EP ENGR.MECH.:DYNAMICS-REV.MOD.MAS.ACC.
14th Edition
ISBN: 9780133976588
Author: HIBBELER
Publisher: PEARSON CO
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Chapter 21.6, Problem 78P
To determine
The steady-state precession about the z axis.
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3 The object below can rotate in the plane of the page about a fixed axis at A. The object
is symmetric about A in the vertical and horizontal directions. A time=0, the object is
rotating counterclockwise at 5 rad/s. The material has a uniform area density of 120
kg/m².
a. What is the mass moment of inertia of the object about Point A?
b. The net moment applied about Point A is shown on the graph. What is the angular
velocity, w₁5, of the object at t-15 seconds?
MA [Nm]
16
0.15 m
120 kg/m²
0.3 m
H
wo = 5 rad/s
A
0.8 m
0.3 m
0.6 m
0
-8
0.15 m
10
15
time [s]
Consider a satellite moving in a torque-free environment. The inertial frame and satellite body-fixed frame
are represented by N-frame and B-frame, where {^₁, ŵ2, ñ3} and {b₁, 62, 63} are right-handed vector bases
fixed in N-frame and B-frame, respectively. {1;} is aligned with the principal axis of inertia, where ☎₁ and
3 are associated with the minimum and maximum moments of inertia, respectively.
Denote the satellite angular velocity by w = wib; and the inertia tensor about the CoM by Ic. Suppose
that I at time t = 0 is given by:
Ic(t = 0) = 2ñ₁ñ₁ +2.25 ñ¿Ñ₂ +2.25 ñ³Ñ3 – 0.75 ñ¿ñ3 −0.75 3₂ (dimensionless)
Express the satellite inertia tensor about the CoM in B-frame.
Determine [BN] at time t = 0, i.c., the direction cosine matrix (DCM) that represents the
orientation of B-frame relative to N-frame.
Consider a cylinder of radius R = 0.6 m and radius of gyration k = 0.33 m rolling (without slipping)
down an inclined plane. The plane makes an angle of ø = 10 deg with the horizontal plane. How long
(in seconds) will it take for the center of cylinder to travel a distance of 1.3 m.
Chapter 21 Solutions
EP ENGR.MECH.:DYNAMICS-REV.MOD.MAS.ACC.
Ch. 21.1 - Show that the sum of the moments of inertia of a...Ch. 21.1 - Determine the moment of inertia of the cone with...Ch. 21.1 - Determine moment of inertia Iy of the solid formed...Ch. 21.1 - Determine the moments of inertia Ix and Iy of the...Ch. 21.1 - The density of the material is . Express the...Ch. 21.1 - Prob. 6PCh. 21.1 - Prob. 7PCh. 21.1 - Prob. 8PCh. 21.1 - The weight of the cone is 15 lb, the height is h =...Ch. 21.1 - The density of the material is .
Ch. 21.1 - Prob. 11PCh. 21.1 - Determine the moment of inertia Ixx of the...Ch. 21.1 - Determine the product of inertia Iyz of the...Ch. 21.1 - Prob. 14PCh. 21.1 - Prob. 15PCh. 21.1 - Determine the moment of inertia of the rod about...Ch. 21.1 - Prob. 17PCh. 21.1 - Prob. 18PCh. 21.1 - Prob. 19PCh. 21.1 - Prob. 20PCh. 21.1 - Prob. 21PCh. 21.3 - If a body contains no planes of symmetry, the...Ch. 21.3 - Prob. 23PCh. 21.3 - Prob. 24PCh. 21.3 - The large gear has a mass of 5 kg and a radius of...Ch. 21.3 - Prob. 26PCh. 21.3 - Prob. 27PCh. 21.3 - Prob. 28PCh. 21.3 - Prob. 29PCh. 21.3 - Prob. 30PCh. 21.3 - Prob. 31PCh. 21.3 - Prob. 32PCh. 21.3 - The 20-kg sphere rotates about the axle with a...Ch. 21.3 - The 200-kg satellite has its center of mass at...Ch. 21.3 - Prob. 35PCh. 21.3 - Prob. 36PCh. 21.3 - Prob. 37PCh. 21.3 - Prob. 38PCh. 21.3 - Prob. 39PCh. 21.3 - Prob. 40PCh. 21.4 - Derive the scalar form of the rotational equation...Ch. 21.4 - Prob. 42PCh. 21.4 - Prob. 43PCh. 21.4 - Prob. 44PCh. 21.4 - The disk has a weight of 15 lb. Neglect the weight...Ch. 21.4 - Prob. 46PCh. 21.4 - Prob. 47PCh. 21.4 - Prob. 48PCh. 21.4 - Prob. 49PCh. 21.4 - Prob. 50PCh. 21.4 - Prob. 51PCh. 21.4 - The 5-kg circular disk is mounted off center on a...Ch. 21.4 - Prob. 53PCh. 21.4 - Prob. 54PCh. 21.4 - Prob. 55PCh. 21.4 - The 4-kg slender rod AB is pinned at A and held at...Ch. 21.4 - Prob. 57PCh. 21.4 - Prob. 58PCh. 21.4 - Prob. 59PCh. 21.4 - Show that the angular velocity of a body, in terms...Ch. 21.4 - Prob. 61PCh. 21.6 - The gyroscope consists of a uniform 450-g disk D...Ch. 21.6 - Prob. 63PCh. 21.6 - Prob. 64PCh. 21.6 - Prob. 65PCh. 21.6 - When viewed from the front of the airplane, the...Ch. 21.6 - Prob. 67PCh. 21.6 - Prob. 68PCh. 21.6 - Prob. 69PCh. 21.6 - Prob. 70PCh. 21.6 - Prob. 71PCh. 21.6 - Prob. 72PCh. 21.6 - Prob. 73PCh. 21.6 - Prob. 74PCh. 21.6 - Prob. 75PCh. 21.6 - Prob. 76PCh. 21.6 - Prob. 77PCh. 21.6 - Prob. 78P
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