Summary
Highlights
Linear momentum (p) is defined as mass times velocity (p = mv) and is a vector quantity with units of kilograms times meters per second. It is particularly useful for modeling motions during collisions or explosions because the net external force is often negligible compared to internal forces.
Newton's Second Law can be expressed as net force equals the change in momentum over the change in time (F_net = Δp/Δt). This derivation assumes constant system mass and that forces and accelerations are averages.
Impulse (J), represented by uppercase J, is equal to the change in momentum (Δp) and also to the average force of impact times the change in time during a collision (F_avg * Δt). Impulse is a vector, has units of Newton-seconds, and its direction is the same as the average force of impact. It can also be found as the area under a force versus time graph. The impulse approximation states that the average force of impact is much larger than other forces during a collision.
Impulse highlights that while the total impulse might be constant, increasing the collision time can significantly reduce the average force of impact, as demonstrated by the example of wearing a bike helmet to mitigate injury.
A practical example shows how to use the relationship between impulse, area under a force-time graph, and change in momentum to calculate the final velocity of an object after a collision.
During collisions and explosions where the net external force on a system is zero, the total momentum of the system remains constant. This means the sum of initial momenta equals the sum of final momenta (Σp_initial = Σp_final).
If the net external force on a system is zero, the velocity of the center of mass of the system remains constant, even if objects within the system collide or explode. The 'i' in the center of mass equation refers to the number of particles, not initial conditions.
Collisions are categorized into elastic and inelastic. In elastic collisions, the total kinetic energy of the system is conserved. In inelastic collisions, the total kinetic energy decreases due to conversion into other energy forms like thermal energy or sound. Perfectly inelastic collisions are a type of inelastic collision where objects stick together after impact. Linear momentum is conserved in both elastic and inelastic collisions.