=√x² + y² and above by the plane z = 1. Find the center of mass and the moment of inertia about the z-axis if the density is 8(r,0,z) = 5z. A solid is bounded below by the cone z = The center of mass is (x,y,z) = ( (Type an integer or a simplified fraction.)

Given the figure below. Find (a) location of the centroid, (b) moments of inertia with respect to the x- y axes, (c) centroidal moments of inertia, and (d) the radii of gyration. y 130 mm 30 mm 30 mm -40 mm→-40 mm→ SITY

Find MOI about the x-axis of the area shown in below fig. *Moment of Inertia *

PROBLEM 4: The region is symmetric about the x-axis. Calculate the moment of inertial about the centroidal x and y axes. ANS: I = 10.35 x 106 mm², I = 1.74 × 106 mm² 17 mm y 68 mm 17 mm 18'mm 27 mm --x

Show using analytical methods how the mass moment of inertia changes for a uniform rod by changing the axis about which it rotates. Z Figure 1 - Uniform Rod Q1 dr L

The shaded area shown is bounded by y axis, line y = 2.42 m and the curve y(x)=(1/(4.4))x3 m, where x is in m. Suppose that a = 2.2 m and h = 2.42 m . Determine the moment of inertia for the shaded area about the y axis. Iy = ?

L3 X = Number y = Number L6 Z = Number 4₁ Find the center of mass (x, y, z) of the object shown, given: L₁ = 120 mm, L2= 90 mm, L3= 25 mm, L4 = 25 mm, L5 = 30 mm, L6 = 20 mm, L7 = Ø 20 mm mm mm LA mm -L7 5 L₂

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

Please do your own

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.