Key Equations

Key Equations

Work done by a force over an infinitesimal displacement	$dW=\overrightarrow{F}·d\overrightarrow{r}=\left|\overrightarrow{F}\right|\left|d\overrightarrow{r}\right|\text{cos}\theta$
Work done by a force acting along a path from A to B	$W_{AB}={\displaystyle \underset{\text{path}AB}{\int }\overrightarrow{F}·d\overrightarrow{r}}$
Work done by a constant force of kinetic friction	$W_{\text{fr}}=\text{−}{f}_k\left|l_{AB}\right|$
Work done going from A to B by Earth’s gravity, near its surface	$W_{\text{grav,}AB}=\text{−}mg\left(y_B-y_A\right)$
Work done going from A to B by one-dimensional spring force	$W_{\text{spring,}AB}=\text{−}\left(\frac{1}{2}k\right)\left(x_B^2-x_A^2\right)$
Kinetic energy of a non-relativistic particle	$K=\frac{1}{2}m{v}^2=\frac{p^2}{2m}$
Work-energy theorem	$W_{\text{net}}=K_B-K_A$
Power as rate of doing work	$P=\frac{dW}{dt}$
Power as the dot product of force and velocity	$P=\overrightarrow{F}·\overrightarrow{v}$