Linear Momentum and Collisions (Physics)

Recall cards on linear momentum and collisions: linear momentum p = mv as a vector pointing along the velocity, measured in kg·m/s, characterizing an object's quantity of motion and depending linearly on mass and velocity. Impulse J as force times time, the infinitesimal and integral forms, the impulse-momentum theorem J = delta p, Newton's second law as F = dp/dt, and the average force in a collision. Conservation of linear momentum for a closed system, why internal Newton's-third-law pairs cancel while external forces change total momentum. Types of collisions: momentum always conserved, kinetic energy conserved only in elastic collisions, inelastic and perfectly inelastic collisions, and explosions. Collisions in multiple dimensions with per-direction conservation and component equations. The center of mass as the weighted average position of mass, r_CM and its component and integral forms, F_ext = M a_CM, and the constant center-of-mass velocity of a system with zero external force. And rocket propulsion as a variable-mass system, exhaust velocity, the Tsiolkovsky rocket equation delta v = u ln(m_0/m), and the effect of gravity on a launch.