\magnification=\magstep1 

$$
{\rm displacement\ \ } x   \qquad \Longleftrightarrow 
          \qquad {\rm angular\ displacement\ \ } \theta
$$


$$
{\rm velocity\ \ } v   \qquad \Longleftrightarrow 
          \qquad {\rm angular\ velocity\ \ } \omega
$$


$$
{\rm acceleration\ \ } a   \qquad \Longleftrightarrow 
          \qquad {\rm angular\ acceleration\ \ } \alpha
$$

$$
v \quad = \quad {{dx}\over{dt}}  \qquad \Longleftrightarrow 
          \qquad \omega \quad = \quad {{d\theta}\over{dt}}
$$

$$
a \quad = \quad {{dv}\over{dt}} \quad = \quad {{d^2x}\over{dt^2}}  
                 \qquad \Longleftrightarrow  \qquad
          \alpha \quad = \quad {{d\omega}\over{dt}} \quad = 
                  \quad {{d^2\theta}\over{dt^2}}
$$

$$
x \quad = \quad R \thinspace \theta
$$

$$
v \quad = \quad R \thinspace \omega
$$

$$
a \quad = \quad R \thinspace \alpha
$$


$$
x_f \quad = \quad x_i \ + \ v t \ + \ {{1}\over{2}} a t^2
$$

$$
x_f \quad = \quad x_i \ + \ {{1}\over{2}} ( v_f + v_i ) t
$$

$$
v_f \quad = \quad v_i \ + \ a t  
$$

$$
v_f^2 \quad = \quad v_i^2 \ + \ 2 a (x_f - x_i)
$$


$$
\theta_f \quad = \quad \theta_i \ + \ \omega t \ + \ {{1}\over{2}} \alpha t^2
$$

$$
\theta_f \quad = \quad \theta_i \ + \ {{1}\over{2}} ( \omega_f + \omega_i ) t
$$

$$
\omega_f \quad = \quad \omega_i \ + \ \alpha t  
$$

$$
\omega_f^2 \quad = \quad \omega_i^2 \ + \ 2 \alpha (\theta_f - \theta_i)
$$






\bye
