Vector Mechanics For Engineers
12th Edition
ISBN: 9781259977305
Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.
Publisher: Mcgraw-hill Education,
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Chapter 18.3, Problem 18.137P
To determine
(a)
The Expression
To determine
(b)
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5. Consider a thin homogeneous plate with principal momenta of inertia
along the principal axis x1
along the principal axis x2
I
I,> I,
I3=I;+I¡ along the principal axis x3
Let the origins of the x; and x; systems coincide and be located at the center of
mass 0 of the plate. At time =0, the plate is set rotating in a force-free manner
with an angular velocity 2 about an axis inclined at an angle a from the plane of
the plate and perpendicular to the x-axis. If I,/I, = cos 2a, show that at time t
%3D
the angular velocity about the x-axis is
w, (1) = N cos a · tanh(2t sin a)
Two masses, meach, are placed at the points (x, y) =(a, a) and (-a, -a), and two masses, 2m each, are
placed at the points (a,-a) and (-a, a). The principal moments of inertia of the system are
(a) 2ma', 4ma?
-(b) 4ma², 8ma?
(c) 4ma', 4ma?
(d) 8ma", 8ma?
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
has mass 3 kg and length 30 cm.
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.
Chapter 18 Solutions
Vector Mechanics For Engineers
Ch. 18.1 - Prob. 18.1PCh. 18.1 - Prob. 18.2PCh. 18.1 - Prob. 18.3PCh. 18.1 - A homogeneous disk of weight W=6 lb rotates at the...Ch. 18.1 - Prob. 18.5PCh. 18.1 - A solid rectangular parallelepiped of mass m has a...Ch. 18.1 - Solve Prob. 18.6, assuming that the solid...Ch. 18.1 - Prob. 18.8PCh. 18.1 - Determine the angular momentum HD of the disk of...Ch. 18.1 - Prob. 18.10P
Ch. 18.1 - Prob. 18.11PCh. 18.1 - Prob. 18.12PCh. 18.1 - Prob. 18.13PCh. 18.1 - Prob. 18.14PCh. 18.1 - Prob. 18.15PCh. 18.1 - For the assembly of Prob. 18.15, determine (a) the...Ch. 18.1 - Prob. 18.17PCh. 18.1 - Determine the angular momentum of the shaft of...Ch. 18.1 - Prob. 18.19PCh. 18.1 - Prob. 18.20PCh. 18.1 - Prob. 18.21PCh. 18.1 - Prob. 18.22PCh. 18.1 - Prob. 18.23PCh. 18.1 - Prob. 18.24PCh. 18.1 - Prob. 18.25PCh. 18.1 - Prob. 18.26PCh. 18.1 - Prob. 18.27PCh. 18.1 - Prob. 18.28PCh. 18.1 - Prob. 18.29PCh. 18.1 - Prob. 18.30PCh. 18.1 - Prob. 18.31PCh. 18.1 - Prob. 18.32PCh. 18.1 - Prob. 18.33PCh. 18.1 - Prob. 18.34PCh. 18.1 - Prob. 18.35PCh. 18.1 - Prob. 18.36PCh. 18.1 - Prob. 18.37PCh. 18.1 - Prob. 18.38PCh. 18.1 - Prob. 18.39PCh. 18.1 - Prob. 18.40PCh. 18.1 - Prob. 18.41PCh. 18.1 - Prob. 18.42PCh. 18.1 - Determine the kinetic energy of the disk of Prob....Ch. 18.1 - Prob. 18.44PCh. 18.1 - Prob. 18.45PCh. 18.1 - Prob. 18.46PCh. 18.1 - Prob. 18.47PCh. 18.1 - Prob. 18.48PCh. 18.1 - Prob. 18.49PCh. 18.1 - Prob. 18.50PCh. 18.1 - Prob. 18.51PCh. 18.1 - Prob. 18.52PCh. 18.1 - Determine the kinetic energy of the space probe of...Ch. 18.1 - Prob. 18.54PCh. 18.2 - Determine the rate of change H.G of the angular...Ch. 18.2 - Prob. 18.56PCh. 18.2 - Determine the rate of change H.G of the angular...Ch. 18.2 - Prob. 18.58PCh. 18.2 - Prob. 18.59PCh. 18.2 - Prob. 18.60PCh. 18.2 - Prob. 18.61PCh. 18.2 - Prob. 18.62PCh. 18.2 - Prob. 18.63PCh. 18.2 - Prob. 18.64PCh. 18.2 - A slender, uniform rod AB of mass m and a vertical...Ch. 18.2 - A thin, homogeneous triangular plate of weight 10...Ch. 18.2 - Prob. 18.67PCh. 18.2 - Prob. 18.68PCh. 18.2 - Prob. 18.69PCh. 18.2 - Prob. 18.70PCh. 18.2 - Prob. 18.71PCh. 18.2 - Prob. 18.72PCh. 18.2 - Prob. 18.73PCh. 18.2 - Prob. 18.74PCh. 18.2 - Prob. 18.75PCh. 18.2 - Prob. 18.76PCh. 18.2 - Prob. 18.77PCh. 18.2 - Prob. 18.78PCh. 18.2 - Prob. 18.79PCh. 18.2 - Prob. 18.80PCh. 18.2 - Prob. 18.81PCh. 18.2 - Prob. 18.82PCh. 18.2 - Prob. 18.83PCh. 18.2 - Prob. 18.84PCh. 18.2 - Prob. 18.85PCh. 18.2 - Prob. 18.86PCh. 18.2 - Prob. 18.87PCh. 18.2 - Prob. 18.88PCh. 18.2 - Prob. 18.89PCh. 18.2 - The slender rod AB is attached by a clevis to arm...Ch. 18.2 - The slender rod AB is attached by a clevis to arm...Ch. 18.2 - Prob. 18.92PCh. 18.2 - The 10-oz disk shown spins at the rate 1=750 rpm,...Ch. 18.2 - Prob. 18.94PCh. 18.2 - Prob. 18.95PCh. 18.2 - Prob. 18.96PCh. 18.2 - Prob. 18.97PCh. 18.2 - Prob. 18.98PCh. 18.2 - Prob. 18.99PCh. 18.2 - Prob. 18.100PCh. 18.2 - Prob. 18.101PCh. 18.2 - Prob. 18.102PCh. 18.2 - Prob. 18.103PCh. 18.2 - A 2.5-kg homogeneous disk of radius 80 mm rotates...Ch. 18.2 - For the disk of Prob. 18.99, determine (a) the...Ch. 18.2 - Prob. 18.106PCh. 18.3 - Prob. 18.107PCh. 18.3 - A uniform thin disk with a 6-in. diameter is...Ch. 18.3 - Prob. 18.109PCh. 18.3 - Prob. 18.110PCh. 18.3 - Prob. 18.111PCh. 18.3 - A solid cone of height 9 in. with a circular base...Ch. 18.3 - Prob. 18.113PCh. 18.3 - Prob. 18.114PCh. 18.3 - Prob. 18.115PCh. 18.3 - Prob. 18.116PCh. 18.3 - Prob. 18.117PCh. 18.3 - Prob. 18.118PCh. 18.3 - Show that for an axisymmetric body under no force,...Ch. 18.3 - Prob. 18.120PCh. 18.3 - Prob. 18.121PCh. 18.3 - Prob. 18.122PCh. 18.3 - Prob. 18.123PCh. 18.3 - Prob. 18.124PCh. 18.3 - Prob. 18.125PCh. 18.3 - Prob. 18.126PCh. 18.3 - Prob. 18.127PCh. 18.3 - Prob. 18.128PCh. 18.3 - An 800-lb geostationary satellite is spinning with...Ch. 18.3 - Solve Prob. 18.129, assuming that the meteorite...Ch. 18.3 - Prob. 18.131PCh. 18.3 - Prob. 18.132PCh. 18.3 - Prob. 18.133PCh. 18.3 - Prob. 18.134PCh. 18.3 - Prob. 18.135PCh. 18.3 - Prob. 18.136PCh. 18.3 - Prob. 18.137PCh. 18.3 - Prob. 18.138PCh. 18.3 - Prob. 18.139PCh. 18.3 - Prob. 18.140PCh. 18.3 - Prob. 18.141PCh. 18.3 - Prob. 18.142PCh. 18.3 - Prob. 18.143PCh. 18.3 - Prob. 18.144PCh. 18.3 - Prob. 18.145PCh. 18.3 - Prob. 18.146PCh. 18 - Prob. 18.147RPCh. 18 - Prob. 18.148RPCh. 18 - A rod of uniform cross-section is used to form the...Ch. 18 - A uniform rod of mass m and length 5a is bent into...Ch. 18 - Prob. 18.151RPCh. 18 - Prob. 18.152RPCh. 18 - A homogeneous disk of weight W=6 lb rotates at the...Ch. 18 - Prob. 18.154RPCh. 18 - Prob. 18.155RPCh. 18 - Prob. 18.156RPCh. 18 - Prob. 18.157RPCh. 18 - Prob. 18.158RP
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