The discussion centers on the relationship between force and momentum, specifically how the integral of force over time relates to changes in momentum. It is established that force is the time derivative of momentum, leading to the equation Fdt = dp. The integration of this equation reveals that the integral of force with respect to time equals momentum, but it is crucial to include the integration constant. The correct formulation is that the final momentum equals the initial momentum plus the change in momentum.
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Look at your first equation. It defines the integral of F (in your sense) as a change in momentum.Kyuutoryuu said:
Kyuutoryuu said:
(Change in momentum is the area under a force against time curve.)
(Force is the time derivative of momentum.)
Using separation of varibles, you get Fdt=dp. Integrate both sides, you get that the integral of Force with respect to time is equal to p. This seems to imply that p, momentum, is equal to change in momentum?