Problem $2(10$ pts$)$ Refer to Fig. $2$ where a small mass $\backslash ($ m $\backslash )$ is sliding frictionless on a bar. The bar is rotating at constant angular velocity $\backslash (\backslash$omega $\backslash ).$ Assume there is gravity $\backslash ($ g $\backslash )$ in the $\backslash (-\backslash$mathbf$\{$e$\}\_\{2\}\backslash )$ direction.

$($a$)$ Determine the acceleration vector of the mass $\backslash ($ m $\backslash )$ with respect to the inertial frame $\backslash ($ E $\backslash ).$ Express it in the body frame B$.(2\mathrm{.}5$ pts$)$

$($b$)$ Determine all the forces acting on the mass. Express them in the frame B$.(2\mathrm{.}5$ pts$)$

$($c$)$ Determine the equations of motion of the particle. $(2\mathrm{.}5$ pts$)$

$($d$)$ Determine the angular momentum. Reason whether the angular momentum is conserved or not without taking the time derivative. $(2\mathrm{.}5$ pts$)$