Momentum
Momentum, P, is the product of an object’s velocity and its mass. It is a vector quantity that represents how much “push“ or “drive“ something has. In a closed system, where there are no external forces, momentum is conserved throughout collisions, meaning the total initial momentum of any number of objects will equal the final momentum of that same number of objects.
When there are multiple objects colliding with each other, energy is transferred along with momentum, creating movement. The total momentum of a closed system is equal to the sum of each individual momentum. In a Newton’s cradle, all the potential energy of the raised ball is transferred to kinetic energy, raising the ball’s momentum. When the balls collide, the energy is transferred, and the momentum is conserved, which is why each ball moves slower because the mass is increased and the total momentum must stay the same.
Impulse, J, is a quantity that is defined as the change in momentum over time. It can be found using the equation J = mΔv = FΔt. Impulse is very useful when looking at single-object collisions, such as a ball bouncing off the ground.
When looking at entire systems, the total momentum is found with the total mass times the total velocity of the center of mass. To locate the center of mass, you add up all the mass, mi, then multiply it by the sum of all the positions, ri, then divide the remaining quantity by the total mass again.
In calculus, momentum can be found using the derivative of energy, and impulse can be found with the integral of F(t)dt.