A rotor assembly can be broken down into $3$ parts all rotating in the same plane. The

weight of each component is $22$ lb$.,35$ lb$.,$ and $50$ lb$.$; the center of gravity is $\mathrm{.}5$ inch, $\mathrm{.}25$ inch and

$1\mathrm{.}3$ inch respectively; the location from a horizontal $0$ degree reference plane is $30,75$ and $165$

degrees respectively. Construct a table to balance the system static and dynamically. What is the

angular position and value of a balance weight that must be added to balance the system if a

convenient location is $14$ inch from the axis of rotation? If weight is to be removed instead of

added at a convenient location of $4$ inch?