Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 21.6, Problem 73P
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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)?
Match 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?
6
Given the system of points A,B,C with A(1,-1,1), B(2,0,2), C(-1,1,0) and
masses m₁= 2,m₂=1,m3=4 respectively. Determine the moments and
events inertia of the system with respect to the system of axes Oxyz.
Then find the moments of inertia with respect to the primary axis system
with origin O and to define the addresses of these axes.
Chapter 21 Solutions
Engineering Mechanics: Dynamics (14th Edition)
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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- 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?arrow_forwardConsider 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.arrow_forward3 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]arrow_forward
- 1. The slotted link is pinned at 0, and as a result of the constant angular velocity é = 6 rad's it drives the peg P for a short distance along the spiral guide r = (0.6 0) m where e is in radians. When e = 80 deg, Find: a. Find e, é, ë,r,r, ř. (in radians) b. The radial components, transverse components, and magnitudes of the velocity [4maeie). - The radial components, transverse components, and magnitudes of the acceleration of P at the instant. asks). %3D 0.8 m r=0.6 0 ô =6 rad/sarrow_forwardFor the shape below, the moment :of inertia about X-axis is 25 mm 250 mm 25 mm 25 mm |x= 1791666667 mm^4 O |x= 1792226667 mm^4 O Ix= 222135416.7 mm^4 O 200 mmarrow_forward| Link BC has a mass mgc = 4 kg, with a moment of inertia about its mass center of: laac = maclic Link AB has a mass mAR = 2.4 kg, with a moment of inertia about point A of: The wheel at point C is of negligible mass. At the moment pictured below, the velocity of point C is 1.5 m/s to the right. Find the velocity of pin B after link AB has rotated through 90°.arrow_forward
- Find the equivalent moment of inertia of the rocker arm assembly with respect to the location of kt. mass1=10kg Jo=20kg-m2 mass2=15kg, a is half of b. The rocker is 30 centimeters long. (kg-m2) * k1 Jo- k2 m2arrow_forwardM M 1.5m m M m = 2kg. M = 3.5kg a) justify whether the moment of inertia about the vertical or horizontal axis have smaller value. Show your calculation. (b) Given angular velocity of 80 rev s¹ in 240 rev. Has a moment of inertia of 1.41x10-3 kg m2. Find: (i) angular acceleration. (ii) net constant torque must apply (c) A space station consists of a giant rotating hollow cylinder of mass 10 kg including people on the station and a radius of 100 m. Given initial angular velocity of 3.3rpm in order to generate artificial gravity. If 100. people, each with an average mass of 65 kg spacewalk to an awaiting spaceship. Find the new angular velocity (in rpm) once all the people are off the station. (d) Suppose a child walks from the outer edge of a rotating merry-go-round to the center. What happend to the angular velocity of the merry-go-round does it increase, decrease, or remain the same? By using the conservation of angular momentum, explain your answer qualitatively.. A large train has…arrow_forwardA wheel has a string of length 4 m wrapped round its shaft. The string is pulled with a constant force of 150 N. It is observed that when the string leaves the axle, the wheel is rotating at 3 revolutions in a second. Find the moment of inertia of the wheel.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