Tham khảo tài liệu 'dynamics of mechanical systems 2009 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 232 Dynamics of Mechanical Systems and IS O O See Problem . Find the x y z coordinates of the mass center G of S. Find ISfG iyG IS G ISfG and ISG. See Problem . Let G have an associated mass of 9 kg equal to the sum of the masses of P1 P2 and P3 . Find IGf0 I 0 I 0 IGf0 and I 0. See Problems and . Show that Is 0 IS G IG0 x X X Is 0 iSg IG0 y y y ISO IS G IGO z z z ISO ISG IGO a a a and ISO S G IGO b b b See Problem . Find a unit vector n perpendicular to the plane of P1 P2 and P3. Find also If0. Show that If0 is parallel to n. Section Moments and Products of Inertia See Problem . A particle P with mass of 3 slug has coordinates 2 -1 3 measured in feet in a Cartesian coordinate system as represented in Figure . Determine the following moments and products of inertia If0 If0 If0 IP 0 IP 0 IP 0 If0 xx xy xz yy yz zz aa IP 0 IP 0 and IP0. x yy y FIGURE A particle P and a point Q. See Problems and . Let Q have coordinates -1 2 4 . Repeat Problem with Q instead of 0 being the reference point. That is determine IPQ IPq IP q IpyQ I IPzQ IPQ IPblQ IT and IfQ. xx xy xz See Problem . Let a set S of three particles P1 P2 and P3 be located at the vertices of a triangle as shown in Figure . Let the particles have masses 2 3 and Inertia Second Moment Vectors Moments and Products of Inertia Inertia Dyadics 233 4 kg respectively. Find the following moments and products of inertia of S relative to the origin o of the X- Y- Z-axis system of Figure e l ISO if ISyO and If0. FIGURE Particles at the vertices of a triangle. See Problems and . For the system S shown in Figure find the following moments and products of inertia lSyG ISG IyyG IyZG and where G is the mass center of S as determined in Problem . Compare the magnitudes of these results with those of Problem