Key Equations

Net external force	${\vec{F}}_{net} = \sum \vec{F} = {\vec{F}}_{1} + {\vec{F}}_{2} + ⋯$
Newton’s first law	$\vec{v} = constant when {\vec{F}}_{net} = \vec{0} N$
Newton’s second law, vector form	${\vec{F}}_{net} = \sum \vec{F} = m \vec{a}$
Newton’s second law, scalar form	$F_{net} = m a$
Newton’s second law, component form	$\sum {\vec{F}}_{x} = m {\vec{a}}_{x}, \sum {\vec{F}}_{y} = m {\vec{a}}_{y}, and \sum {\vec{F}}_{z} = m {\vec{a}}_{z} .$
Newton’s second law, momentum form	${\vec{F}}_{net} = \frac{d \vec{p}}{d t}$
Definition of weight, vector form	$\vec{w} = m \vec{g}$
Definition of weight, scalar form	$w = m g$
Newton’s third law	${\vec{F}}_{AB} = − {\vec{F}}_{BA}$
Normal force on an object resting on a horizontal surface, vector form	$\vec{N} = − m \vec{g}$
Normal force on an object resting on a horizontal surface, scalar form	$N = m g$
Normal force on an object resting on an inclined plane, scalar form	$N = m g cos θ$
Restoring force by a spring displaced by x from the relaxed position	$\vec{F} = − k \vec{x} .$
Tension in a cable supporting an object of mass m at rest, scalar form	$T = w = m g$