Explanation Given information: The relative angular velocity ω 2 of the cylinder with respect to rod CD is 8 r a d / s . The angular velocity ω 1 of rod CD is 6 r a d / s . The velocity in a three dimensional motion of a particle relative to rotating frame is defined as: v P = v P 1 + v P / F In the above equation, v P - Absolute velocity of particle P. v P 1 - Velocity of point P 1 of moving frame F Coinciding with P. v P / F - Velocity of P relative to moving frame F. The acceleration in a three dimensional motion of a particle relative to rotating frame is defined as: a P = a P 1 + a P / F + a C In the above equation, a P - Absolute acceleration of particle P. a P 1 - Acceleration of point P 1 of moving frame F coinciding with P a P / F - Acceleration of P relative to moving frame F a C -The Coriolis acceleration The Coriolis acceleration is defined as a C = 2 Ω × v P / F Calculation: The relative position vector r B of point B r B = 6 i − 14 j Assume Dxyz as the rotating frame of reference. The constant angular velocity Ω of reference frame Ω = ω 1 i The relative angular velocity ω 2 of cylinder with respect to the frame ω 2 = − ω 2 j Assume B 1 as the point on frame that coincides with point B. The velocity v B 1 of point B 1 v B 1 = Ω × r B = 6 i × [ 6 i − 14 j ] = − 84 k The relative velocity v B / F of point B with respect to frame v B / F = ω 2 × r B = − 8 j × [ 6 i − 14 j ] = 48 k The velocity v B of point B v B = v B 1 + v B / F = − 84 k + 48 k = − (

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,

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Chapter 15.7, Problem 15.243P

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Velocity and acceleration of point B

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Chapter 15.7, Problem 15.242P

Chapter 15.7, Problem 15.244P

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Chapter 15 Solutions

Vector Mechanics For Engineers

Ch. 15.1 - A rectangular plate swings from arms of equal...Ch. 15.1 - Knowing that wheel A rotates with a constant...Ch. 15.1 - The brake drum is attached to a larger flywheel...Ch. 15.1 - The motion of an oscillation flvdee1 is defined by...Ch. 15.1 - The motion of an oscillation flywheel is defined...Ch. 15.1 - Prob. 15.4P Ch. 15.1 - A small grinding wheel is attached to the shaft of...Ch. 15.1 - A connecting rod is supported by a knife-edge at...Ch. 15.1 - When studying whiplash resulting from rear-end...Ch. 15.1 - The angular acceleration of an oscillating disk is...

Ch. 15.1 - The angular acceleration of a shaft is defined by...Ch. 15.1 - Prob. 15.10P Ch. 15.1 - Prob. 15.11P Ch. 15.1 - The rectangular block shown rotates about the...Ch. 15.1 - The rectangular block shown rotates about the...Ch. 15.1 - A circular plate of 120-mm radius is supported by...Ch. 15.1 - In Prob. 15.14, determine the velocity and...Ch. 15.1 - The earth makes one complete revolution around the...Ch. 15.1 - The earth makes one complete revolution on its...Ch. 15.1 - The sprocket wheel and chain shown initially at...Ch. 15.1 - Prob. 15.19P Ch. 15.1 - The belt sander shown is initially at rest. If the...Ch. 15.1 - The rated speed of drum B of the belt sander shown...Ch. 15.1 - The two pulleys shown may be operated with the V...Ch. 15.1 - A cyclist uses a statior.ary trainer during the...Ch. 15.1 - gear reduction system consists of three gears A,...Ch. 15.1 - A belt is pulled to the right between cylinders A...Ch. 15.1 - Ring C has an inside radius of 55 mm and an...Ch. 15.1 - At the instant shown, the angular velocity of...Ch. 15.1 - A plastic film moves over two drums. During a 4-s...Ch. 15.1 - Cylinder A is moving downward with a velocity of 3...Ch. 15.1 - The system shown is held at rest by the...Ch. 15.1 - A load is to be raised 20 ft by the hoisting...Ch. 15.1 - A simple friction drive consists of two disks A...Ch. 15.1 - Two friction wheels A and B are both rotating...Ch. 15.1 - Two friction disks A and B are to be brought into...Ch. 15.1 - Two friction disks A and B are brought into...Ch. 15.1 - Steel tape is being wound onto a spool that...Ch. 15.1 - Prob. 15.37P Ch. 15.2 - The ball rolls without slipping on the fixed...Ch. 15.2 - Three uniform rods—ABC, DCE, and FGH—are connected...Ch. 15.2 - An automobile travel, to the right at a constant...Ch. 15.2 - Prob. 15.39P Ch. 15.2 - A painter is halfway up a 10-m ladder when the...Ch. 15.2 - Rod AB can slide freely along the floor and the...Ch. 15.2 - Rod AB can slide freely along the floor and the...Ch. 15.2 - Rod AB moves over a small wheel at C while end A...Ch. 15.2 - The disk shown moves in the xy plane. Knowing that...Ch. 15.2 - The disk shown moves in the xy p1ane. Knowing that...Ch. 15.2 - Prob. 15.46P Ch. 15.2 - Velocity sensors are placed on a satellite that is...Ch. 15.2 - In the planetary gear system shown, the radius of...Ch. 15.2 - In the planetary gear system shown, the radius of...Ch. 15.2 - The outer gear C rotates with an angular velocity...Ch. 15.2 - In the simplified sketch of a ball bearing shown,...Ch. 15.2 - A simplified gear system for a mechanical watch is...Ch. 15.2 - Arm ACB rotates about point C with an angular...Ch. 15.2 - Arm ACB rotates about point C with an angular...Ch. 15.2 - Knowing that at the instant shown the angular...Ch. 15.2 - Prob. 15.56P Ch. 15.2 - Knowing that the disk has a constant angular...Ch. 15.2 - The disk has a constant angular velocity of 20...Ch. 15.2 - The test rig is shown was developed to perform...Ch. 15.2 - In the concentric shown, a disk of 2-in. radius...Ch. 15.2 - In the engine system shown, l=160mmandb=60mm ....Ch. 15.2 - In the engine system shown, l=160 mm and b=60 mm....Ch. 15.2 - Knowing that the angular velocity of rod DE is a...Ch. 15.2 - In the position shown bar AB has an anu1ar...Ch. 15.2 - Linkage DBEF is part of a windshield wiper...Ch. 15.2 - Roberts linkage is named after Richard Roberts...Ch. 15.2 - Roberts linkage is named after Richard Roberts...Ch. 15.2 - For the oil pump rig shown, link AB causes the...Ch. 15.2 - For the oil pump rig shown, link AB causes the...Ch. 15.2 - Both 6-in.-radius wheels roll without slipping on...Ch. 15.2 - The 80-mm-radius wheel shown rolls to the left...Ch. 15.2 - For the gearing shown, derive an expression for...Ch. 15.3 - The disk rolls without sliding on the fixed...Ch. 15.3 - Bar BDE is pinned to two links, AB and CD. At the...Ch. 15.3 - A juggling club is thrown vertically into the air....Ch. 15.3 - At the instant shown during deceleration, the...Ch. 15.3 - A helicopter moves horizontally in the x direction...Ch. 15.3 - A 60-mm-radius drum is rigidly attached to a...Ch. 15.3 - Prob. 15.77P Ch. 15.3 - In order to uncoil electrical wire from a...Ch. 15.3 - In order to uncoil electrical wire from a spool...Ch. 15.3 - The arm ABC rotates with an angular velocity of 4...Ch. 15.3 - The double gear rolls on the stationary left rack...Ch. 15.3 - An overhead door is guided by wheels at A and B...Ch. 15.3 - Rod ABD is guided by wheels at A and B that roll...Ch. 15.3 - Knowing that at the instant shown the angular...Ch. 15.3 - Prob. 15.85P Ch. 15.3 - A motor at O drives the windshield wiper mechanism...Ch. 15.3 - A motor at O drives the windshield wiper mechanism...Ch. 15.3 - Rod AB can slide freely along the floor and the...Ch. 15.3 - Small wheels have been attached to the ends of bar...Ch. 15.3 - Two slots have been cut in plate FG and the plate...Ch. 15.3 - The disk is released from rest and rolls down the...Ch. 15.3 - The pin at B is attached to member ABD and can...Ch. 15.3 - Two identical rods ABF and DBE are Connected by a...Ch. 15.3 - Ann ABD is connected by pins to a collar at B and...Ch. 15.3 - Two rods ABD and DE are Connected to three collars...Ch. 15.3 - Two 500-mm rods are pin-connected at D as shown....Ch. 15.3 - At the instant shown, the velocity of collar A is...Ch. 15.3 - Prob. 15.98P Ch. 15.3 - Describe the space centrode and the body centrode...Ch. 15.3 - Describe the space centrode and the body centrode...Ch. 15.3 - Using the method of Sec. 15.3, solve Prob. 15.60.Ch. 15.3 - Using the method of Sec. 15.3, solve Prob. 15.64.Ch. 15.3 - Using the method of Sec. 15.3, solve Prob. 15.65.Ch. 15.3 - Using the method of Sec. 15.3, solve Prob. 15.38.Ch. 15.4 - A rear-wheel-drive car starts from rest and...Ch. 15.4 - A 5-m steel beam is lowered by means of two cables...Ch. 15.4 - For a 5-m steel beam AE, the acceleration of point...Ch. 15.4 - A 900-mm rod rests on a horizontal table A force P...Ch. 15.4 - In Prob. 15.107, determine the point of the rod...Ch. 15.4 - Knowing that point A is moving to the right at a...Ch. 15.4 - Knowing that at the instant shown crank BC has a...Ch. 15.4 - automobile travels to the left at a constant speed...Ch. 15.4 - The 18-in.-radius flywheel is rigidly attached to...Ch. 15.4 - A 3-in.-radius drum is rigidly attached to a...Ch. 15.4 - A 3-in.-radius drum is rigidly attached to a...Ch. 15.4 - A heavy crate is being moved a sbo1 distance using...Ch. 15.4 - A wheel rolls without slipping on a fixed...Ch. 15.4 - The 100-nun-radius drum rolls without slipping on...Ch. 15.4 - In the planetary gear system shown, the radius of...Ch. 15.4 - The 200-mm-radius disk rolls without sliding on...Ch. 15.4 - Knowing that crank AB rotates about point A with a...Ch. 15.4 - Knowing that crank AB rotates about point A with a...Ch. 15.4 - In the two-cylinder air compressor shown, the...Ch. 15.4 - Prob. 15.123P Ch. 15.4 - Arm AB has a constant angular velocity of 16 rad/s...Ch. 15.4 - Arm AB has a constant angular velocity of 16 rad/s...Ch. 15.4 - A straight rack rests on a gear of radius r=3 in....Ch. 15.4 - The elliptical exercise machine has fixed axes of...Ch. 15.4 - The elliptical exercise machine has fixed axes of...Ch. 15.4 - Prob. 15.129P Ch. 15.4 - Knowing that at the instant shown bar DE has an...Ch. 15.4 - Knowing that at the instant shown bar AB has a...Ch. 15.4 - Prob. 15.132P Ch. 15.4 - Prob. 15.133P Ch. 15.4 - Prob. 15.134P Ch. 15.4 - Roberts linkage is named after Richard Roberts...Ch. 15.4 - For the oil pump rig shown, link AB causes the...Ch. 15.4 - Denoting by rA the position vector of a point A of...Ch. 15.4 - The drive disk of the Scotch crosshead mechanism...Ch. 15.4 - The wheels attached to the ends of rod AB roll...Ch. 15.4 - The wheels attached to the ends of rod AB roll...Ch. 15.4 - A disk of radius r rolls to the right with a...Ch. 15.4 - Ladder AB moves over a smooth corner at C while...Ch. 15.4 - Prob. 15.143P Ch. 15.4 - Crank4B rotates with a constant c1ockise angular...Ch. 15.4 - Crank 4B rotates with a constant clockwise angular...Ch. 15.4 - Solve the engine system from Sample Prob. 15.15...Ch. 15.4 - The position of rod AB is controlled by a disk of...Ch. 15.4 - A wheel of radius r rolls without slipping along...Ch. 15.4 - In Prob. 15. 148, show that the path of P is a...Ch. 15.5 - A person walks radially inward on a platform that...Ch. 15.5 - Prob. 15.150P Ch. 15.5 - Prob. 15.151P Ch. 15.5 - Two rotating rods are connected by slider block P....Ch. 15.5 - Two rotating rods are connected by slider block P....Ch. 15.5 - Pin P is attached to the wheel shown and slides in...Ch. 15.5 - Knowing that at the instant shown the angular...Ch. 15.5 - Knowing that at the instant shown the anu1ar...Ch. 15.5 - The motion of pin P is guided by slots cut in...Ch. 15.5 - Four pins slide in four separate slots cut in a...Ch. 15.5 - Solve Prob. 15.158, assuming that the plate...Ch. 15.5 - The cage of a mine elevator moves downward at a...Ch. 15.5 - Prob. 15.161P Ch. 15.5 - A rocket sled is tested o a straight track that is...Ch. 15.5 - Prob. 15.163P Ch. 15.5 - Prob. 15.164P Ch. 15.5 - Prob. 15.165P Ch. 15.5 - In the automated welding setup shown, the position...Ch. 15.5 - In the automated welding setup shown, the position...Ch. 15.5 - A chain is looped around two gears of radius 40 mm...Ch. 15.5 - A chain is looped around two gears of radius 40 mm...Ch. 15.5 - Prob. 15.170P Ch. 15.5 - The human leg can be crudely approximated as two...Ch. 15.5 - The collar P slides outward at a constant relative...Ch. 15.5 - Pin P slides in a circular slot cut in the plate...Ch. 15.5 - Rod AD is bent in the shape of an are of a circle...Ch. 15.5 - Solve Prob. 15.l74 when =90 .Ch. 15.5 - Prob. 15.176P Ch. 15.5 - Prob. 15.177P Ch. 15.5 - In Prob. 15.177, determine the angular velocity...Ch. 15.5 - Prob. 15.179P Ch. 15.5 - Prob. 15.180P Ch. 15.5 - Rod AB passes through a collar that is welded to...Ch. 15.5 - Solve Prob. 15.181 assuming block A moves to the...Ch. 15.5 - In Prob. 15.157, determine the acceleration of pin...Ch. 15.6 - The bowling ball shown rolls without slipping on...Ch. 15.6 - The bowling ball shown rolls without slipping on...Ch. 15.6 - Prob. 15.186P Ch. 15.6 - At the instant considered, the radar antenna shown...Ch. 15.6 - Prob. 15.188P Ch. 15.6 - The disk of a portable sander rotates at the...Ch. 15.6 - Prob. 15.190P Ch. 15.6 - Prob. 15.191P Ch. 15.6 - In the system shown, disk A is free to rotate...Ch. 15.6 - Prob. 15.193P Ch. 15.6 - A radar system is used to track a new experimental...Ch. 15.6 - Prob. 15.195P Ch. 15.6 - A 3-in-radius disk spins at the constant rate 2=4...Ch. 15.6 - The cone shown rolls on the zx plane with its apex...Ch. 15.6 - At the instant shown, the robotic arm ABC is being...Ch. 15.6 - Prob. 15.199P Ch. 15.6 - In Prob. 15.199, determine (a) the common angular...Ch. 15.6 - Several rods are brazed together to form the...Ch. 15.6 - In Prob. 15.201, the speed of point B is known to...Ch. 15.6 - Rod AB of length 25 in. is connected by ball...Ch. 15.6 - Rod AB has a length of 13 in. and is connected by...Ch. 15.6 - Rod BC and BD are each 840 mm long and are...Ch. 15.6 - Rod AB is connected by ball-and-socket joints to...Ch. 15.6 - Rod AB of length 29 in. is connected by...Ch. 15.6 - Rod AB of length 300 mm is connected by ball...Ch. 15.6 - Rod AB of length 300 mm is connected by...Ch. 15.6 - Two shafts AC and EG, which lie in the vertical yz...Ch. 15.6 - Solve Prob. 15.210, assuming that the arm of the...Ch. 15.6 - Rod BC has a length of 42 in. and is connected by...Ch. 15.6 - Rod AB has a length of 275 mm and is connected by...Ch. 15.6 - For the mechanism of Prob.15.204, determine the...Ch. 15.6 - In Prob. 15.205, determine the acceleration of...Ch. 15.6 - In Prob. 15.206, determine the acceleration of...Ch. 15.6 - In Prob. 15.207, determine the acceleration of...Ch. 15.6 - In Prob. 15.208, determine the acceleration of...Ch. 15.6 - In Prob. 15.209, determine the acceleration of...Ch. 15.7 - A flight simulator is used to train pilots on how...Ch. 15.7 - A flight simulator is used to train pilots on how...Ch. 15.7 - Prob. 15.222P Ch. 15.7 - Prob. 15.223P Ch. 15.7 - Rod AB is welded to the 0.3-m-radius plate that...Ch. 15.7 - The bent rod shown rotates at the constant rate of...Ch. 15.7 - The bent pipe shown rotates at the constant rate...Ch. 15.7 - The circular plate shown rotates about its...Ch. 15.7 - Manufactured items are spray-painted as they pass...Ch. 15.7 - Solve Prob. 15.227, assuming that at the instant...Ch. 15.7 - Solve Prob. 15.225, assuming that at the instant...Ch. 15.7 - Using the method of Sec. 15.7A, solve Prob....Ch. 15.7 - Using the method of Sec. 15.7A, solve Prob....Ch. 15.7 - Using the method of Sec. 15.7A, solve Prob....Ch. 15.7 - The 400-mm bar AB is made to rotate at the...Ch. 15.7 - The 400-mm bar AB is made to rotate at the rate...Ch. 15.7 - The arm AB of length 16 ft is used to provide an...Ch. 15.7 - The remote manipulator system (RMS) shown is used...Ch. 15.7 - A disk with a radius of 120 mm rotates at the...Ch. 15.7 - The crane shown rotates at the constant rate...Ch. 15.7 - Prob. 15.240P Ch. 15.7 - Prob. 15.241P Ch. 15.7 - Prob. 15.242P Ch. 15.7 - Prob. 15.243P Ch. 15.7 - A square plate of side 2r is welded to a vertical...Ch. 15.7 - Two disks, each of 130-mm radius, are welded to...Ch. 15.7 - In Prob. 15.245, determine the velocity and...Ch. 15.7 - The position of the stylus tip A is controlled by...Ch. 15 - A wheel moves in the xy plane in such a way that...Ch. 15 - Two blocks and a pulley e connected by...Ch. 15 - A baseball pitching machine is designed to deliver...Ch. 15 - The flywheel OD on the elliptical machine analyzed...Ch. 15 - Prob. 15.252RP Ch. 15 - Knowing that at the instant shown rod AB has zero...Ch. 15 - Rod AB is attached to a collar at A and is fitted...Ch. 15 - flows through a curved pipe .AB that rotates with...Ch. 15 - A disk of 0.15-m radius rotates at the constant...Ch. 15 - Two rods AE and BD pass through holes drilled into...Ch. 15 - Rod BC of length 24 in. is connected by ball...Ch. 15 - In the positions shown, the thin rod moves at a...

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Velocity and acceleration of point B

Solution Summary: The author explains the velocity and acceleration of point B. The velocity in a three dimensional motion of particle relative to rotating frame is defined as:

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