Match the most appropriate form of the equation for the moment of inertia to the image shown. All objects are rotating about point O. Note: r is a distance, m is a mass, k is a radius of gyration and d is a distance from the mass moment of inertia IG about the center of mass A. D. A. Z y X Mass element Z O Rotation axis A.1=1+md² =SM, B. r²dm C.1=mk² D.1= Σmr?

1. A circular disk has a density p(r) which varies as a function of distance from the center of the disk. The disk has a radius R and a thickness t. Assuming p(r) = Po(1-r/R): Calculate the total mass of the disk. a. b. Calculate the moment of inertia of the disk about an axis out of the plane of the page and passing through Point G. C. Calculate the moment of inertia of the disk about an axis out of the plane of the page and passing through Point O. G R

A rigid body is rotating around O in the vertical plane. It consists of two slender rods, each of mass m and length L. At the instant shown, the rigid body has angular velocity w and angular acceleration a. Determine the following: L 0 8 Motion L ,ليا

6 Given the system of points A,B,C with A(1,-1,1), B(2,0,2), C(-1,1,0) and masses m₁= 2,m₂=1,m3=4 respectively. Determine the moments and events inertia of the system with respect to the system of axes Oxyz. Then find the moments of inertia with respect to the primary axis system with origin O and to define the addresses of these axes.