If a particle and a system have zero momentum

[DJW]

Is it true that they both must also have zero kinetic energy?

 

[qspeechc]

If we are talking of one particle, and it has zero momentum, it must have zero velocity (mass cannot be zero), and so its kinetic energy is zero.
If a system of particles has zero momentum, anyone particle in the system may still have momentum, say ,if it is vibrating in a lattice, but the system as a whole does not.

 

[Moetasim]

No, it is not necessarily true that if a particle and a system have zero momentum, they must also have zero kinetic energy. Kinetic energy is a measure of an object's motion, while momentum is a measure of an object's mass and velocity. It is possible for an object to have zero momentum, meaning it is not moving, but still have some amount of kinetic energy due to its internal motion or vibrations. Similarly, a system can have a net momentum of zero if the momenta of its individual particles cancel out, but the particles may still have kinetic energy due to their internal motion. Therefore, while zero momentum may indicate a lack of overall motion, it does not necessarily mean that there is no kinetic energy present.