EBK ENGINEERING MECHANICS
15th Edition
ISBN: 9780137616909
Author: HIBBELER
Publisher: VST
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Chapter 21, Problem 69P
To determine
The spin
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The assembly in figure 1 is rotating counterclockwise from above at w = 10 rad/s
about the z axis. The thin disk has mass 12 kg and radius 15 cm, while, and the thin rod CD
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axis.
@=10 rad/s
B
C
A
15 cm
Figure 1
30 cm
Find the inertia tensor for the disk and rod CD about the axis CD.
Calculate the moment of inertia of the disk and rod CD about the vertical z
Determine the angular momentum of the disk and rod CD about the z axis.
h
y
g(x)
density p = 800
kg
m³
Determine the cone's radius of gyration about the x-axis.
2h
x
An engineering student has modelled a truncated cone in CAD software by rotating the coloured area about
the x-axis. The y-coordinate can be described by the equation g(x) = + 1 and the cup has constant
6
The cone has dimensions h = 1 m and l = 6 m.
X
Given that P = 50N, and the rod has mass = 0.370 kg with centroidal mass moment of inertia l = 37/19200 kg-m²:a. Which of the equations given in the second image can be used to solve for the angular acceleration of rod BD?b. What is the angular acceleration of rod BD?
Chapter 21 Solutions
EBK ENGINEERING MECHANICS
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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- The top is in steady precession with nutation angle 0 = 15° and precession rate $= 1 revolution per second. The mass of the top is 8 x 10* slugs, its center of mass is I in. from the point, and its moments of inertia are Ixx = 6 x 106 slug-ft and Iz= 2 x 10 slug-ft. What is the spin rate of the top in revolutions per second? -Yarrow_forwardBy joining two equal cones, the similar shaped object has a side length u cm and = 90⁰. The mass of this object with respect to the ysymmetry axis is kgm2 until its moment of inertia? (Ρ = 2700kg / m3) the volume of a cone is (1/3) πR2h and its mass moment of inertia = (3/10) mR2 with respect to its axis of metrics. u = 46arrow_forwardMatch the most appropriate form of the equation for the moment of inertia to the image shown. All objects are rotating about point O. Note: ris 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. O M X Mass element Z Rotation axis X A.1=1+md² G B. = SM √² r²dm C.I=mk²_ D.1= Σm,r?arrow_forward
- 2. Determine the number of degrees of freedom necessary for the analysis of the system shown in the figure below. 0.1L 0.4L+ 0.3LS-+ 0.2L 2k G 2k Slender rod of mass m m2 moment of inertia Iarrow_forwardFind 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_forwardTwo thin hoops of masses m1 and m2 have radii a1 and a2, respectively. They are mounted rigidly on a frame of negligible mass. Find the systems moment of inertia about an axis through the center and perpendicular to the page. How large a torque must be applied to the system to give it an angular acceleration α about this axis, provided it is free to turn? Repeat tor the axis AA’.arrow_forward
- A car is moving on a curved horizontal road of radius 100 m with a speed of 20 m/s. The rotating masses of the engine have an angular speed of 100 rad/s in clockwise direction when viewed from the front of the car The combined moment of inertia of the rotating masses is 10 kg-m².what is the magnitude of the gyroscopic moment in (N-m)?arrow_forwardFor the body shown. If point P3 is the center of mass for rod part P1-P2, and point P4 is the center of mass for rod part P3-P5, and P6 is the center of mass of the disk part. Find the mass moment of inertia around axis perpendicular to the page and passes through point P5. Given; L = 1 m, mass density of rod parts = 5 kg / m, mass density of disk = 12 Kg / m?arrow_forward2. Determine the radius of gyration kz for the column's cross-sectional area. 4d The dimension d is given. 2d 4d 4d 4d Zarrow_forward
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