Q.A shell of mass $10\ \text{kg}$ moving horizontally at $20\ \text{m/s}$ explodes in mid-air (an internal force only) into two fragments of masses $4\ \text{kg}$ and $6\ \text{kg}$. If the $4\ \text{kg}$ fragment continues along the original direction at $35\ \text{m/s}$, find the velocity of the $6\ \text{kg}$ fragment, and state what this implies about the motion of the centre of mass of the shell.

From Newton's second law, $\vec{F}=\frac{d\vec{p}}{dt}$, it follows immediately that if the net force on a system is zero, its total linear momentum does not change -- it is conserved. This gives the principle of conservation of linear momentum: the total momentum of an isolated system (one with no net external force) is conserved during any interaction, whether a collision or an explosion. This holds because internal forces between parts of the system always occur as equal-and-opposite Newton's-third-law pairs, which exactly cancel when summed over the whole system, leaving only external forces able to change the system's total momentum. …