Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 21.6, Problem 62P
The gyroscope consists of a uniform 450-g disk D which is attached to the axle AB of negligible mass. The supporting frame has a mass of 180 g and a center of mass at G. If the disk is rotating about the axle at ωD = 90 rad/s, determine the constant angular velocity ωP at which the frame precesses about the pivot point O. The frame moves in the horizontal plane.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The circular disk of 270-mm radius has a mass of 36 kg with centroidal radius of gyration k = 235 mm and has a concentric circular
groove of 105-mm radius cut into it. A steady force T is applied at an angle to a cord wrapped around the groove as shown. If T = 59N,
0 = 29°, μs = 0.08, and μk = 0.07, determine the angular acceleration a of the disk, the acceleration a of its mass center G, and the
friction force F which the surface exerts on the disk. The angular acceleration a is positive if counterclockwise, negative if clockwise;
the acceleration a is positive if to the right, negative if to the left; and the friction force F is positive if to the right, negative if to the left.
m= 36 kg
k 235 mm
270 mm
T
G
Ug = 0.08
Uh = 0.07
105
mm.
The 21-kg wheel has a radius of gyration about its center O of ko =260 mm, and
radius r = 0.5 m. When the wheel is subjected to the constant force F = 247 N,
applied to the wheel's center axle at an angle = 6°, it starts rolling from rest.
Determine the wheel's angular velocity W (in rad/s) after 4.0 seconds if the wheel
has been rolling without slipping. Please pay attention: the numbers may change
since they are randomized. Your answer must include 1 place after the decimal point.
Take g = 9.81 m/s².
Your Answer:
G
Answer
r
0
F
The 27-kg wheel has a radius of gyration about its center O of ko = 260 mm, and
radius r = 0.5 m. When the wheel is subjected to the constant force F = 354 N,
applied to the wheel's center axle at an angle = 6°, it starts rolling from rest.
Determine the wheel's angular velocity W (in rad/s) after 3.2 seconds if the wheel
has been rolling without slipping. Please pay attention: the numbers may change
since they are randomized. Your answer must include 1 place after the decimal point.
Take g = 9.81 m/s².
F
0
Your Answer:
Answer
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
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
- 3. The wheel has a mass of 100 kg and a radius of gyration about the z-axis of k: = 300 mm rests on a smooth horizontal plane. If the belt is subjected to a force of P= 170 N, determine the angular velocity of the wheel and the speed of its center of mass two seconds after the 400 mm force is applied.arrow_forwardThe 31-kg reel is mounted on the 16-kg cart. Part A: If the cable wrapped around the inner hub of the reel is subjected to a force of P=50N, determine the velocity of the cart when t = 4.2 s. The radius of gyration of the reel about its center of mass O is kO=250mm. Neglect the size of the small wheels. Part B: Determine the angular velocity of the reel when t = 4.2 s.arrow_forwardThe concrete block weighing 644 lb is elevated by the hoisting mech- anism shown, where the cables are securely wrapped around the re- spective drums. The drums, which are fastened together and turn as a single unit about their mass center at 0, have a combined weight of 322 lb and a radius of gyration about O of 18 in. If a constant tension P = 400 lb is maintained by the power unit at A, determine the vertical acceleration of the block and the resultant force on the bearing at O. Solve using; 24" 12" P = 400 lb (a) Two free body diagrams for concrete block and drum. W = 322 lb ko = 18" (b) One system block diagram ( concrete block and drum as one system). 45° A 644 lbarrow_forward
- The 30-kg wheel has a radius of gyration about its center O of ko = 240 mm, and radius r = 0.5 m. When the wheel is subjected to the constant force F = 388 N, applied to the wheel's center axle at an angle = 6°, it starts rolling from rest. Determine the total angular impulse L (in N•m.s) about the wheel's IC after 3.7 seconds if the wheel has been rolling without slipping. Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point. Take g = 9.81 m/s². Your Answer: G Answer Ө Farrow_forwardEach of the two links has a mass of 2 kg and a centroidal radius of gyration of 60mm. The slider at B has a mass of 3 kg and moves freely in the vertical guide. The springhas a stiffness of 6 kN/m. If a constant torque M = 20 N∙m is applied to link OA throughits shaft at O starting from the rest position at θ = 45°, determine the angular velocity ofOA when θ = 0.arrow_forwardThe 213-kg wheel has a radius of gyration about its center O of ko = 240 mm, and radius r = 0.4 m. When the wheel is subjected to the constant couple moment M = 85 N·m, it starts rolling from rest. Determine the wheel's angular velocity W (in rad/s) after 4.4 seconds if the wheel has been rolling without slipping. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g = 9.81 m/s². M Your Answer: Answerarrow_forward
- Gear B is rigidly attached to drum A and is supported by two small rollers at E and D. Gear B is in mesh with gear C which is subjected to a torque of M= 60 N.m. Determine the angular velocity of the drum A after C has rotated 5 revolutions, starting from rest. Gear B and the drum have a mass of 100 kg and a radius of gyration about their rotating axis of 250 mm. Gear C has a mass of 30 kg and the radius of gyration about its rotating axis of 125 mm. 300 mm 200 mm E ΕΟ 150 mm M Barrow_forwardThe double pulley consists of two parts that are attached to one another. It has a mass of 20 kg and a radius of gyration about its center of ko= 200 mm and is turning with an angular velocity of 15 rad/s clockwise. Determine the kinetic energy of the system. Assume that neither cable slips on the pulley.arrow_forwardEach of the two links has a mass of 1.5 kg and a centroidal radius of gyration of 55 mm. The slider at B has a mass of 3.4 kg and moves freely in the vertical guide. The spring has a stiffness of 5.9 kN/m. If a constant torque M = 14.0 N-m is applied to link OA through its shaft at O starting from the rest position at = 45°, determine the angular velocity of OA when 0 = 0. 40 mm 330 mm O Answer: w= i 165 mm 165 mm rad/sarrow_forward
- The 250-kg wheel has a radius of gyration about its center O of ko = 260 mm, and radius r = 0.4 m. When the wheel is subjected to the constant couple moment M = 64 N.m, it starts rolling from rest. Determine the total angular impulse L (in N.m.s) about the wheel's IC after 7.3 seconds if the wheel has been rolling without slipping. Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point. Take g = 9.81 m/s². M Your Answer: Answerarrow_forwardThe 20-kg wheel has a radius of gyration about its center O of ko = 280 mm, and radius r = 0.5 m. When the wheel is subjected to the constant force F= 388 N, applied to the wheel's center axle at an angle = 11°, it starts rolling from rest. Determine the total angular impulse L (in N.m.s) about the wheel's /C after 5.5 seconds if the wheel has been rolling without slipping. Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point. Take g = 9.81 m/s². F Ө Your Answer: Answerarrow_forwardThe dump truck carries 5 m³ of dirt with a density of 1600 kg /m³, and the elevating mechanism rotates the dump about the pivot A at a constant angular rate of 4 deg /s. The mass center of the dump and load is at G. Determine the maximum power P required during the tilting of the load. 1500 mm 900 mmarrow_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 Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering 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
EVERYTHING on Axial Loading Normal Stress in 10 MINUTES - Mechanics of Materials; Author: Less Boring Lectures;https://www.youtube.com/watch?v=jQ-fNqZWrNg;License: Standard YouTube License, CC-BY