VECTOR MECH. FOR EGR: STATS & DYNAM (LL
12th Edition
ISBN: 9781260663778
Author: BEER
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 18.3, Problem 18.108P
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.
Fig. P18.107 and P18.108
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents 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 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.
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,
For an axisymmetric body under no force, prove (a) that the rate of retrograde precession can never be less than twice the rate of spin of the body about its axis of symmetry, (b) that in Fig. 18.24 the axis of symmetry of the body can never lie within the space cone.
Reference to Figure 18.24:
Chapter 18 Solutions
VECTOR MECH. FOR EGR: STATS & DYNAM (LL
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
- 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_forwardA uniform disc having a mass of 10 kg and a radius of gyration of 175 mm is mounted on one end of a horizontal arm of 500-mm length. The other end of the arm can rotate freely in a universal bearing. The disc is given a clockwise spin of 350 rpm as seen from the disc end of the arm. Determine the angular velocity of precession.arrow_forward
- A flywheel of mass 10 kg and radius of gyration 200 mm is spinning about its axis, which is horizontaland is suspended at a point distant 150 mm from the plane of rotation of the flywheel. Determine theangular velocity of precession of the flywheel. The spin speed of flywheel is 900 r.p.m.arrow_forwardA space station consists of two sections A and B of equal masses that are rigidly connected. Each section is dynamically equivalent to a homogeneous cylinder with a length of 15 m and a radius of 3 m. Knowing that the station is precessing about the fixed direction GD at the constant rate of 2 rev/h, determine the rate of spin of the station about its axis of symmetry CC’arrow_forwardA 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.arrow_forward
- The 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_forwardAn aeroplane makes a complete half circle of 50 metres radius, towards left, when flying at 200 km per hour. The rotary engine and the propeller of the plane has a mass of 400 kg with a radius of gyration of 300 mm. The engine runs at 2400 r.p.m. clockwise, when viewed from the rear. Find the gyroscopic couple on the aircraft and state its effect on it. What will be the effect, if the aeroplane turns to its right instead of to the left ?arrow_forward3. A simple connecting rod mechanism has a rod 250mm long and a crank radius of 75 mm. The connecting rod has a mass of 1.5kg, its centre of gravity is 75mm from the large end and it has a radius of gyration about the centre of gravity of 100mm. When the crank angle is 30° and the crankshaft speed is 3000rpm clockwise: (a) (i) Show by kinematic analysis that the angular acceleration of the connecting rod is 13,940 rad/s² (clockwise) (ii) Show also that the acceleration of the centre of gravity (C) in the X and Y direction is respectively, fcx = 6759m/s² (to the right) and fcy = 2590.8m/s² (downwards). Hence, find the magnitude and direction of the forces acting on the frame of the engine due to the inertia of the connecting rod as follows: (b) The force exerted by the cylinder wall on the piston at B (c) The force on the main bearing at O (d) The torque input or output at the crank B Figure 3. Connecting rod mechanism C A 30° Oarrow_forward
- Referring to Prob. 18.143, (a) prove that the Poinsot ellipsoid is tangent to the invariable plane, (b) show that the motion of the rigid body must be such that the Poinsot ellipsoid appears to roll on the invariable plane. [Hint: In part a, show that the normal to the Poinsot ellipsoid at the tip of w is parallel to HO. It is recalled that the direction of the normal to a surface of equation F (x,y,z), ) = constant at a point is the same as that of grad F at point P.Jarrow_forwardplease solve this questions in 40 mins i will give you positive feedbackarrow_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
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
Understanding Thermal Radiation; Author: The Efficient Engineer;https://www.youtube.com/watch?v=FDmYCI_xYlA;License: Standard youtube license