Vector Mechanics For Engineers
12th Edition
ISBN: 9781259977305
Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.
Publisher: Mcgraw-hill Education,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 18.2, Problem 18.97P
To determine
(a)
The minimum angular velocity when the mass is concentrated in the rim.
To determine
(b)
The minimum angular velocity when the wheel is equal to the thin disk is.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A stationary horizontal plate is attached to the ceiling by means of a fixed vertical tube. A wheel of radius a and mass m is mounted on a light axle AC which is attached by means of a clevis at A to a rod AB fitted inside the vertical tube. The rod AB is made to rotate with a constant angular velocity Omega causing the wheel to roll on the lower face of the stationary plate. Determine the minimum angular velocity and acceleration for which contact is maintained between the wheel and the plate. Consider the particular cases (a) when the mass of the wheel is concentrated in the rim, (b) when the wheel is equivalent to a thin disk of a radius a.
Assuming that the wheel of Prob. 18.97 weights 8lb, has a radius a=4in., and a radius of gyration of 3in., and that R = 20in. determine the force exerted by the plate on the wheel when omega = 25 rad/s
When the 18-kg wheel shown is attached to a balancing machine and made to spin at a rate of 12.5 rev/s, it is found that the forces exerted by the wheel on the machine are equivalent to a force-couple system consisting of a force F = (160 N)j applied at and a couple where the unit vectors form a triad that rotates with the wheel. (a ) Determine the distance from the axis of rotation to the mass center of the wheel and the products of inertia Ixy and Ixz (b) If only two corrective masses are to be used to balance the wheel statically and dynamically, what should these masses be and at which of the points A, B, D or E, should they be placed?
The essential structure of a certain type of aircraft turn indicator is shown. Each spring has a constant of 500 N/m, and the 200-g uniform disk of 40-mm radius spins at the rate of 10 000 rpm. The springs are stretched and exert equal vertical forces on yoke AB when the airplane is traveling in a straight path. Determine the angle through which the yoke will rotate when the pilot executes a horizontal turn of 750-m radius to the right at a speed of 800 km/h. Indicate whether point A will move up or down.
Chapter 18 Solutions
Vector Mechanics For Engineers
Ch. 18.1 - Prob. 18.1PCh. 18.1 - Prob. 18.2PCh. 18.1 - Prob. 18.3PCh. 18.1 - A homogeneous disk of weight W=6 lb rotates at the...Ch. 18.1 - Prob. 18.5PCh. 18.1 - A solid rectangular parallelepiped of mass m has a...Ch. 18.1 - Solve Prob. 18.6, assuming that the solid...Ch. 18.1 - Prob. 18.8PCh. 18.1 - Determine the angular momentum HD of the disk of...Ch. 18.1 - Prob. 18.10P
Ch. 18.1 - Prob. 18.11PCh. 18.1 - Prob. 18.12PCh. 18.1 - Prob. 18.13PCh. 18.1 - Prob. 18.14PCh. 18.1 - Prob. 18.15PCh. 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. 18.19PCh. 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 - Prob. 18.29PCh. 18.1 - Prob. 18.30PCh. 18.1 - Prob. 18.31PCh. 18.1 - Prob. 18.32PCh. 18.1 - Prob. 18.33PCh. 18.1 - Prob. 18.34PCh. 18.1 - Prob. 18.35PCh. 18.1 - Prob. 18.36PCh. 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 - Determine the kinetic energy of the disk of Prob....Ch. 18.1 - Prob. 18.44PCh. 18.1 - Prob. 18.45PCh. 18.1 - Prob. 18.46PCh. 18.1 - Prob. 18.47PCh. 18.1 - Prob. 18.48PCh. 18.1 - Prob. 18.49PCh. 18.1 - Prob. 18.50PCh. 18.1 - Prob. 18.51PCh. 18.1 - Prob. 18.52PCh. 18.1 - Determine the kinetic energy of the space probe of...Ch. 18.1 - Prob. 18.54PCh. 18.2 - Determine the rate of change H.G of the angular...Ch. 18.2 - Prob. 18.56PCh. 18.2 - Determine the rate of change H.G of the angular...Ch. 18.2 - Prob. 18.58PCh. 18.2 - Prob. 18.59PCh. 18.2 - Prob. 18.60PCh. 18.2 - Prob. 18.61PCh. 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 - A thin, homogeneous triangular plate of weight 10...Ch. 18.2 - Prob. 18.67PCh. 18.2 - Prob. 18.68PCh. 18.2 - Prob. 18.69PCh. 18.2 - Prob. 18.70PCh. 18.2 - Prob. 18.71PCh. 18.2 - Prob. 18.72PCh. 18.2 - Prob. 18.73PCh. 18.2 - Prob. 18.74PCh. 18.2 - Prob. 18.75PCh. 18.2 - Prob. 18.76PCh. 18.2 - Prob. 18.77PCh. 18.2 - Prob. 18.78PCh. 18.2 - Prob. 18.79PCh. 18.2 - Prob. 18.80PCh. 18.2 - Prob. 18.81PCh. 18.2 - Prob. 18.82PCh. 18.2 - Prob. 18.83PCh. 18.2 - Prob. 18.84PCh. 18.2 - Prob. 18.85PCh. 18.2 - Prob. 18.86PCh. 18.2 - Prob. 18.87PCh. 18.2 - Prob. 18.88PCh. 18.2 - Prob. 18.89PCh. 18.2 - The slender rod AB is attached by a clevis to arm...Ch. 18.2 - The slender rod AB is attached by a clevis to arm...Ch. 18.2 - Prob. 18.92PCh. 18.2 - The 10-oz disk shown spins at the rate 1=750 rpm,...Ch. 18.2 - Prob. 18.94PCh. 18.2 - Prob. 18.95PCh. 18.2 - Prob. 18.96PCh. 18.2 - Prob. 18.97PCh. 18.2 - Prob. 18.98PCh. 18.2 - Prob. 18.99PCh. 18.2 - Prob. 18.100PCh. 18.2 - Prob. 18.101PCh. 18.2 - Prob. 18.102PCh. 18.2 - Prob. 18.103PCh. 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. 18.2 - Prob. 18.106PCh. 18.3 - Prob. 18.107PCh. 18.3 - A uniform thin disk with a 6-in. diameter is...Ch. 18.3 - Prob. 18.109PCh. 18.3 - Prob. 18.110PCh. 18.3 - Prob. 18.111PCh. 18.3 - A solid cone of height 9 in. with a circular base...Ch. 18.3 - Prob. 18.113PCh. 18.3 - Prob. 18.114PCh. 18.3 - Prob. 18.115PCh. 18.3 - Prob. 18.116PCh. 18.3 - Prob. 18.117PCh. 18.3 - Prob. 18.118PCh. 18.3 - Show that for an axisymmetric body under no force,...Ch. 18.3 - Prob. 18.120PCh. 18.3 - Prob. 18.121PCh. 18.3 - Prob. 18.122PCh. 18.3 - Prob. 18.123PCh. 18.3 - Prob. 18.124PCh. 18.3 - Prob. 18.125PCh. 18.3 - Prob. 18.126PCh. 18.3 - Prob. 18.127PCh. 18.3 - Prob. 18.128PCh. 18.3 - An 800-lb geostationary satellite is spinning with...Ch. 18.3 - Solve Prob. 18.129, assuming that the meteorite...Ch. 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 - Prob. 18.136PCh. 18.3 - Prob. 18.137PCh. 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 - Prob. 18.143PCh. 18.3 - Prob. 18.144PCh. 18.3 - Prob. 18.145PCh. 18.3 - Prob. 18.146PCh. 18 - Prob. 18.147RPCh. 18 - Prob. 18.148RPCh. 18 - A rod of uniform cross-section is used to form the...Ch. 18 - A uniform rod of mass m and length 5a is bent into...Ch. 18 - Prob. 18.151RPCh. 18 - Prob. 18.152RPCh. 18 - A homogeneous disk of weight W=6 lb rotates at the...Ch. 18 - Prob. 18.154RPCh. 18 - Prob. 18.155RPCh. 18 - Prob. 18.156RPCh. 18 - Prob. 18.157RPCh. 18 - Prob. 18.158RP
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
- Consider a steel plate of mass m with dimensions L and w that is equally supported by two ball bearings (one on each end of the shaft shown at pointa A and B). At the instant shown below, the plate is released from rest. Part A: Determine an expression for the plate's angular acceleration magnitude a at this in- stant. (Hint: Use Euler's 2nd Law for pinned rotation and the parallel axis theorem.) Part B: Show that the magnitude of the reaction force at each bearing at this instant is R = mg/8. (Hint: Use the kinematics to relate the acceleration of the center of mass G to the angular acceleration. Use Euler's 1st Law to find the reaction forces with the acceleration you determined. As viewed from the side there are two forces acting on the system weight and two reaction forces both pointing upward at the same location.) A foye مر B L २arrow_forwardA 3 kg disk shown is pin supported at its center. The disk is rotated from rest and attains a constant angular velocity of 15 rad/s. If the mass of the rope is negligible and the radius of gyration of the drum is 50 mm; Find out the angular acceleration of the drum, the tension in the rope, and the torque experienced by the drum.arrow_forwardChapter 6, Problem 6.185 The base B has a mass of 6.3 kg and a radius of gyration of 126 mm about the central vertical axis shown, Each plate P has a mass of 3.2 kg. If the system is freely rotating about the vertical axis with an angular speed N, = 17 rev/min with the plates in the vertical position, estimate the angular speed N, when the plates have moved to the horizontal positions indicated. Neglect friction. 185 mm 185 mm 155 mm 155 mm 510 mm Answer: N2 = rev/minarrow_forward
- A 3 kg disk shown is pin supported at its center. The disk is rotated from rest and attains a constant angular velocity of 15 rad/s. If the mass of the rope is negligible and the radius of gyration of the drum is 50 mm; Find out the angular acceleration of the drum and the tension in the rope.arrow_forwardConsider the mechanism shown. Members PQ and QR are joined by a hinge at Q. End P of member PQ is pin-supported and end R of member QR is constrained to move along a horizontal surface. Member PQ rotates clockwise at a constant rate of 12 rad/s. Member QR rotates counterclockwise at a rate of 3.84 rad/s. Which of the following gives the closest value to the magnitude of the angular acceleration of rod QR? 9.16, 6.18, 1.609, 35.2 rad/s^2?? Which of the following gives the closest value to the magnitude of the acceleration of point R? 3.13, 9.89, 10.28, 12.88 m/s^2??arrow_forwardA wheel of radius r and centroidal radius of gyration _ k is released from rest on the incline and rolls without sliding. Derive an expression for the acceleration of the center of the wheel in terms of r, _ k , β, and g.arrow_forward
- The 10-oz disk shown spins at the rate w1= 750 rpm, while axle AB rotates as shown with an angular velocity w2 of magnitude 6 rad/s. Determine the dynamic reactions at A and B.arrow_forwardGiven: The gear shown moves on a fixed horizontal rack. The gear has mass m and a radius of gyration of k equal to its radius. The rod BC connected to the gear has length 1, and mass 2m with center of mass located at pt. G. The slider at B has negligible mass, and the attached spring has a spring constant k equal to mg/l. The system is released from rest in a vertical position (the bar BC is vertical). In this position, the spring is unstretched. The system has negligible friction and mass of the spring. k mrod G R mrod = 2m mgear = m l, I= mgear, k Find: Find the velocity of the point C on the gear after it has moved a distance of 1,/2 to the right.arrow_forwardProblem (1) Gears A and B each have a mass of 4 kg and a radius of gyration of 75 mm about their centers, while gear C has a mass of 15 kg and a radius of gyration of 180 mm about its center. A couple moment M = (0.20) N-m is applied to gear C. Determine the number of revolutions gears A and B experience if gear C increases its angular velocity from 25 rpm to 500 rpm. B 80 mm S0 mm 200 mmarrow_forward
- In the helicopter shown; a vertical tail propeller is used to pre- vent rotation of the cab as the speed of the main blades is changed. Assuming that the tail propeller is not operating determine the final angular velocity of the cab after the speed of the main blades has been changed from I80 to 240 rpm. (The speed of the main blades is measured relative to the cab, and the cab has a centroidal moment of inertia of 650 lb.ft.s2. Each of the four main blades is assumed to be a slender rod 14 ft weighing 55 lb.)arrow_forwardTwo shafts the axes of which intersect but are inclined to each other at 20 degreeconnected by means of a universal joint. At what position in the rotation cycle of thedrive shaft (i) velocity ratio will be maximum, minimum and unity (ii) the accelerationis maximum?arrow_forward6. The turbine of a ship has a mass of 4000 kg. and a radius of gyration of 480 mm. It rotates at 2400 rev/min. clockwise when looking forward from the stern. In each of the following cases determine, the magnitude and indicate clearly with suitable diagrams. the effect of the gyroscopic couple acting on the ship: (a) If the ship, when travelling at 15 ms¹ turns to starboard in a curve 1000 m radius. (b) If the ship is pitching and the bow is descending with maximum velocity. The pitching motion is simple harmonic, the period being 20 seconds and the total angular movement is 12º. (c) If the ship is rolling and at a certain instant has an angular velocity of 0.02 rad. s-¹ clockwise when looking forward from the stern.arrow_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