Momentum:

$$ \vec F_{a->b} = -\vec F_{b->a}\\ 0 = \vec F_{b->a} +F_{b->a}\\ 0 = \vec F_{net}\\ \vec F_{int} = 0 $$

$$ \vec F_{ext} = \vec F_{net} = \frac {\Delta p} {\Delta t}\\ $$

$$ \vec F_{net} = m\ \frac {d\vec v} {dt} \\ =\frac d {dt} (m\vec v)\\ =\frac d {dt} \vec P $$

Impulse:

If there is a net external forces, we define am impulse as:

$$ \vec J = \vec F_{net} \Delta t =\vec F_{ext} = \vec F_{net} $$

Unit: Ns or kg m

Center of Mass

$$ M = \Sigma _im_i $$

$$ \vec x_{cm} = \frac 1 M \Sigma_i\vec x_i m_i \\\vec v_{cm} = \frac 1 M \Sigma_i\vec v_i m_i \\\vec a_{cm} = \frac 1 M \Sigma_i\vec a_i m_i $$

$$ \frac d {dt} = \vec l \ 0 $$