VECTOR MECHANIC
12th Edition
ISBN: 9781264095032
Author: BEER
Publisher: MCGRAW-HILL HIGHER EDUCATION
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 18.3, Problem 18.107P
A uniform thin disk with a 6-in. diameter is attached to the end of a rod AB of negligible mass that is supported by a ball-and-socket joint at point A. Knowing that the disk is observed to precess about the vertical axis AC at the constant rate of 36 rpm in the sense indicated and that its axis of symmetry AB forms an angle β = 60° with AC, determine the rate at which the disk spins about rod AB.
Fig. P18.107 and P18.108
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A uniform thin disk with a 6-in. diameter is attached to the end of a rod AB of negligible mass that is supported by a ball-and-socket joint at point A. Knowing that the disk is spinning about its axis of symmetry AB at the rate of 2100 rpm in the sense indicated and that AB forms an angle β = 45° with the vertical axis AC, determine the two possible rates of steady precession of the disk about the axis AC.
A homogeneous cone with a height of h = 12 in. and a base with a diameter of d = 6 in. is attached as shown to a cord AB. Knowing that the angles that cord AB and the axis BC β=45 = 45° and 0= 30° and that the cone precesses at the constant rate O=8rd/s in the sense indicated, determine (a ) the rate of spin of the cone about its axis BC, (b ) the length of cord AB,
A coin is tossed into the air. It is observed to spin at the rate of 600 rpm about an axis GC perpendicular to the coin and to precess about the vertical direction GD Knowing that GC forms an angle of 15° with GD, determine (a) the angle that the angular velocity w of the coin forms with G (b) the rate of precession of the coin about GD.
Chapter 18 Solutions
VECTOR MECHANIC
Ch. 18.1 - A thin, homogeneous disk of mass m and radius r...Ch. 18.1 - Prob. 18.2PCh. 18.1 - Prob. 18.3PCh. 18.1 - A homogeneous disk of weight W = 6 lb rotates at...Ch. 18.1 - A homogeneous disk of mass m = 8 kg rotates at the...Ch. 18.1 - A solid rectangular parallelepiped of mass m has a...Ch. 18.1 - Prob. 18.8PCh. 18.1 - Determine the angular momentum HD of the disk of...Ch. 18.1 - Prob. 18.10PCh. 18.1 - Determine the angular momentum HO of the disk of...
Ch. 18.1 - Prob. 18.12PCh. 18.1 - Prob. 18.13PCh. 18.1 - Two L-shaped arms each have a mass of 5 kg and are...Ch. 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. 18.20PCh. 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 - A circular plate of mass m is falling with a...Ch. 18.1 - Prob. 18.30PCh. 18.1 - Prob. 18.31PCh. 18.1 - Determine the impulse exerted on the plate of...Ch. 18.1 - The coordinate axes shown represent the principal...Ch. 18.1 - Prob. 18.34PCh. 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 - Determine the kinetic energy of the solid...Ch. 18.1 - Prob. 18.45PCh. 18.1 - Determine the kinetic energy of the disk of Prob....Ch. 18.1 - Determine the kinetic energy of the assembly of...Ch. 18.1 - Determine the kinetic energy of the shaft of Prob....Ch. 18.1 - Prob. 18.49PCh. 18.1 - Prob. 18.50PCh. 18.1 - Determine the kinetic energy lost when edge C of...Ch. 18.1 - Prob. 18.52PCh. 18.1 - Prob. 18.53PCh. 18.1 - Determine the kinetic energy of the space probe of...Ch. 18.2 - Determine the rate of change HG of the angular...Ch. 18.2 - Prob. 18.56PCh. 18.2 - Determine the rate of change HG of the angular...Ch. 18.2 - Prob. 18.58PCh. 18.2 - Prob. 18.59PCh. 18.2 - Determine the rate of change HG of the angular...Ch. 18.2 - Prob. 18.61PCh. 18.2 - Determine the rate of change HD of the angular...Ch. 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 - Prob. 18.66PCh. 18.2 - The assembly shown consists of pieces of sheet...Ch. 18.2 - The 8-kg shaft shown has a uniform cross-section....Ch. 18.2 - Prob. 18.69PCh. 18.2 - Prob. 18.70PCh. 18.2 - Prob. 18.71PCh. 18.2 - Knowing that the plate of Prob. 18.66 is initially...Ch. 18.2 - Prob. 18.73PCh. 18.2 - The shaft of Prob. 18.68 is initially at rest ( =...Ch. 18.2 - The assembly shown weighs 12 lb and consists of 4...Ch. 18.2 - Prob. 18.76PCh. 18.2 - Prob. 18.79PCh. 18.2 - Prob. 18.80PCh. 18.2 - Prob. 18.81PCh. 18.2 - Prob. 18.82PCh. 18.2 - The uniform, thin 5-lb disk spins at a constant...Ch. 18.2 - The essential structure of a certain type of...Ch. 18.2 - A model of a type of crusher is shown. A disk of...Ch. 18.2 - Prob. 18.86PCh. 18.2 - Prob. 18.87PCh. 18.2 - The 2-lb gear A is constrained to roll on the...Ch. 18.2 - Prob. 18.89PCh. 18.2 - Prob. 18.90PCh. 18.2 - 18.90 and 18.91The slender rod AB is attached by a...Ch. 18.2 - The essential structure of a certain type of...Ch. 18.2 - The 10-oz disk shown spins at the rate 1 = 750...Ch. 18.2 - Prob. 18.94PCh. 18.2 - Prob. 18.95PCh. 18.2 - Two disks each have a mass of 5 kg and a radius of...Ch. 18.2 - Prob. 18.97PCh. 18.2 - Prob. 18.98PCh. 18.2 - A thin disk of mass m = 4 kg rotates with an...Ch. 18.2 - Prob. 18.101PCh. 18.2 - Prob. 18.102PCh. 18.2 - A 2.5-kg homogeneous disk of radius 80 mm rotates...Ch. 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. 18.3 - A uniform thin disk with a 6-in. diameter is...Ch. 18.3 - A uniform thin disk with a 6-in. diameter is...Ch. 18.3 - Prob. 18.109PCh. 18.3 - The top shown is supported at the fixed point O...Ch. 18.3 - Prob. 18.111PCh. 18.3 - Prob. 18.112PCh. 18.3 - Prob. 18.113PCh. 18.3 - A homogeneous cone with a height of h = 12 in. and...Ch. 18.3 - Prob. 18.115PCh. 18.3 - Prob. 18.116PCh. 18.3 - Prob. 18.117PCh. 18.3 - The propeller of an air boat rotates at 1800 rpm....Ch. 18.3 - Prob. 18.119PCh. 18.3 - Prob. 18.120PCh. 18.3 - Prob. 18.121PCh. 18.3 - Prob. 18.122PCh. 18.3 - Prob. 18.123PCh. 18.3 - A coin is tossed into the air. It is observed to...Ch. 18.3 - Prob. 18.125PCh. 18.3 - Prob. 18.126PCh. 18.3 - Prob. 18.127PCh. 18.3 - Prob. 18.128PCh. 18.3 - Prob. 18.129PCh. 18.3 - Prob. 18.130PCh. 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 - A homogeneous disk with a radius of 9 in. is...Ch. 18.3 - The top shown is supported at the fixed point O....Ch. 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 - Consider a rigid body of arbitrary shape that is...Ch. 18.3 - Prob. 18.144PCh. 18.3 - Prob. 18.145PCh. 18 - Three 25-lb rotor disks are attached to a shaft...Ch. 18 - Prob. 18.148RPCh. 18 - Prob. 18.149RPCh. 18 - A uniform rod of mass m and length 5a is bent into...Ch. 18 - Prob. 18.151RPCh. 18 - Prob. 18.152RPCh. 18 - Prob. 18.153RPCh. 18 - Prob. 18.154RPCh. 18 - Prob. 18.155RPCh. 18 - The space capsule has no angular velocity when the...Ch. 18 - A homogeneous rectangular plate of mass m and...Ch. 18 - The essential features of the gyrocompass are...
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
- 125 mm B The blade of an oscillating fan and the rotor of its motor shown have a total weight of 1 kg and a combined radius of gyration (for all axes) of 100 mm. They are supported by bearings at A and B, 125 mm apart, and rotate at the rate o = 2000 rpm. Determine; a) the dynamic reactions at A and B when the motor casing has an angular velocity m2 = (0.5 j+1.5 k) rad/s. b) the static reactions at A and B when the fan has stopped. Note: Assume that the center of mass of the entire system is between the middle of the bearings of A and B, that is 62.5 mm away from bearing A.arrow_forward4. The link EF of mass 2 kg is welded at point A to a link ABC of mass 2 kg, which rotates about a pivot B. A spring of constant k =300 N/m and of un-stretched length 150 mm is attached to the link ABC as shown. Knowing that in the position shown the assembly has an angular velocity of 10 rad/s clockwise, (a) Determine the angular velocity when the assembly has rotated 90° clockwise, (b) Find the corresponding angular acceleration of part (a), and (c) Find the corresponding reaction force at point B. (For (b) and (c), set up all the required equations with a Free-Body-Diagram 150 mm and a Kinetic Diagram) 150 mm, 150 mm, E 150 mm 360 mmarrow_forwardA rope drum of diameter 850 mm and mass 1000 kg is used in a machine lifting procedure. The drum reaches a top rotational speed of 475 rev/min from rest in a time of 25 s. Determine: (i) the maximum linear speed of the rope;(ii) the angular acceleration of the rope drum;(iii) the moment of inertia of the rope drum, given that its radius of gyration is 250 mm;(iv) the accelerating torque applied to the rope drum.arrow_forward
- A solid cube of side c= 120 mm is attached as shown to a cord AB of length 240 mm. The cube spins about its diagonal BC and precesses about the vertical axis AD Knowing that 0= 25° and β= 40°, determine (a) the rate of spin of the cube, (b) its rate of precession. (See hint of Prob. 18.115.)arrow_forwardThe angular velocity vector of a football that has just been kicked is horizontal, and its axis of symmetry OC is oriented as shown. Knowing that the magnitude of the angular velocity is 200 rpm and that the ratio of the axis and transverse moments of inertia is determine (a) the orientation of the axis of precession OA (a) the rates of precession and spin.arrow_forwardThe moment of inertia of a pair of locomotive driving wheels with the axle is 150 kg.m². The distance between the wheel centres is 1.2 m and the diameter of the wheel treads is 2m. Due to defective ballasting one wheel falls by 5 mm and raises again in a total time of 0.2 seconds while the locomotive travels on a level track at 100 kmph. Assuming that the displacement of the wheel takes place with simple harmonic motion about mid point of total fall. Determine the gyroscopic couple produced. Hint: Consider this motion as pitching motion in ship. Draw free body diagram of each link for the following figure E 250 N 200 mm B NT 75° AD-150mm BC-AD-500mm DC-300mm [F450mmarrow_forward
- A 6-lb homogeneous disk of radius 3 in. spins as shown at the constant rate w1 = 60 rad/s. The disk is supported by the fork-ended rod AB , which is welded to the vertical shaft CBD The system is at rest when a couple M0 is applied as shown to the shaft for 3 s and then removed. Knowing that the maximum angular velocity reached by the shaft is 18 rad/s, determine (a) the couple M0) the dynamic reactions at C and D after the couple has been removed.arrow_forward1. Two uniform thin disks are bolted together with rope wrapped around each of them with weights attached to the end of each rope. Knowing the system is released from rest, determine the rpm (revolutions per minute) of the conjoined disks and which direction they will spin after 10s. A = 8 in, rB = 6 in. C 15 lb O B o O O D 18 lbarrow_forwardThe 100-kg projectile shown has a radius of gyration of 100 mm about its axis of symmetry Gx and a radius of gyration of 250 mm about the transverse axis Gy. Its angular velocity v can be resolved into two components; one component, directed along Gx, measures the rate of spin of the projectile, while the other component, directed along GD, measures its rate of precession. Knowing that θ= 6° and that the angular momentum of the projectile about its mass center G is determine (a) the rate of spin, (b) ) the rate of precession.arrow_forward
- A thin, homogeneous triangular plate of weight 10 lb is welded to a light, vertical axle supported by bearings at A and B. Knowing that the plate rotates at the constant rate w = 8 rad/s, determine the dynamic reactions at A and B.arrow_forwardThe blade of an oscillating fan and the rotor of its motor shown have a total weight of 1 kg and a combined radius of gyration (for all axes) of 100 mm. They are supported by bearings at A and B, 125 mm apart, and rotate at the rate ω1 = 2000 rpm. Determine; a) the dynamic reactions at A and B when the motor casing has an angular velocity ω2 = (0.5 j+1.5 k) rad/s. b) the static reactions at A and B when the fan has stopped. Note: Assume that the center of mass of the entire system is between the middle of the bearings of A and B, that is 62.5 mm away from bearing A.arrow_forwardThe circular platform A is fitted with a rim of 200-mm inner radius and can rotate freely about the vertical shaft. It is known that the platform-rim unit has a mass of 5 kg and a radius of gyration of 175 mm with respect to the shaft. At a time when the platform is rotating with an angular velocity of 50 rpm, a 3-kg disk B of radius 80 mm is placed on the platform with no velocity. Knowing that disk B then slides until it comes to rest relative to the platform against the rim, determine the final angular velocity of the platform.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 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
Understanding Thermal Radiation; Author: The Efficient Engineer;https://www.youtube.com/watch?v=FDmYCI_xYlA;License: Standard youtube license