Conservation of momentum in two dimensions

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

• 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 (tip-to-tail 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

$c^2 = a^2 + b^2 - 2ab \,cosC$