What is the physical significance of momentum. Like velocity gives us how position is changing with respect to time, what does momentum of an object show?

Question

unklerhaukus · Answer

$$F=ma=m\frac{\text d v}{\text d t}=\frac{\text dp}{\text d t}$$
 the change in momentum is how much force is acting on the particle

kainui · Answer

You can also consider that momentum is conserved within a system and that the derivative of momentum is the formula for kinetic energy. Momentum is a measure of an object's "staying" ability I like to think. There are two things that make an object's momentum go up, and that's velocity and mass. So consider a bowling ball and a pingpong ball moving at the same speed and hitting you. It's a little more that just mass you're concerned about here, it's also their momentum. A pingpong ball has little momentum, so it will bounce off of you and readily change its velocity vector into the other direction in a collision. Bowling ball won't because that mass gives it that extra inertia.

To also show that it varies with velocity, consider getting hit by a bowling ball by someone throwing it at you our of a moving car at 60 mph or having a small child roll it at you. Again, the bowling ball with less speed is going to change direction much easier because of the less momentum it has.

I hope that helps explain a very abstract kind of idea. It took me a while to wrap my head around it, and it's still kind of hard for me to understand, and I can only barely explain why the integral of kinetic energy is momentum.