Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 19.2, Problem 2P
At a given Instant, the body has a linear momentum L = mvG and an angular momentum HG = IGω computed about its mass center. Show that the angular momentum of the body computed about the instantaneous center of zero velocity IC can be expressed as HIG = IIGω, where IIG represents the body's moment of inertia computed about the instantaneous axis of zero velocity. As shown, the IC is located at a distance rG/IC away from the mass center G.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The link AC (6 kg) rotates in the vertical plane about the point B. A spring (k = 600 N/m, points C to
D) of unstretched length 225 mm is fixed to the link as shown. If the link is released from rest in the position
shown below, determine its angular velocity after it has rotated 90°. You may take the moment of inertia of the
link AC about its mass center as Igac =÷ml?.
180
900 mm
The 10-kg bar is released from rest in the horizontal position 1 and falls to positions 2. The unstretched lengthy of the spring is 0.6 m and the spring constant is k=20 N/m .what will be the bar 's angular velocity when it is in position 2.
For the three scenarios shown below, determine the angular velocity about point O, if each rigid body
has the same angular momentum of 0.1 kg-m²/s. System 1: r = 45 cm, m = 600 g. System 2: rod L = 90
cm, m = 350 g. System 3: rod length, d = 67 cm, m = 630 g.
(0)
00₂
L2
G
L2
2
3
2
G
Chapter 19 Solutions
Engineering Mechanics: Dynamics (14th Edition)
Ch. 19.2 - Determine the angular momentum of the 100-kg disk...Ch. 19.2 - Determine the angular impulse about point O for t...Ch. 19.2 - If it is subjected to a couple moment of M = (3t2)...Ch. 19.2 - The 300-kg wheel has a rad1us of gyration about...Ch. 19.2 - If rod OA of negligible mass is subjected lo the...Ch. 19.2 - Gears A and B of mass 10 kg and 50 kg have radii...Ch. 19.2 - The 50-kg spool is subjected to a horizontal force...Ch. 19.2 - The reel has a weight of 150 lb and a radius of...Ch. 19.2 - The rigid body (slab) has a mass m and rotates...Ch. 19.2 - At a given Instant, the body has a linear momentum...
Ch. 19.2 - Show that if a slab is rotating about a fixed axis...Ch. 19.2 - The 40-kg disk is rotating at = 100 rad/s. When...Ch. 19.2 - The Impact wrench cons1sts of a slender 1-kg rod...Ch. 19.2 - The airplane is traveling in a straight line with...Ch. 19.2 - The double pulley consists of two wheels which are...Ch. 19.2 - The assembly weighs 10 lb and has a radius of...Ch. 19.2 - The disk has a weight of 10 lb and is pinned at...Ch. 19.2 - The 30-kg gear A has a radius of gyration about...Ch. 19.2 - Determine the angular velocity of the pulley when...Ch. 19.2 - The 40-kg roll of paper rests along the wall where...Ch. 19.2 - The slender rod has a mass m and is suspended at...Ch. 19.2 - The rod of length L and mass m lies on a smooth...Ch. 19.2 - A 4-kg disk A is mounted on arm BC. which has a...Ch. 19.2 - The frame of a tandem drum roller has a weight of...Ch. 19.2 - The 100-lb wheel has a radius of gyration of kG =...Ch. 19.2 - The 4-kg slender rod rests on a smooth floor If it...Ch. 19.2 - The double pulley consists of two wheels which are...Ch. 19.2 - The 100-kg spool is resting on the inclined...Ch. 19.2 - The spool has a weight of 30 lb and a radius of...Ch. 19.2 - The two gears A and B have weights and radii of...Ch. 19.2 - The hoop (thin ring) has a mass of 5 kg and is...Ch. 19.2 - The 30-kg gear is subjected to a force of P =...Ch. 19.2 - The 30-lb flywheel A has a radius of gyration...Ch. 19.2 - If the shaft is subjected to a torque of M = (...Ch. 19.2 - The double pulley consists of two wheels which are...Ch. 19.2 - The crate has a mass mc. Determine the constant...Ch. 19.4 - The turntable T of a record player has a mass of...Ch. 19.4 - The 10-g bullet having a velocity of 800 m/s is...Ch. 19.4 - The 10-g bullet having a velocity of 800 m/s is...Ch. 19.4 - The circular disk has a mass m and is suspended at...Ch. 19.4 - The 80-kg man is holding two dumbbells while...Ch. 19.4 - The platform swing consists of a 200-lb flat plate...Ch. 19.4 - The 2-kg rod ACB supports the two 4-kg disks at...Ch. 19.4 - The satellite has a mass of 200 kg and a radius of...Ch. 19.4 - Disk A has a weight of 20 lb. An inextensible...Ch. 19.4 - The plank has a weight of 30 lb, center of gravity...Ch. 19.4 - The 12-kg rod AB is pinned to the 40-kg disk. If...Ch. 19.4 - A thin rod of mass m has an angular velocity o...Ch. 19.4 - Tests of impact on the fixed crash dummy are...Ch. 19.4 - The vertical shaft is rotating with an angular...Ch. 19.4 - The mass center of the 3-lb ball h3s a velocity of...Ch. 19.4 - Prob. 44PCh. 19.4 - The 10-lb block is sliding on the smooth surface...Ch. 19.4 - Determine the height hat which a billiard ball of...Ch. 19.4 - The pendulum consists of a 15-kg solid ball and...Ch. 19.4 - The 4-lb rod AB is hanging in the vertical...Ch. 19.4 - Determine the largest angular velocity 1 the disk...Ch. 19.4 - The solid ball of mass m is dropped with a...Ch. 19.4 - The wheel has a mass of 50 kg and a radius of...Ch. 19.4 - The wheel has a mass of 50 kg and a radius of...Ch. 19.4 - The rod of mass m and length L is released from...Ch. 19.4 - Prob. 55PCh. 19.4 - A ball having a mass of 8 kg and initial speed of...Ch. 19.4 - A solid ball with a mass m is thrown on the ground...Ch. 19.4 - The pendulum consists of a 10-lb solid ball and...Ch. 19.4 - The cable is subjected to a force of P = (10t2)...Ch. 19.4 - The space capsule has a mass of 1200 kg and a...Ch. 19.4 - The tire has a mass of 9 kg and a rad1us of...Ch. 19.4 - The wheel having a mass of 100 kg and a radius of...Ch. 19.4 - The spool has a weight of 30 lb and a radius of...Ch. 19.4 - Spool B is at rest and spool A is rotating at 6...Ch. 19.4 - A thin disk of mass m has an angular velocity 1...Ch. 19.4 - Prob. 8RP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- The dynamic system is initially at rest. The rod has a mass of m=0.5kg and a length of L=1m. The CG of the rod is located at G, and the rod is rotated about the point O, a distance, h=0.25m, away from point G. At the time of releasing find a. Acceleration at the CG (point G) b. Reaction at O (Use moment of inertia of the rod I= mL2/12)arrow_forwardIn his mission as a spy, Loid Forger fired a bullet weighing mB = 0.007 kg with a horizontal speed of VB= 550 m/s into the lower end of a gate which can be modeled into a slender m=16-kg bar of length L=1.5m for simplified analysis only. Know that h=0.25 m and that the gate, which has a pin connection at point C, is initially at rest. The bullet becomes embedded into the gate after impact. 1.5 m с A D 0.25 m VB= 550 m/sarrow_forwardThe four balls, each of mass m = 2.3 kg, are rigidly mounted to the rotating frame and shaft, which are initially rotating freely about the vertical z-axis at the angular rate of 19.5 rad/s clockwise when viewed from above. The distances r = 0.25 m and R = 0.52 m. If a constant torque M = 23.1 N·m is applied to the shaft, calculate the time t to reverse the direction of rotation and reach an angular velocity = 19.5 rad/s in the same sense as M. m R m r M m R marrow_forward
- A bar of 30 kg mass is in the rest position for the position θ = 0 °, for which the spring is in its unstretched (relaxed) state. Find the angular velocity of the bar when it is at the position θ = 90 °. Take the acceleration due to gravity as 9.81 m / s ^ 2arrow_forward11m 3m 9m A K- 7m What is the mass moment of Inertia about the "A axis" (orange) of a cuboid with cylindrical hole drilled through the centre of a face as shown in the figure. The mass of the cuboid before the hole was drilled M1 = 12kg and after the hole was drilled M2 = 6. 6kg.arrow_forwardDraw the impulse-momentum diagram and line of action for e. Solve for the following: 1. Determine the angular velocity of the slender bar (B) immediately after impact. angular velocity of A = 57.1 rad/s since there is no external torque 2. Determine the linear velocities of both the sphere (A) and the slender bar (B) immediately after impact at their centroids ANSWERS I GOT BUT ARE INCORRECT: (the unit is given) angular velocity of the slender bar (B) immediately after impact: 8.089 rad/s , 18.49 rad/s linear velocity of the sphere (A) immediately after impact at the centroid: 0.485 rad/s^2, 0.16 rad/s^2, 2.11 rad/s^2 linear velocity of the slender bar (B) immediately after impact at the centroid: 0.485 rad/s^2, 0.49 rad/s^2, 2.21 rad/s^2arrow_forward
- 3. A thin piece of metal of mass 80 g has the cross section shown in Fig. 17. Find the moment and products of inertia for the axes Ox and Oy. Through what angles must these axes be rotated to coincide with the principal axes? Suppose the body is rotating at a given instant about the Ox axis with an angular velocityarrow_forward)= The disk with radius r is rolling (without slipping) with angular velocity @ through the bottom of the circular path of radius R. If @= 2 rad/sec, R = 0.5 m, r = 0.2 m, and the mass of the disk is 3 kg, calculate the magnitude of the normal force exerted by the path on the disk at that instant. Present your answer in Newtons using 3 significant figures. wwwwwarrow_forwardof stion The man stands on the platform at O and runs out toward the edge such that when he is at A, y = 5 ft, his mass center has a velocity of 2 ft/s and an acceleration of 3 ft/s², both measured relative to the platform and directed along the positive y axis. If the platform has an angular velocity of 0.4 rd/s and angular acceleration of 0.2 rad/s² as shown in the figure below, determine the following: Note that i, j represent the unit vectors of x and y axes, respectively. Z The velocity of his mass center at this instant is The acceleration of his mass center at this instant is 00 # ft/s. W # ft/s². Aarrow_forward
- The two identical links, each of length b= 500 mm and mass m = 20 kg may be treated as uniform slender bars. The distance between A and the instantaneous center of zero velocity of AB at the current location (0= 30°) isarrow_forwardURGENT! PLEASE HELP WITH THISarrow_forwardThe rod AB has a mass of 20 kg,the mass of the piston A and B are both 5kg. Piston B is attached to a spring of constant k = 1200 N/m. The spring is un-stretched when θ = 0. If the rod is released from rest whenθ = 45° Please find÷ (1) the moment inertia of the rod AB about its mass center G (2)The angular velocity of rod AB at θ = 0° (3)the velocity of piston A at θ = 0° (4) the velocity of Piston B at θ = 0° (hint: regard the piston A, B, rod as a system, during the motion, except the spring, the weight of rod AB, the weight of pistonB also does work). g = 9.8 m/s2arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Dynamics - Lesson 1: Introduction and Constant Acceleration Equations; Author: Jeff Hanson;https://www.youtube.com/watch?v=7aMiZ3b0Ieg;License: Standard YouTube License, CC-BY