Momentum Analysis in Rest Frame Decay of Particle with Mass M

[whatisreality]

Homework Statement

A particle with mass M at rest decays into two particles with masses m_a=0.15M and m_b=0.65M .
i) Discuss the relative directions and magnitudes of the momenta of these two particles in the centre of mass reference frame.

Homework Equations

The Attempt at a Solution

What's the centre of mass reference frame?! Isn't there really only one relevant frame here?

As for the relative directions - just in opposite directions, by conservation of momentum? And with the same magnitude of momentum? Although them having the same magnitude of momentum seems weird, because that would be just like Newtonian mechanics, and using that never seems to work anymore ;)

 

[BvU]

What's the centre of mass reference frame

Use the definition ! For one particle (your initial situation) it is really easy and quite intuitive !

As for the relative directions - just in opposite directions, by conservation of momentum? And with the same magnitude of momentum? Although them having the same magnitude of momentum seems weird, because that would be just like Newtonian mechanics, and using that never seems to work anymore.

Yes, yes, and: never say never again! Newton always works in the nonrelativistic limit. It's just that with high velocities you have to use the right relationships for velocity-momentum, kinetic-total energy etc.