Chapter 10, Problem 8RP

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 uniform rod of length 4b and mass m is bent into the shape shown. The diameter of the rod is small compared with its length. Determine the moments of inertia of the rod about the three coordinate axes. Use the values m = 9.7 kg and b = 650 mm. Answers: Ixx = i lyy= Izz i i kg-m² kg.m² kg.m²

Determine the moment of inertia of the wheel about an axis which is perpendicular to the page and passes through point O. The material has a specific weight of 90 lb/ft3.

Determine the moment of inertia of mass with respect to the x' axis that passes through the structure's center of gravity and is parallel to the x axis. The cone has a density of 6000 kg/m3 and the cylinder a density of 8000 kg/m3. Consider H = 83

Show the complete solution.

The pendulum consists of the 3-kg slender rod and the 5-kg thin plate. Determine the location ỹ of the center of mass G of the pendulum; then calculate the moment of inertia of the pendulum about an axis perpendicular to the page and passing through G. y 2 m G 0.5 m Eim-

The molded plastic block has a density of 1300 kg/m³. Calculate its moment of inertia about the y-y axis. What percentage error e is introduced by using the approximate relation 1/3 ml² for lxx? Answers: lyy e = = 200 y 495 200 Dimensions in millimeters textes kg m² % 60 60

Determine the moment of inertia about an axis perpendicular to the pageand passing through the pin at O. The thin plate has a hole in its center. Its thicknessis 50 mm, and the material has a density ⍴ = 75 kg/m3

Determine the moment of inertia of the thin plate about an axis perpendicular to the page and passing through the pin at O. The plate has a hole in its center. Its thickness is 50 mm and the material has a density of 50 kg/m^3