# Conservation of momentum

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In the absence of external forces, momentum is always conserved. The momenta of individual objects in a system may vary, but the vector sum of all the momenta will not change if there are no external forces exerted on the objects in the system. Therefore, momentum is said to be conserved.

If an external force -- that is, a force exerted by an object outside the system -- is exerted on any objects within the system, then the total momentum will change.

The conservation of momentum in a glancing collision between two objects is expressed as ${\displaystyle \left(M_{\mathrm {1} }V_{\mathrm {1i} }\right)+\left(M_{\mathrm {2} }V_{\mathrm {2i} }\right)=\left(M_{\mathrm {1} }V_{\mathrm {1f} }\right)+\left(M_{\mathrm {2} }V_{\mathrm {2f} }\right)}$

The conservation of momentum in a collision between two objects where the two objects become one is expressed as ${\displaystyle \left(M_{\mathrm {1} }V_{\mathrm {1i} }\right)+\left(M_{\mathrm {2} }V_{\mathrm {2i} }\right)=\left(M_{\mathrm {1} }+M_{\mathrm {2} }\right)V_{\mathrm {f} }}$