Vector Mechanics for Engineers: Statics and Dynamics
11th Edition
ISBN: 9780073398242
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 16.1, Problem 16.58P
To determine
Find the angular acceleration of the roll
To determine
Find the acceleration of the mass center of the roll
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The steel roll shown has a mass of 1200 kg,
a centroidal radius of gyration of 150 mm,
and is lifted by two cables looped around
its shaft. Knowing that for each cable
= 3100 N and TR = 3300 N
TA
TB
A
В
TA
determine (a) the angular acceleration of
the roll, (b) the acceleration of its mass
TA
TB
A
В
center.
100 mm
A 40-kg flywheel of radius R = 0.5 m is rigidly attached to a shaft
of radius r = 0.05 m that can roll along parallel rails. A cord is
attached as shown and pulled with a force P of magnitude 150 N.
Knowing the centroidal radius of gyration is k = 0.4 m, determine
(a) the angular acceleration of the flywheel, (b) the velocity of the
center of gravity after 5 s.
15°
P
A 6000-lb flywheel requires 1500 revolutions to coast to rest from an
angular velocity of 300 rpm. Knowing that the radius of gyration of the
flywheel is 36 in. and I = m-k^2, determine the magnitude of the couple M
due to kinetic friction in the bearings in Ib-ft.
Chapter 16 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Ch. 16.1 - Two pendulums, A and B, with the masses and...Ch. 16.1 - Two pendulums, A and B, with the masses and...Ch. 16.1 - Two solid cylinders, A and B, have the same mass m...Ch. 16.1 - Prob. 16.1FBPCh. 16.1 - Prob. 16.2FBPCh. 16.1 - Prob. 16.3FBPCh. 16.1 - The 400-lb crate shown is lowered by means of two...Ch. 16.1 - A 60-lb uniform thin panel is placed in a truck...Ch. 16.1 - A 60-lb uniform thin panel is placed in a truck...Ch. 16.1 - 16.3 Knowing that the coefficient of static...
Ch. 16.1 - Prob. 16.4PCh. 16.1 - A uniform rod BC of mass 4 kg is connected to a...Ch. 16.1 - A 2000-kg truck is being used to lift a 400-kg...Ch. 16.1 - The support bracket shown is used to transport a...Ch. 16.1 - Prob. 16.8PCh. 16.1 - A 20-kg cabinet is mounted on casters that allow...Ch. 16.1 - Solve Prob. 16.9, assuming that the casters are...Ch. 16.1 - 16.11 A completely filled barrel and its contents...Ch. 16.1 - Prob. 16.12PCh. 16.1 - The retractable shelf shown is supported by two...Ch. 16.1 - Bars AB and BE, each with a mass of 4 kg, are...Ch. 16.1 - At the instant shown, the tensions in the vertical...Ch. 16.1 - Three bars, each of mass 3 kg, are welded together...Ch. 16.1 - Members ACE and DCB are each 600 mm long and are...Ch. 16.1 - 16.18 A prototype rotating bicycle rack is...Ch. 16.1 - Prob. 16.19PCh. 16.1 - The coefficients of friction between the 30-lb...Ch. 16.1 - Prob. 16.21PCh. 16.1 - Prob. 16.22PCh. 16.1 - For a rigid body in translation, show that the...Ch. 16.1 - For a rigid body in centroidal rotation, show that...Ch. 16.1 - It takes 10 min for a 2.4-Mg flywheel to coast to...Ch. 16.1 - The rotor of an electric motor has an angular...Ch. 16.1 - Prob. 16.27PCh. 16.1 - Prob. 16.28PCh. 16.1 - The 100-mm-radius brake drum is attached to a...Ch. 16.1 - The 180-mm-radius disk is at rest when it is...Ch. 16.1 - Solve Prob. 16.30, assuming that the direction of...Ch. 16.1 - In order to determine the mass moment of inertia...Ch. 16.1 - The flywheel shown has a radius of 20 in., a...Ch. 16.1 - Each of the double pulleys shown has a mass moment...Ch. 16.1 - Prob. 16.35PCh. 16.1 - Prob. 16.36PCh. 16.1 - Gear A weighs 1 lb and has a radius of gyration of...Ch. 16.1 - The 25-lb double pulley shown is at rest and in...Ch. 16.1 - A belt of negligible mass passes between cylinders...Ch. 16.1 - Prob. 16.40PCh. 16.1 - Disk A has a mass of 6 kg and an initial angular...Ch. 16.1 - Prob. 16.42PCh. 16.1 - Disk A has a mass mA = 4 kg, a radius rA = 300 mm,...Ch. 16.1 - Disk B is at rest when it is brought into contact...Ch. 16.1 - Prob. 16.45PCh. 16.1 - Prob. 16.46PCh. 16.1 - For a rigid body in plane motion, show that the...Ch. 16.1 - Prob. 16.48PCh. 16.1 - Prob. 16.49PCh. 16.1 - Prob. 16.50PCh. 16.1 - Prob. 16.51PCh. 16.1 - A 250-lb satellite has a radius of gyration of 24...Ch. 16.1 - A rectangular plate of mass 5 kg is suspended from...Ch. 16.1 - Prob. 16.54PCh. 16.1 - A drum with a 200-mm radius is attached to a disk...Ch. 16.1 - A drum with a 200-mm radius is attached to a disk...Ch. 16.1 - The 12-lb uniform disk shown has a radius of r =...Ch. 16.1 - Prob. 16.58PCh. 16.1 - Prob. 16.59PCh. 16.1 - Prob. 16.60PCh. 16.1 - Prob. 16.61PCh. 16.1 - Two uniform cylinders, each of weight W = 14 lb...Ch. 16.1 - Prob. 16.63PCh. 16.1 - Prob. 16.64PCh. 16.1 - A uniform slender bar AB with a mass m is...Ch. 16.1 - Prob. 16.66PCh. 16.1 - 16.66 through 16.68A thin plate of the shape...Ch. 16.1 - 16.66 through 16.68A thin plate of the shape...Ch. 16.1 - A sphere of radius r and mass m is projected along...Ch. 16.1 - Solve Prob. 16.69, assuming that the sphere is...Ch. 16.1 - A bowler projects an 8-in.-diameter ball weighing...Ch. 16.1 - Prob. 16.72PCh. 16.1 - A uniform sphere of radius r and mass m is placed...Ch. 16.1 - A sphere of radius r and mass m has a linear...Ch. 16.2 - A cord is attached to a spool when a force P is...Ch. 16.2 - Prob. 16.5CQCh. 16.2 - Prob. 16.6CQCh. 16.2 - Prob. 16.7CQCh. 16.2 - Prob. 16.5FBPCh. 16.2 - Two identical 4-lb slender rods AB and BC are...Ch. 16.2 - Prob. 16.7FBPCh. 16.2 - Prob. 16.8FBPCh. 16.2 - Show that the couple I of Fig. 16.15 can be...Ch. 16.2 - Prob. 16.76PCh. 16.2 - 16.77 In Prob. 16.76, determine (a) the distance r...Ch. 16.2 - A uniform slender rod of length L = 36 in. and...Ch. 16.2 - In Prob. 16.78, determine (a) the distance h for...Ch. 16.2 - An athlete performs a leg extension on a machine...Ch. 16.2 - Prob. 16.81PCh. 16.2 - Prob. 16.82PCh. 16.2 - Prob. 16.83PCh. 16.2 - A uniform rod of length L and mass m is supported...Ch. 16.2 - 16.84 and 16.85 A uniform rod of length L and mass...Ch. 16.2 - An adapted launcher uses a torsional spring about...Ch. 16.2 - Prob. 16.87PCh. 16.2 - Prob. 16.88PCh. 16.2 - The object ABC consists of two slender rods welded...Ch. 16.2 - A 3.5-kg slender rod AB and a 2-kg slender rod BC...Ch. 16.2 - A 9-kg uniform disk is attached to the 5-kg...Ch. 16.2 - Derive the equation MC=IC for the rolling disk of...Ch. 16.2 - Prob. 16.93PCh. 16.2 - Prob. 16.94PCh. 16.2 - Prob. 16.95PCh. 16.2 - Prob. 16.96PCh. 16.2 - A 40-kg flywheel of radius R = 0.5 m is rigidly...Ch. 16.2 - Prob. 16.98PCh. 16.2 - Prob. 16.99PCh. 16.2 - Prob. 16.100PCh. 16.2 - 16.98 through 16.101 A drum of 60-mm radius is...Ch. 16.2 - Prob. 16.102PCh. 16.2 - 16.102 through 16.105 A drum of 4-in. radius is...Ch. 16.2 - Prob. 16.104PCh. 16.2 - Prob. 16.105PCh. 16.2 - 16.106 and 16.107A 12-in.-radius cylinder of...Ch. 16.2 - 16.106 and 16.107A 12-in.-radius cylinder of...Ch. 16.2 - Gear C has a mass of 5 kg and a centroidal radius...Ch. 16.2 - Two uniform disks A and B, each with a mass of 2...Ch. 16.2 - A single-axis personal transport device starts...Ch. 16.2 - A hemisphere of weight W and radius r is released...Ch. 16.2 - A hemisphere of weight W and radius r is released...Ch. 16.2 - The center of gravity G of a 1.5-kg unbalanced...Ch. 16.2 - A small clamp of mass mB is attached at B to a...Ch. 16.2 - Prob. 16.115PCh. 16.2 - A 4-lb bar is attached to a 10-lb uniform cylinder...Ch. 16.2 - The uniform rod AB with a mass m and a length of...Ch. 16.2 - Prob. 16.118PCh. 16.2 - Prob. 16.119PCh. 16.2 - Prob. 16.120PCh. 16.2 - End A of the 6-kg uniform rod AB rests on the...Ch. 16.2 - End A of the 6-kg uniform rod AB rests on the...Ch. 16.2 - End A of the 8-kg uniform rod AB is attached to a...Ch. 16.2 - The 4-kg uniform rod ABD is attached to the crank...Ch. 16.2 - The 3-lb uniform rod BD is connected to crank AB...Ch. 16.2 - The 3-lb uniform rod BD is connected to crank AB...Ch. 16.2 - The test rig shown was developed to perform...Ch. 16.2 - Solve Prob. 16.127 for = 90. 16.127The test rig...Ch. 16.2 - The 4-kg uniform slender bar BD is attached to bar...Ch. 16.2 - The motion of the uniform slender rod of length L...Ch. 16.2 - At the instant shown, the 20-ft-long, uniform...Ch. 16.2 - Prob. 16.132PCh. 16.2 - Prob. 16.133PCh. 16.2 - The hatchback of a car is positioned as shown to...Ch. 16.2 - The 6-kg rod BC connects a 10-kg disk centered at...Ch. 16.2 - Prob. 16.136PCh. 16.2 - In the engine system shown, l = 250 mm and b = 100...Ch. 16.2 - Solve Prob. 16.137 when = 90. 16.137In the engine...Ch. 16.2 - The 4-lb uniform slender rod AB, the 8-lb uniform...Ch. 16.2 - The 4-lb uniform slender rod AB, the 8-lb uniform...Ch. 16.2 - Two rotating rods in the vertical plane are...Ch. 16.2 - Two rotating rods in the vertical plane are...Ch. 16.2 - Two disks, each with a mass m and a radius r, are...Ch. 16.2 - A uniform slender bar AB of mass m is suspended as...Ch. 16.2 - A uniform rod AB, of mass 15 kg and length 1 m, is...Ch. 16.2 - The uniform slender 2-kg bar BD is attached to the...Ch. 16.2 - Prob. 16.147PCh. 16.2 - Prob. 16.148PCh. 16.2 - Prob. 16.149PCh. 16.2 - Prob. 16.150PCh. 16.2 - (a) Determine the magnitude and the location of...Ch. 16.2 - Prob. 16.152PCh. 16 - A cyclist is riding a bicycle at a speed of 20 mph...Ch. 16 - 16.154 The forklift truck shown weighs 2250 lb and...Ch. 16 - The total mass of the Baja car and driver,...Ch. 16 - Identical cylinders of mass m and radius r are...Ch. 16 - Prob. 16.157RPCh. 16 - The uniform rod AB of weight W is released from...Ch. 16 - Prob. 16.159RPCh. 16 - Prob. 16.160RPCh. 16 - A cylinder with a circular hole is rolling without...Ch. 16 - Prob. 16.162RPCh. 16 - Prob. 16.163RPCh. 16 - The Geneva mechanism shown is used to provide an...
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
- 4. Each of the gears A and B has a mass of 2.4 kg and a radius of gyration of 60 mm, while gear C has a mass of 12 kg and a radius of gyration of 150 mm. A couple M of constant magnitude 10 Nm is applied to gear C. Determine (a) the number of revolutions of gear C required for its angular velocity to increase from 100 to 450 rpm, (b) the corresponding tangential force acting on gear A. В S0 mm, S0 mm 200 mm. Marrow_forwardCan you explain the radius of gyration ? why is it 480mm for the rod & 120mm for the disk. How do we figure this out ? thank youarrow_forward16.97 through 16.100 A drum of 4-in. radius is attached to a disk of 8-in. radius. The disk and drum have a total weight of 10 lb and combined radius of gyration of 6 in. A cord is attached as shown and pulled with a force P of magnitude 5 lb. Knowing that the disk rolls without sliding, determine (a) the angular acceleration of the disk and the acceleration of G, (b) the minimum value of the coefficient of static friction compatible with this motion. Fig. P16.93 and P16.97arrow_forward
- The 8-inch radius brake drum is attached to a flywheel not shown. The total mass moment of inertia of the drum and the flywheel is 20 slug ft2, about an axis perpendicular to the wall through its center D, and the coefficient of kinetic friction between the drum and the brake shoe at B is 0.3. Knowing that the angular velocity of the flywheel is 330 rev/min, clockwise, when a force P of magnitude 115 lb is applied to pedal C, determine the number of revolutions the flywheel makes before coming to a stop... C 10 in. B 15 in.. 6 in. A 8 in. Darrow_forwardThe flywheel of a punching machine has a mass of 300 kg and a radius of gyration of 600 mm. Each punching operation requires 2500 J of work. (a ) Knowing that the speed of the flywheel is 300 rpm just before a punching, determine the speed immediately after the punching. (b) If a constant 25-N.m couple is applied to the shaft of the flywheel, determine the number of revolutions executed before the speed is again 300 rpm.arrow_forwardThe steel roll shown has a mass of 1200 kg, has a centroidal radius of gyration of 150 mm, and is lifted by two cables looped around its shaft. Knowing that at the instant shown the acceleration of the roll is 150 mm/s2 downward and that for each cable TA = 3000 N, determine (a) the corresponding tension TB, (b) the angular acceleration of the roll.arrow_forward
- The rotor of an electric motor has an angular velocity of 3600 rpm when the load and power are cut off. The 50-kg rotor then coasts to rest after 5000 revolutions. Knowing that the kinetic friction of the rotor produces a couple of magnitude 4 N - m, determine the centroidal radius of gyration of the rotor (I = mk ). (Answer: k = 188.1mm)arrow_forwardThe 10-in.-radius brake drum is attached to a larger flywheel which is not shown. The total mass moment of inertia of the flywheel and drum is 22 lb ⋅ ft ⋅ s 2 and the coefficient of kinetic friction between the drum and the brake shoe is 0.41. Knowing that the initial angular velocity is 255 rpm clockwise, determine the force which must be exerted by the hydraulic cylinder at point B if the system is to stop in 85 revolutions.arrow_forwardGear A weighs 1 lb and has a radius of gyration of 1.3 in.; gear B weighs 6 lb and has a radius of gyration of 3 in.; gear C weighs 9 lb and has a radius of gyration of 4.3 in. Knowing a couple M of constant magnitude of 40 lb-in. is applied to gear A, determine (a) the angular acceleration of gear C, (b) the tangential force that gear B exerts on gear C. M A 2 in. 2 in. borg J 4 in. B 6 in. с w ណarrow_forward
- 10 in. B 15 in. 6 in. A 8 in. D The 8-inch radius brake drum is attached to a flywheel not shown. The total mass moment of inertia of the drum and flywheel is 13 slug ft2, about an axis perpendicular to the wall through its center D, and the coefficient of kinetic friction between the drum and brake shoe at B is 0.40. Knowing that the angular velocity of the flywheel is 390 rev/min, clockwise, when a force P of magnitude 100 lb is applied to pedal C, determine the number of revolutions the flywheel makes before coming to a stop..arrow_forwardThe 8-in. radius brake drum is attached to a larger flywheel that is not shown. The total mass moment of inertia of the drum and the flywheel is 15 Ib.ft.s2 and the coefficient of kinetic friction between the drum and the brake shoe is 0.40. Knowing that the angular velocity of the flywheel is 450 rpm clockwise when a force P of magnitude 65 lbf. is applied to the pedal C, determine the number of the revolutions executed by the flywheel before it comes to rest. 6 in. 10 in. 8 in. 15 in.arrow_forward0.54 m -1.08 m- Fig. P16.61 Fig. P16.60 16.62 Two uniform cylinders, each of mass 7 kg and radius r= 125 mm. are connected by a belt as shown. If the system is released from rest. determine (a) the angular acceleration of each cylinder, (b) the tension in the portion of belt connecting the two cylinders, (c) the velocity of the center of the cylinder A after it has moved through I m. Fig. P16.62arrow_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
Dynamics - Lesson 1: Introduction and Constant Acceleration Equations; Author: Jeff Hanson;https://www.youtube.com/watch?v=7aMiZ3b0Ieg;License: Standard YouTube License, CC-BY