# Conservation of momentum when two objects collide

member 529879
when two objects collide some kinetic energy can be lost to heat, so some of the kinetic energy of the two colliding objects transfers to the individual particles of these objects. Does the same thing happen for momentum?

## Answers and Replies

jfizzix
Science Advisor
Gold Member
It's illuminating to consider the center of masses of each of these objects.

For each object:
$KE_{object} = KE_{CM} + KE_{internal}$

As you say, the total kinetic energy of a pair of objects is conserved in a collision, though energy may be transferred between the center-of-mass degree of freedom, and internal degrees of freedom.

As for as momentum goes, the total linear momentum of an object can be expressed just as the momentum of its center of mass. So no linear momentum is lost to internal degrees of freedom in a collision.

However, angular momentum breaks up into (orbital) angular momentum of the center of mass, and (spin) angular momentum with respect to the center of mass:
$L_{total}=L_{CM} + L_{internal}$

So in a collision, the total angular momentum is conserved, though some may be transferred to internal angular momentum. The objects could glance off each other, and be spinning as a result.

member 529879
But linear momentum is not lost to internal linear momentum? If the atoms can have more kinetic energy after a collision would that also mean that they have more momentum?

jfizzix
Science Advisor
Gold Member
The atoms of an object can be moving around the center of mass of the object, but if you add up all those momenta, the parts of the object moving forward plus the parts of the object moving backward ass up to a total momentum that is just the total mass times the velocity of the center of mass.

• member 529879
Khashishi
Science Advisor
If some particles are lost in the collision (as fragments or radiation), they can carry some momentum away. But as long as a bulk mass stays intact, the momentum of the bulk mass is just the sum of momenta of its constituent particles.