Vector Mechanics for Engineers: Statics and Dynamics
11th Edition
ISBN: 9780073398242
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Chapter 18.3, Problem 18.127P
(a)
To determine
The angle between the spin axis and the new precession axis of section A.
(b)
To determine
The rate of precession of section A.
(c)
To determine
The spin rate of section A.
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Students have asked these similar questions
A solid cube of side c= 120 mm is attached as shown to a cord AB of length 240 mm. The cube spins about its diagonal BC and precesses about the vertical axis AD Knowing that 0= 25° and β= 40°, determine (a) the rate of spin of the cube, (b) its rate of precession. (See hint of Prob. 18.115.)
A homogeneous cone with a height of h = 12 in. and a base with a diameter of d = 6 in. is attached as shown to a cord AB. Knowing that the angles that cord AB and the axis BC β=45 = 45° and 0= 30° and that the cone precesses at the constant rate O=8rd/s in the sense indicated, determine (a ) the rate of spin of the cone about its axis BC, (b ) the length of cord AB,
Problem 1
A disk, mass 2kg, radius 0.5m spins at a constant angular speed w = 12s about an axle
that is at an angle 0 = π/6 to the normal to the disk. We choose our y-axis so that the axle
lies in the xz-plane as shown below.
w
You may use without proof that the moment of inertia of a disk around its center of mass is
Io = MR² and about its diameter is ID = MR². All options are in SI units.
(a) What is the angular velocity vector?
(i) (6√√3,0,6)
(ii) (6,0,-6√3)
(iii) (6,0,6√3)
(b) Using the Euler equations, find 7₁?
(i) 0.
(ii) -9√3/2.
(iii) 9√3/2.
(c) Using the Euler equations, find 72?
(i) 0.
(ii) -9√3/2.
(iii) 9√3/2.
Chapter 18 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Ch. 18.1 - A thin, homogeneous disk of mass m and radius r...Ch. 18.1 - Prob. 18.2PCh. 18.1 - 18.3 Two uniform rods AB and CE, each of weight 3...Ch. 18.1 - A homogeneous disk of weight W = 6 lb rotates at...Ch. 18.1 - Prob. 18.5PCh. 18.1 - A solid rectangular parallelepiped of mass m has a...Ch. 18.1 - Prob. 18.8PCh. 18.1 - Determine the angular momentum HD of the disk of...Ch. 18.1 - Prob. 18.10PCh. 18.1 - Prob. 18.11P
Ch. 18.1 - Prob. 18.12PCh. 18.1 - Prob. 18.13PCh. 18.1 - Two L-shaped arms each have a mass of 5 kg and are...Ch. 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. 18.20PCh. 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 - A circular plate of mass m is falling with a...Ch. 18.1 - Prob. 18.30PCh. 18.1 - Prob. 18.31PCh. 18.1 - Determine the impulse exerted on the plate of...Ch. 18.1 - The coordinate axes shown represent the principal...Ch. 18.1 - Prob. 18.34PCh. 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 - Prob. 18.43PCh. 18.1 - Determine the kinetic energy of the solid...Ch. 18.1 - Prob. 18.45PCh. 18.1 - Determine the kinetic energy of the disk of Prob....Ch. 18.1 - Determine the kinetic energy of the assembly of...Ch. 18.1 - Determine the kinetic energy of the shaft of Prob....Ch. 18.1 - Prob. 18.49PCh. 18.1 - Prob. 18.50PCh. 18.1 - Determine the kinetic energy lost when edge C of...Ch. 18.1 - Prob. 18.52PCh. 18.1 - Prob. 18.53PCh. 18.1 - Determine the kinetic energy of the space probe of...Ch. 18.2 - Determine the rate of change HG of the angular...Ch. 18.2 - Prob. 18.56PCh. 18.2 - Prob. 18.57PCh. 18.2 - Prob. 18.58PCh. 18.2 - Prob. 18.59PCh. 18.2 - Determine the rate of change HG of the angular...Ch. 18.2 - 18.61 Determine the rate of change of the angular...Ch. 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 - Prob. 18.66PCh. 18.2 - The assembly shown consists of pieces of sheet...Ch. 18.2 - The 8-kg shaft shown has a uniform cross-section....Ch. 18.2 - Prob. 18.69PCh. 18.2 - Prob. 18.70PCh. 18.2 - Prob. 18.71PCh. 18.2 - Knowing that the plate of Prob. 18.66 is initially...Ch. 18.2 - Prob. 18.73PCh. 18.2 - The shaft of Prob. 18.68 is initially at rest ( =...Ch. 18.2 - The assembly shown weighs 12 lb and consists of 4...Ch. 18.2 - Prob. 18.76PCh. 18.2 - Prob. 18.79PCh. 18.2 - Prob. 18.80PCh. 18.2 - Prob. 18.81PCh. 18.2 - Prob. 18.82PCh. 18.2 - The uniform, thin 5-lb disk spins at a constant...Ch. 18.2 - The essential structure of a certain type of...Ch. 18.2 - Prob. 18.85PCh. 18.2 - Prob. 18.86PCh. 18.2 - Prob. 18.87PCh. 18.2 - The 2-lb gear A is constrained to roll on the...Ch. 18.2 - Prob. 18.89PCh. 18.2 - Prob. 18.90PCh. 18.2 - 18.90 and 18.91The slender rod AB is attached by a...Ch. 18.2 - The essential structure of a certain type of...Ch. 18.2 - The 10-oz disk shown spins at the rate 1 = 750...Ch. 18.2 - Prob. 18.94PCh. 18.2 - Prob. 18.95PCh. 18.2 - Two disks each have a mass of 5 kg and a radius of...Ch. 18.2 - Prob. 18.97PCh. 18.2 - Prob. 18.98PCh. 18.2 - A thin disk of mass m = 4 kg rotates with an...Ch. 18.2 - Prob. 18.101PCh. 18.2 - Prob. 18.102PCh. 18.2 - A 2.5-kg homogeneous disk of radius 80 mm rotates...Ch. 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. 18.3 - A uniform thin disk with a 6-in. diameter is...Ch. 18.3 - A uniform thin disk with a 6-in. diameter is...Ch. 18.3 - Prob. 18.109PCh. 18.3 - The top shown is supported at the fixed point O...Ch. 18.3 - Prob. 18.111PCh. 18.3 - Prob. 18.112PCh. 18.3 - Prob. 18.113PCh. 18.3 - A homogeneous cone with a height of h = 12 in. and...Ch. 18.3 - Prob. 18.115PCh. 18.3 - Prob. 18.116PCh. 18.3 - Prob. 18.117PCh. 18.3 - Prob. 18.118PCh. 18.3 - Prob. 18.119PCh. 18.3 - Prob. 18.120PCh. 18.3 - Prob. 18.121PCh. 18.3 - Prob. 18.122PCh. 18.3 - Prob. 18.123PCh. 18.3 - A coin is tossed into the air. It is observed to...Ch. 18.3 - Prob. 18.125PCh. 18.3 - Prob. 18.126PCh. 18.3 - Prob. 18.127PCh. 18.3 - Prob. 18.128PCh. 18.3 - Prob. 18.129PCh. 18.3 - Prob. 18.130PCh. 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 - A homogeneous disk with a radius of 9 in. is...Ch. 18.3 - The top shown is supported at the fixed point O....Ch. 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 - Consider a rigid body of arbitrary shape that is...Ch. 18.3 - Prob. 18.144PCh. 18.3 - Prob. 18.145PCh. 18 - Three 25-lb rotor disks are attached to a shaft...Ch. 18 - Prob. 18.148RPCh. 18 - Prob. 18.149RPCh. 18 - A uniform rod of mass m and length 5a is bent into...Ch. 18 - Prob. 18.151RPCh. 18 - Prob. 18.152RPCh. 18 - Prob. 18.153RPCh. 18 - Prob. 18.154RPCh. 18 - Prob. 18.155RPCh. 18 - The space capsule has no angular velocity when the...Ch. 18 - Prob. 18.157RPCh. 18 - The essential features of the gyrocompass are...
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