$-\backslash (\backslash$Omega $\backslash )$ is constant.

$-\backslash ($ p $\backslash )$ has masss $\backslash ($ m $\backslash ).$

$($a$)$ Determine the velocity vector of the particle $\backslash ($ p $\backslash )$ with respect to the inertial frame $\backslash ($ E $\backslash ).$ EXPRESS IN THE FRAME $\backslash ($ D $\backslash ).(2\mathrm{.}5$ pts$)$

$($b$)$ Determine the linear momentum of $\backslash ($ p $\backslash ).$ EXPRESS IN THE FRAME$\backslash ($ D $\backslash ).(2\mathrm{.}5$ pts $)$

$($c$)$ Determine the angular momentum of $\backslash ($ p $\backslash )$ on point $\backslash ($ o $\backslash ).$ Express it in reference frame $\backslash ($ D $\backslash ).(2\mathrm{.}5$ pts $)$

$($d$)$ Determine the time derivative of the linear momentum of $\backslash ($ p $\backslash )$ with respect to the inertial frame. Express it in reference frame $\backslash ($ D $.(2\mathrm{.}5\backslash$mathrm$\{$pts$\})\backslash )$

$($e$)$ Determine the time derivative of the angular momentum of $\backslash ($ p $\backslash )$ on point $\backslash ($ o $\backslash ).$ Express it in reference frame D$.(2\mathrm{.}5$ pts$)$

$($f$)$ Determine the kinetic energy of $\backslash ($ p $\backslash ).(2\mathrm{.}5$ pts$\backslash ()\backslash )$