missing ???

Thanks for your thoughts

Momentum is conserved when the net external force on a system is 0 N during a collision (or some other happenstance.)

Energy is conserved when there is no net non-conservative work done on the system during a change in state of some kind.

Yes, Newton's 1st does describe the notion of what happens to the velocity of an object when the net external force on it is 0 N. But the idea of Newton's 1st is to define what "inertia" is (or, depending on your Philosophy, how to define if a net force is acting on an object. The two concepts are inextricably linked at this level.) It really has nothing to do about whether the velocity of an object stays the same during some kind of process, which is what a conservation law would usually refer to.

-Dan

 

[PeroK]

Conservation of Energy is valid in the absence of External Forces.
Conservation of Momentum is valid in the absence of External Forces.
Velocity is constant in the absence of External Forces too ! !

It seems so obvious to me.
What am I missing ???

Thanks for your thoughts

Energy and momentum are conserved for any system of particles (in the absence of external forces). The "conservation of velocity" applies to the centre of mass - although it's usually exemplified by the existence of a "zero momentum" or "centre of momentum/mass" frame. Note that in the CoM frame, the total momentum is zero, but the sum of the particle velocities may not be zero.

Newton's laws extend beyond the kinematics of a single particle.

 

[A.T.]

Can anyone give me a reason why it should NOT be called Conservation of Velocity ???

Mainly because of what the other "conservation laws" represent: The sum of all momenta / energies is always conserved for an isolated system, no mater how its parts exchange them between each other. This is not the case for the sum of all velocities, so it would be confusing to use the same name.

 

[vanhees71]

Momentum is conserved when the net external force on a system is 0 N during a collision (or some other happenstance.)

Energy is conserved when there is no net non-conservative work done on the system during a change in state of some kind.

Yes, Newton's 1st does describe the notion of what happens to the velocity of an object when the net external force on it is 0 N. But the idea of Newton's 1st is to define what "inertia" is (or, depending on your Philosophy, how to define if a net force is acting on an object. The two concepts are inextricably linked at this level.) It really has nothing to do about whether the velocity of an object stays the same during some kind of process, which is what a conservation law would usually refer to.

-Dan

I think Newton 1, expressed in modern terms, is the postulate that there exists a global inertial frame of reference, which implies that there exist infinitely many inertial frames of reference, because any frame moving with constant velocity relative to an inertial frame is itself an inertial frame. That's the invariance of Newtonian spacetime under Galilei boosts. From a Noetherian point of view the corresponding conservation law for closed mechanical systems (i.e., systems, where all constituents are considered and all forces are interaction forces between the constituents) the corresponding conserved quantity is the center-of-mass velocity.