Question $1$:

$[5$ Marks$]$

A rotor has the following properties.

If the shaft is balanced by two counter masses located at $100$ mm radii and $120$ mm respectively and revolving in planes midway of planes $1$ and $2,$ and on a distance of $80$ mm on the right of plane $4,$ find the followings:

$($a$)$ Draw two space diagrams: $($i$)$ the positions of the planes along the shaft and $($ii$)$ the angular positions of the masses $($angles measured from positive x $-$ axis$).$

$($b$)$ Construct a table and tabulate all necessary data.

$($c$)$ Choose appropriate scales for the couple and force diagrams and write them clearly.

$($d$)$ Draw the couple diagram.

$($e$)$ Draw the force diagram.

$($f$)$ Determine the magnitude of the balance masses.

$($g$)$ Determine the angular positions of the balance masses from the positive $\backslash ($ x $\backslash )-$axis.