Matching Numerical $1$: A round, rigid object starts from rest and rolls without slipping down a ramp with angle $=30.$ The object has mass $M=3\mathrm{.}0kg,$ radius $R=0\mathrm{.}32m,$ and rotational inertia $\frac{4}{5}M{R}^2.$ The coefficient of static friction between the object and the ramp is $=0\mathrm{.}64.$ For the object rolling a distance $d=1\mathrm{.}1m$ down the ramp, match the magnitude of each quantity on the left with the correct value in SI units $($with angular speed in rad$/$s and angular acceleration in $ra\frac{d}{s^2})$ on the right. Each value on the right is used only once.

change of internal energy A$)8\mathrm{.}5$

change of kinetic energy divided by $M$

B$)5\mathrm{.}4$

angular speed at the bottom of the ramp

C$)6\mathrm{.}5$

angular acceleration

D$)7\mathrm{.}6$

friction force on the $R=0\mathrm{.}32m$ object

E$)0$

$M=3\mathrm{.}0kg$