Chapter 9 AP Physics - Linear Momentum and Collisions

Impulse of Time Averaged Force

I = ∑Favg∆t

Impulse of a force

I = ∫∑Fdt

Thrust

M(dv/dt) = ve(dM/dt)

Total Momentum of a system of particles

MVcm = ∑mivi

Acceleration of the center of mass of a system of particles

Macm = ∑miai = ∑Fi

Velocity of center of mass of a system of particles

Vcm = 1/M ∑mivi = drcm/dt

Conservation of Momentum expanded

m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f

Linear Momentum

p = mv

Rocket Propulsion

vf - vi = ve ln (Mi/Mf)

Perfectly Inelastic Collision Final Velocity

vf = (m₁v₁i + m₂v₂i)/(m₁ + m₂)

One dimensional elastic collision formula

v₁i - v₂i = -(v₁f - v₂f)

Conservation of Kinetic Energy expanded

½m₁v₁i² + ½m₂v₂i² = ½m₁v₁f² +½m₂v₂f²

Deformable System

∆Esystem = ∑T

Impulse Momentum Theorem

∆p = I

Isolated System of Momentum/Conservation of Momentum

∆ptot = 0; ∆p1 = ∆p2

Newton's Second Law (in terms of Momentum)

∑F = d(mv)/dt = dp/dt

Newton's Second Law for a system of particles

∑Fext = Macm