Proof: Conservation of Momentum
March 6, 2025 | Section: Writings
I love this simple profound proof, and it’s worth understanding. For those unfamiliar with calculus, the notation $\dot{\bf{p}}$ or $\frac{d \bf{p}}{dt}$ denotes the rate of change of $\bf{p}$ with respect to time ($t$). We need to show that the net force ($\mathbf{F}$) applied on an object is proportional to the rate of change of that object’s momentum with respect to time ($\dot{\mathbf{p}}$). We know Newton’s second law: $\mathbf{F} = m\mathbf{a}$, and $\mathbf{p} = m \mathbf{v}$.