A structure forming a $"$T$"$ shape is made from three thin rods, each of different mass $(m_1=0\mathrm{.}150kg,m_2=0\mathrm{.}080kg$ and $m_3=0\mathrm{.}200kg).$ The structure is free to rotate about an axis located at the joint between the two vertical rods $($as shown in the figure$).$ The axis is oriented such that the structure rotates within the plane of the figure. The length of the two vertical rods $(m_1$ and $m_2)$ is $0\mathrm{.}40$ m $($each$).$ The horizontal rod has length $0\mathrm{.}70$ m $.$ Ignore friction and air resistance.

$($a$)$ What is the total rotational inertia of the structure about the rotation axis?

$I=$

$kg*m^2$

$($b$)$ The structure rotates, starting from rest, from the position shown until the upper rod $($mass $m_3)$ is at the bottom $($i$.$e$.,$ a rotation of $180).$ What will its angular velocity be after the $180$ rotation?

$=,ra\frac{d}{s}$

$($c$)$ What is the maximum magnitude of the torque acting on the structure during this rotation?

${}_{\text{m}\text{a}\text{x}}=$

Nm

$($d$)$ What is the maximum magnitude of the angular acceleration of the structure during this rotation?

${}_{\text{m}\text{a}\text{x}}=,ra\frac{d}{s^2}$