# Center of Mass Velocity Question [duplicate]

How does the center of mass of a collision change after a collision has occurred compared to before. For instance, I know that it is moving, but does the velocity change and if so does it depend on whether the collision is elastic or inelastic

• -1 I recall hearing things about how the COM can not move is rather vague. A good question provides evidence, rather than appeals to vague memories. – sammy gerbil Jan 10 '18 at 12:51
• Possible duplicate of Can the velocity of the center of mass of two spheres change after a collision? – sammy gerbil Jan 10 '18 at 12:53
• – sammy gerbil Jan 10 '18 at 12:57
• The centre of mass of an object depends on what you define as the object. A totally inelastic collision will lead (if not to destruction) to the objects sitting adjacent to each other and moving as one, so it may (depending on the application) lose meaning to talk of their centre of masses independently. – Steve Jan 10 '18 at 13:15

## 2 Answers

If you have a system which consists of two blocks then the velocity in a given direction of the centre of mass of the system of two blocks does not charge if there are no external forces acting on the blocks in that direction.

So if the blocks are moving on a flat and friction-less horizontal table the horizontal velocity of the centre of mass of the two blocks will not change irrespective of what type of collision they undergo.

The collision is said to happen in an instant, changing the velocity and rotational speed of a body, but the position and orientation do not change.

The change in velocity can be expressed as $$\Delta v = \frac{1}{m} \int F\,{\rm d} t$$

where the force $F$ is short lived and very high in value such as the impulse $J = \int F \, {\rm d}t$ is a finite value. The result is that $\Delta v$ is finite.

But the change in position is zero because the finite velocity is multiplied by an infinitesimally small time

$$\Delta x = \int v\, {\rm d}t \rightarrow 0$$