\(\def \u#1{\,\mathrm{#1}}\)
\(\def \us#1{\,\mathrm{\scriptsize #1}}\)
\(\def \abs#1{\left|#1\right|}\)
\(\def \ast{*}\)
\(\def \deg{^{\circ}}\)
\(\def \tau{\uptau}\)
\(\def \ten#1{\times 10^{#1}}\)
\(\def \redcancel#1{{\color{red}\cancel{#1}}}\)
\(\def \BLUE#1{{\color{blue} #1}}\)
\(\def \RED#1{{\color{red} #1}}\)
\(\def \PURPLE#1{{\color{purple} #1}}\)
\(\def \th#1,#2{#1,\!#2}\)
\(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\)
\(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\)
\(\def \dotspot{{\color{lightgray}{\circ}}}\)
\(\def \ccw{\circlearrowleft}\)
\(\def \cw{\circlearrowright}\)
How Things Move
Why Things Move
angular displacement
revolutions
$$\begin{align}
\omega_f&=\omega_i+\alpha\Delta t &\color{blue}{\hbox{no}\,\Delta \theta}\\
\Delta \theta&=\frac{1}{2}(\omega_i+\omega_f)\Delta t &\color{blue}{\hbox{no}\,\alpha}\\
\Delta \theta&=\omega_i\Delta t+\frac12\alpha\Delta t^2 &\color{blue}{\hbox{no}\,\omega_f}\\
\Delta \theta&=\omega_f\Delta t-\frac12\alpha\Delta t^2 &\color{blue}{\hbox{no}\,\omega_i}\\
\omega_f^2&=\omega_i^2+2\alpha\Delta \theta &\color{blue}{\hbox{no}\,\Delta t}\\
\end{align}$$
centripetal acceleration
tangential acceleration
\(s=r\Delta\theta\) \(\mathit{only}\) if \(\Delta\theta\) is in radians
\(v=r\omega\) (where \(\omega\) is in rad/s)
\(a_t=r\alpha\) (where \(\alpha\) is in \(\u{rad/s^2}\))
\(\vec a=\vec a_c+\vec a_t \qquad a=\sqrt{a_c^2+a_t^2}\)