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\begin{document}

\frame{\frametitle{\b Rotational Dynamics - 1} \bigskip

{\bf Bicycle (1):} 
$$\omega=\frac{v}{r}\,{\rm rad}\,,~~~T=\frac{2\pi\,\rm rad}{\omega}\,.$$
\smallskip

{\bf Belt Drive (2):} Use relation of frequencies
$$ f_a\,r_a = f_c\,r_c\,,~~~\omega_a = 2\pi\,f_a\,{\rm rad/rev}\,,
   ~~~\alpha_a\,t = \omega_a\,. $$
\smallskip % \bigskip

{\bf Spinning Wheel and Arrow (3).} Times have to agree:
$$ \frac{L_{\rm arrow}}{v_{\rm arrow}} = 
   \frac{L_{\rm wheel}}{v_{\rm wheel}}\,,~~~
   L_{\rm wheel}=\frac{R}{8}\,.  $$
\smallskip % \bigskip

{\bf Cyclist (4).} 
$$ \theta = \alpha\,\frac{t^2}{2}\,,~~~\omega=\alpha\,t\,,~~~
   d=\theta\, r/\rm rad\,.$$
\smallskip % \bigskip
\vskip 20pt }


\frame{\frametitle{\b Rotational Dynamics - 2} \bigskip

{\bf Rotational Variables (5).} Use just numbers. Fix units on output.
Given is $\theta(t)$. Then
$$ \omega(t)=\frac{d\theta}{d\,t}\,,~~~\alpha=\frac{d\omega}{d\,t}\,,
   ~~~\overline{\alpha}=\frac{\omega_2-\omega_2}{t_2-t_1}\,.$$
\smallskip

{\bf Crumb on rotating table (6):} 
$$ T = \frac{{\rm rev}}{f}\,,~~~v=\frac{2\pi\,r}{T}\,,~~~a = ?\,.$$
\smallskip

{\bf Torque on a Door (7):} 
$$ \tau = r\,F\,\sin(\theta)\,. $$
\smallskip

\vskip 20pt }

\end{document}
