Question $3.[10/50]$ About Rigid object under a net Torque Model

A wheel of radius $R,$ mass $M,$ and moment of inertia I is mounted on a frictionless, horizontal axle as will be seen in Figure.

A light cord wrapped around the wheel supports an object of mass $m.$

When the wheel is released, the object accelerates downward, the cord

unwraps off the wheel, and the wheel rotates with an angular acceleration.

Question $3.$a $[7/50]$ Please find the next expressions:

the magnitude of the angular acceleration of the wheel, $$;

the magnitude of the translational acceleration, $a$;

the magnitude of the tension force, $T,$ in the cord; in terms of $g,m,R,$ and I.

FIGURE$-3$ Angular Acceleration of a Wheel

Question $3.$b $\frac{3}{50}$ Please find the numerical values of $,a,$ and $T$ by taking $g=10\mathrm{.}0\frac{m}{s^2},R=10\mathrm{.}0m,m=10\mathrm{.}0kg,$ and $I=10\mathrm{.}0kg*m^2.$

Please do not forget to put the units!!!

Answer $3.$

Answer $3.$a $[7/50]$ Hint: Please follow the next steps and fill in the blanks below.

$[3/50]$ Step $1.$ Find $$ in terms of $T,R,$ and I :

Use the rigid object under a net torque model $($For the equation of this model, see the table in Question $5.).$ Use the definition of torque: vec$()=$vec$(r)$vec$(F)=>=$rFSin$()$ where $r-=R,F-=T$ and $=90=>$Sin$(90)=1.$