EXERCISE $3$

The pendulum in Figure $3$ consists of two slender bars $AB$ and $OC$ and a hollow circular

thin plate. The slender bars are made of a material whose density is $3k\frac{g}{m}3$ and the

plate of a material whose density is $k\frac{g}{m}3.$ At point $0_{{?}_{?}}$ a torque is applied that makes

the pendulum rotate with respect to a perpendicular axis passing through the fixed

point $O.$ Considering that this torque as a function that varies in time $M=220+100t,$

where $t$ is the time in seconds, as shown in figure $3.$ At a given instant $t=3$ seconds, at

the position shown in figure $3,$ knowing that the rotor that rotates the pendulum

starting from rest, calculate: $(2\mathrm{.}5$ pts$)$

a$)$ the position vector of the center of mass $G$ of the pendulum $(0\mathrm{.}5pts$

b$)$ the inertia with respect to a perpendicular axis passing through the fixed point

pts$)$

c$)$ The vector of the resultant reaction force at the fixed support A $(1\mathrm{.}25$ pts$)$