Key Equations

Net external force	${\overrightarrow{F}}_{\text{net}}={\displaystyle \sum \overrightarrow{F}}={\overrightarrow{F}}_1+{\overrightarrow{F}}_2+\text{⋯}$
Newton’s first law	$\overrightarrow{v}=\text{constant when}{\overrightarrow{F}}_{\text{net}}=\overrightarrow{0}\text{N}$
Newton’s second law, vector form	${\overrightarrow{F}}_{\text{net}}={\displaystyle \sum \overrightarrow{F}=m\overrightarrow{a}}$
Newton’s second law, scalar form	$F_{\text{net}}=ma$
Newton’s second law, component form	${\displaystyle \sum {\overrightarrow{F}}_x}=m{\overrightarrow{a}}_x\text{,}{\displaystyle \sum {\overrightarrow{F}}_y}=m{\overrightarrow{a}}_y,\text{and}{\displaystyle \sum {\overrightarrow{F}}_z}=m{\overrightarrow{a}}_z.$
Newton’s second law, momentum form	${\overrightarrow{F}}_{\text{net}}=\frac{d\overrightarrow{p}}{dt}$
Definition of weight, vector form	$\overrightarrow{w}=m\overrightarrow{g}$
Definition of weight, scalar form	$w=mg$
Newton’s third law	${\overrightarrow{F}}_{\text{AB}}=\text{−}{\overrightarrow{F}}_{\text{BA}}$
Normal force on an object resting on a horizontal surface, vector form	$\overrightarrow{N}=\text{−}m\overrightarrow{g}$
Normal force on an object resting on a horizontal surface, scalar form	$N=mg$
Normal force on an object resting on an inclined plane, scalar form	$N=mg\text{cos}\theta$
Restoring force by a spring displaced by x from the relaxed position	$\overrightarrow{F}=\text{−}k\overrightarrow{x}.$
Tension in a cable supporting an object of mass m at rest, scalar form	$T=w=mg$