111 
equilibrium

\[
\sum\vect{F}=0
\]

114 
law of inertia. Newton’s first law of motion

\[
\sum\vect{F}=0\Rightarrow\vect{a}=0
\]

116 
law of inertia. Newton’s first law of motion

\[
\frac{m_1}{m_2}=\frac{a_2}{a_1}
\]

117 
Newton’s second law of motion

\[
\sum\vect{F}=m\vect{a}
\]

117 
Newton’s second law of motion, component form

\[
\begin{align*}
\sum F_x &=ma_x \\
\sum F_y &=ma_y \\
\sum F_z &=ma_z
\end{align*}
\]

117 
Newton.
SI unit of force

\[
1\,\mathrm{N}=1\,\frac{\mathrm{kg\cdot m}}{\mathrm{s}^2}
\]

117 
unit of force in the British engineering system

\[
1\,\mathrm{lb}=1\,\frac{\mathrm{slug}\cdot\mathrm{ft}}{\mathrm{s}^2}
\]

119 
force of gravity
where $\vect{g}=$ acceleration due to gravity

\[
\vect{F}_g=m\vect{g}
\]

120 
Newton’s third law of motion

\[
\vect{F}_{12}=\vect{F}_{21}
\]

126 
Acceleration of a crate on a frictionless incline.
Note that the acceleration depends only on the angle
of inclination and not on the mass of the crate.

\[
a_x=g\sin{\theta}
\]

131 
static friction.
It is equal and opposite the applied force
while the object is not moving.

\[
v=0\Rightarrow\vect{f}_s=\vect{F}
\]

132 
static friction

\[
f_s\le\mu_sn
\]

132 
maximum force of static friction

\[
f_{s,max}=\mu_sn
\]

132 
kinetic friction

\[
f_k=\mu_kn
\]
