A rod rotates in a plane about a fixed axis of rotation such that its angular position as a function of time is described by the function $($t$)=(24\mathrm{.}8$rad$/$s$2)$t$2.$ The rotation is counterclockwise from the perspective in the diagram. Two small spheres, $1$ and $2,$ are attached to the rod at distances r$1=0\mathrm{.}13$mand r$2=0\mathrm{.}43$m from the axis of rotation, as shown. Take counterclockwise rotation to be positive. In each part of this problem, calculate the quantity at t$=2\mathrm{.}24$s

$$ Part $($a$)$

What is the angular speed, in radians per second, of the rod?

$$ Part $($b$)$

What is the magnitude of the angular acceleration, in radians per second squared, of the rod?

$$ Part $($c$)$

What is the tangential speed, in meters per second, of sphere $1?$

$$ Part $($d$)$

What is the tangential speed, in meters per second, of sphere $2?$

$$ Part $($e$)$

What is the magnitude of the tangential acceleration, in meters per second squared, of sphere $1?$

$$ Part $($f$)$

What is the magnitude of the tangential acceleration, in meters per second squared, of sphere $2?$

$$ Part $($g$)$

What is the magnitude of the centripetal acceleration, in meters per second squared, of sphere $1?$

$$ Part $($h$)$

What is the magnitude of the centripetal acceleration, in meters per second squared, of sphere $2?$