PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 21, Problem 15P
To determine
The moment of inertia of both the rod and disk about the
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Students have asked these similar questions
Determine the mass moment of inertia of the figure shown about the x, y and z axis. The materials weighs 500N/m3. Also determine the radius of gyration about each axis.
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 = 7.9 kg and b = 485 mm.
Answers:
1xxx =
i
lyy= i
Izz =
i
kg.m²
kg-m²
kg-m²
Formulas
Moments of Inertia
x= [y²d
ly = fx²dA
Theorem of Parallel Axis
Ixr = 1 + d² A
* axis going through the centroid
x' axis parallel to x going through the point of interest
d minimal distance (perpendicular) between x and x'
ly₁ = 15+d²A
ỹ axis going through the centroid
y' axis parallel to y going through the point of interest
d minimal distance (perpendicular) between y and y'
Composite Bodies
1=Σ 4
All the moments of inertia should
be about the same axis.
Radius of Gyration
k=
Chapter 21 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
Ch. 21 - Show that the sum of the moments of inertia of a...Ch. 21 - Prob. 2PCh. 21 - Prob. 3PCh. 21 - Determine the moments of inertia Ix and Iy of the...Ch. 21 - Prob. 5PCh. 21 - Determine by direct integration the product of...Ch. 21 - Prob. 9PCh. 21 - Prob. 10PCh. 21 - Determine the moment of inertia Ixx of the...Ch. 21 - Prob. 13P
Ch. 21 - Prob. 14PCh. 21 - Prob. 15PCh. 21 - The bent rod has a weight of 1.5 lb/ft. Locate the...Ch. 21 - If a body contains no planes of symmetry, the...Ch. 21 - Prob. 23PCh. 21 - Prob. 25PCh. 21 - Prob. 28PCh. 21 - Prob. 29PCh. 21 - Prob. 30PCh. 21 - The 2-kg thin disk is connected to the slender rod...Ch. 21 - Prob. 33PCh. 21 - Prob. 36PCh. 21 - Prob. 37PCh. 21 - Prob. 40PCh. 21 - Prob. 41PCh. 21 - Prob. 42PCh. 21 - Prob. 48PCh. 21 - Prob. 51PCh. 21 - Prob. 54PCh. 21 - Show that the angular velocity of a body, in terms...Ch. 21 - A thin rod is initially coincident with the Z axis...Ch. 21 - The top consists of a thin disk that has a weight...Ch. 21 - Prob. 66PCh. 21 - Prob. 69PCh. 21 - Prob. 70PCh. 21 - Prob. 73PCh. 21 - Prob. 74PCh. 21 - Prob. 77P
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- Determine the mass moment of inertia of the figure shown about the x,y, and z axis. The materials weighs 60 kN/meter cubearrow_forwardThe pendulum is suspended from point O and consists of two bars, each weighing 10 lb. Determine the moment of inertia of the pendulum about the axis through the center of mass G.arrow_forwardThe pendulum is suspended from point O and consists of two bars, each weighing 10 lb. Determine the moment of inertia of the pendulum about the axis through pin O.arrow_forward
- Find the moment of inertia and radius of gyration of the section of this bar about an axis parallel to x-axis going through the center of gravity of the bar. The bar is symmetrical about the axis parallel to y-axis and going through the center of gravity of the bar and about the axis parallel to z-axis and going through the center of gravity of the bar. The dimensions of the section are: l=55 mm, h=22 mm The triangle: hT=12 mm, lT=19 mm and the 2 circles: diameter=8 mm, hC=6 mm, dC=8 mm. A is the origin of the referential axis. Provide an organized table and explain all your steps to find the moment of inertia and radius of gyration about an axis parallel to x-axis and going through the center of gravity of the bar. Does the radius of gyration make sense? Enter the y position of the center of gravity of the bar in mm with one decimal.arrow_forwardhe assembly consists of a disk having a mass of 5 kg and slender rods ABand DC which have a mass of 2 kg/m. If L = 0.6 m, determine the moment of inertia and radius of gyration of the assembly about an axis perpendicular to the page and passing through point O. Also, find the position of the center of mass Gin relation to O. Please explain stepsarrow_forwardThe slender bar lies in the x-y plane. Its mass is 6 kg and the material is homogeneous. Use integration to determine its moment of inertia about the z-axisarrow_forward
- . The radius of gyration of the 10kg body about an axis passing through point G (center of mass) and directed perpendicular to the page is rm = 2m. Determine the mass moment of inertia (kg - m²) of the body about an axis passing through point G and directed perpendicular to the page. 4marrow_forwardIf the large ring, small ring and each of the spokes weigh 100 lb, 15 lb, and 20 lb, respectively, determine the mass moment of inertia of the wheel about an axis perpendicular to the page and passing through point A.arrow_forwardROBLEM NO.5 Determine the location y of the center of mass G of the assembly and then calculate the moment of inertia about an axis perpendicular to the page and passing through G. The block has a mass of 3 kg and the semi-cylinder has a mass of 5 kg. 400 mm 300 mm 200 mm MacBook Airarrow_forward
- 3. The pendulum shown is made of a 2-kg rod and 6-kg thin plate. Find ya the location of the center of mass G of the pendulum and the moments of inertia about an axis passing through G and an axis passing through point O. yG 2 m G 0.5 m 1 marrow_forwardThe hammer consists of a cast iron head and wood handle. The iron head has 7000 kg/m density, and its shape is a rectangular prism with a circular hole. The wood handle has 500 kg/m3 density, and its shape is a circular cylinder. Determine the mass moment of inertia about the z axis and the corresponding radius of gyration.arrow_forwardThe wheel consists of a thin ring having a mass of 10 kg and four spokes made from slender rods, each having a mass of 2 kg. Determine the wheel’s moment of inertia about an axis perpendicular to the page and passing through point A.arrow_forward
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moment of inertia; Author: NCERT OFFICIAL;https://www.youtube.com/watch?v=A4KhJYrt4-s;License: Standard YouTube License, CC-BY