\magnification=\magstep2
\baselineskip=25pt


$$
\eqalign{
   {\rm KE \ } &= 
          \thinspace\thinspace  {{1}\over{2}} M_1 v_1^2 \cr
          &= 
          \thinspace\thinspace  {{1}\over{2}} M_1 {( {R_1 \omega} )}^2 \cr
          &= 
          \thinspace\thinspace  {{1}\over{2}} M_1 {R_1}^2 {\omega}^2 \cr
          &= 
          \thinspace\thinspace  {{1}\over{2}} ( M_1 {R_1}^2) {\omega}^2  \cr
}
$$

$$
      I \thinspace = \thinspace M R^2
$$

$$
\eqalign{
   {\rm KE \ } &= 
          \thinspace\thinspace  {{1}\over{2}} I_1 {\omega}^2 \cr
}
$$

$$
\eqalign{
   {\rm KE \ } &= 
          \thinspace\thinspace  {{1}\over{2}} M_1 v_1^2 
           + \thinspace\thinspace  {{1}\over{2}} M_2 v_2^2 
           + \thinspace\thinspace  {{1}\over{2}} M_3 v_3^2 \cr
          &= 
          \thinspace\thinspace  {{1}\over{2}} ( M_1 {R_1}^2) {\omega}^2  
           + \thinspace\thinspace  {{1}\over{2}} ( M_2 {R_2}^2) {\omega}^2  
           + \thinspace\thinspace  {{1}\over{2}} ( M_3 {R_3}^2) {\omega}^2  \cr
          &= 
          \thinspace\thinspace  {{1}\over{2}} I_1 {\omega}^2  
           + \thinspace\thinspace  {{1}\over{2}} I_2 {\omega}^2  
           + \thinspace\thinspace  {{1}\over{2}} I_3 {\omega}^2  \cr
          &= 
          \thinspace\thinspace  {{1}\over{2}} ( I_1 + I_2 + I_3) {\omega}^2   \cr
          &= 
          \thinspace\thinspace  {{1}\over{2}} I_{tot} {\omega}^2   \cr
}
$$

$$
  \lambda(x) \thinspace = \thinspace 3 {\rm {{kg}\over{m}} }
                            + (3 {\rm  {{kg}\over{m}} }) 
                                ( { {x}\over{10 \rm m} } )
$$



\bye
