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
|
\[
f_k=\mu_kn
\]
|