Answer to Question #269786 in Physics for Fanah

Question

The four particles are connected by rigid rods of negligible mass where y1=5.90m.The origin is at the centre of the rectangle.The system rotates in the xy plane about the z axis with an angular speed of 6.60 rad/s.

(a). Calculate the moment of inertia of the system about the z axis.

(b). Calculate the rotational kinetic energy of the system.

Answer 1

(a) $r=0.5\cdot\sqrt{4^2+5.9^2}=3.56\ (m)$

$I=(3+2+2+4)\cdot3.56^2=139.4\ (kg\cdot m^2)$

(b) $KE=I\omega^2/2=139.4\cdot6.6^2/2=3036\ (J)$