# Momentum and kinetic energy

"if kinetic energy of system of particles is zero, then linear momentum of that system of particles is zero but the reverse is not true. That is if linear momentum of a system of particles is zero, then the kinetic energy may not be zero"

This is what I got from my text. Can you provide me with some examples because I am a bit confused. Can you provide some explanation?
Is this true for angular momentum?

Staff Emeritus
2021 Award
Consider two particles with mass m, one with velocity +v and one with velocity -v.

Consider two particles with mass m, one with velocity +v and one with velocity -v.
So momentum is zero and kinetic E is not zero. Can you give an example for kinetic energy zero and momentum non zero?

So momentum is zero and kinetic E is not zero. Can you give an example for kinetic energy zero and momentum non zero?
KE = sum of 1/2 mv2. Can any of those terms be negative?
Or, imagine covering the whole system with a curtain or box and treating it as one object of total mass M and velocity V.
P=MV, while KE= 1/2MV2+ KE(within system, relative to the center of mass)
If KE = 0, what does that imply? Assume masses are never negative.