Linear Momentum

Momentum, p = mv, is the quantity Newton actually wrote his second law in terms of: force is the rate of change of momentum, not just mass times acceleration. A slow truck is harder to stop than a fast bicycle because momentum weighs velocity by mass. The truck might move at 2 m/s but has a mass of 5000 kg, giving p = 10000 kg m/s. A bicycle and rider at 10 m/s with mass 80 kg only reach p = 800 kg m/s. Stopping something means driving its momentum to zero, and that takes more work the bigger p is.

Momentum is a vector, so it points the same direction as velocity and adds like vectors. This matters the moment you have more than one object: the total momentum of a system is the vector sum of each object's mv, not just a sum of sizes. If two objects move at right angles to each other, their momenta don't add directly — you combine them like any two perpendicular vectors, using the Pythagorean theorem for magnitude and trigonometry for direction. That total vector is what stays fixed when no outside net force acts on the system, which is exactly what makes momentum the right tool for collisions.

This sets up everything else in the unit. Impulse, J = integral of F dt, is defined as the change in this same momentum vector, linking force and time to how velocity changes. Collisions and explosions are then just problems where you track the system's total momentum vector before and after, trusting that it stays constant unless something outside pushes on the system.