Conservation of momentum in two dimensions  Momentum
Conservation of momentum in two dimensions
Lessons
Notes:
In this lesson, we will learn:
 Review of conservation of momentum
 Vector nature of momentum and conservation of momentum
 Problem solving with conservation of momentum in two dimensions
Notes:
 Momentum is a conserved quantity and a vector.
 In a collision between a set of objects, total momentum of the objects before collision = total momentum after collision.
 When using conservation of momentum on objects that move in two dimensions, use vector addition (tiptotail method).
Momentum
$\vec{p} = m \vec{v}:$ momentum, in kilogram meters per second (kg∙m/s)
$m:$ mass, in kilograms (kg)
$\vec{v}:$ velocity, in meters per second (m/s)
Impulse
$\vec{J} = \vec{F} \Delta t = \Delta \vec{p} = m\Delta \vec{v}$
$\vec{J}:$ impulse, in newton seconds (N∙s)
$\vec{F}:$ force, in newtons (N)
$\vec{t}:$ time, in seconds (s)
Conservation of Momentum
$\sum\vec{p}_i = \sum\vec{p}_f$
$\vec{p}_i:$ initial momentum, in kilogram meters per second (kg·m/s)
$\vec{p}_f:$ final momentum, in kilogram meters per second (kg·m/s)
Law of Sines
$\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{SinC}$
a,b,c: length of sides a,b,c
A,B,C: angles opposite sides a, b, c
Law of Cosines
$c^2 = a^2 + b^2  2ab \,cosC$

1.
$\bold{\sum\vec{p}_i = \sum\vec{p}_f}:$ Objects that bounce apart after collision in two dimensions

2.
$\bold{\sum\vec{p}_i = \sum\vec{p}_f}:$ Objects that stick together after collision in two dimensions

3.
$\bold{\sum\vec{p}_i = \sum\vec{p}_f}:$ Objects that explode apart in two dimensions