PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 16, Problem 28P
To determine
The magnitude of the velocity and acceleration of point
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b) Find the angular velocity and angular acceleration of disc B shown below, which is spinningatthe constant rate of ω2 = 90/πrpm.
The disc is attached to collar A, which is rotating at the angular speed of ω1 = 5/π rpm, with the angular speed increasing at 0.5/π rpm/sec. Rod AB which connects the disc to the collar ispinned to the collar at A. The rod makes an angle of θ = 300 with the vertical, which is increasing at a constant rate of20/π0/sec.Express theAngularvelocityAcceleration of the disc in terms of a reference frame attached to thecollar.
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has a constant angular velocity w = 3 rad/s about its shaft as shown. Simultaneously the entire assembly revolves
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disc for an instant shown in the figure. Also find angular velocity and angular acceleration of the disc.
20 cm
15.
30 cm
30 cm
30 cm N
20 cm
The disk rotates with the angular motion shown. Determine the angular velocity and
angular acceleration of the slotted link AC at this instant. The peg at B is fixed to the disk.
w = 6 rad/s
a = 10 rad/s²
A
30°
0.3 m
0.75 m
30°
B
Chapter 16 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
Ch. 16 - When the gear rotates 20 revolutions, it achieves...Ch. 16 - The flywheel rotates with an angular velocity of ...Ch. 16 - The flywheel rotates with an angular velocity of (...Ch. 16 - The bucket is hoisted by the rope that wraps...Ch. 16 - A wheel has an angular acceleration of = (0.5 )...Ch. 16 - For a short period of time, the motor turns gear A...Ch. 16 - Prob. 1PCh. 16 - The angular acceleration of the disk is defined by...Ch. 16 - The disk is originally rotating at 0 = 12 rad/s....Ch. 16 - Prob. 4P
Ch. 16 - The disk is driven by a motor such that the...Ch. 16 - A wheel has an initial clockwise angular velocity...Ch. 16 - The disk starts from rest and is given an angular...Ch. 16 - The disk starts from rest and is given an angular...Ch. 16 - The disk starts at o = 1 rad/s when = 0, and is...Ch. 16 - A motor gives gear A an angular acceleration of A...Ch. 16 - A motor gives gear A an angular acceleration of A...Ch. 16 - Prob. 19PCh. 16 - Prob. 20PCh. 16 - If the motor turns gear A with an angular...Ch. 16 - Prob. 23PCh. 16 - Prob. 26PCh. 16 - Prob. 27PCh. 16 - Prob. 28PCh. 16 - At the instant shown, gear A is rotating with a...Ch. 16 - Determine the distance the load W is lifted in t =...Ch. 16 - Prob. 34PCh. 16 - Prob. 35PCh. 16 - Prob. 36PCh. 16 - The rod assembly is supported by ball-and-socket...Ch. 16 - Determine the velocity and acceleration of the...Ch. 16 - Prob. 54PCh. 16 - If roller A moves to the right with a constant...Ch. 16 - Prob. 8FPCh. 16 - Determine the angular velocity of the spool. The...Ch. 16 - If crank OA rotates with an angular velocity of =...Ch. 16 - Prob. 11FPCh. 16 - Prob. 12FPCh. 16 - At the instant shown the boomerang has an angular...Ch. 16 - The link AB has an angular velocity of 3 rad/s....Ch. 16 - The slider block C moves at 8 m/s down the...Ch. 16 - Determine the angular velocity of links AB and BC...Ch. 16 - The pinion gear A rolls on the fixed gear rack B...Ch. 16 - The pinion gear rolls on the gear racks. If B is...Ch. 16 - Prob. 71PCh. 16 - Prob. 72PCh. 16 - Prob. 77PCh. 16 - Prob. 13FPCh. 16 - Prob. 14FPCh. 16 - If the center O of the wheel is moving with a...Ch. 16 - If cable AB is unwound with a speed of 3 m/s, and...Ch. 16 - Prob. 17FPCh. 16 - Determine the angular velocity of links BC and CD...Ch. 16 - Prob. 81PCh. 16 - The conveyor belt is moving to the right at v = 8...Ch. 16 - The conveyor belt is moving to the right at v = 12...Ch. 16 - Prob. 92PCh. 16 - Prob. 93PCh. 16 - As the car travels forward at 80 ft/s on a wet...Ch. 16 - The crankshaft AB rotates at AB = 50 rad/s about...Ch. 16 - At the instant shown, end A of the rod has the...Ch. 16 - Prob. 20FPCh. 16 - The gear rolls on the fixed rack B. At the instant...Ch. 16 - At the instant shown, cable AB has a velocity of 3...Ch. 16 - At the instant shown, the wheel rotates with an...Ch. 16 - At the instant shown, wheel A rotates with an...Ch. 16 - At a given instant the bottom A of the ladder has...Ch. 16 - At a given instant the top B of the ladder has an...Ch. 16 - At a given instant the roller A on the bar has the...Ch. 16 - The rod is confined to move along the path due to...Ch. 16 - At a given instant the slider block A is moving to...Ch. 16 - Determine the angular acceleration of link CD if...Ch. 16 - The disk rolls without slipping such that it has...Ch. 16 - The slider block moves with a velocity of vB = 5...Ch. 16 - The slider block moves with a velocity of vB = 5...Ch. 16 - Water leaves the impeller of the centrifugal pump...Ch. 16 - Prob. 134PCh. 16 - Prob. 135PCh. 16 - Rod AB rotates counterclockwise with a constant...Ch. 16 - Prob. 137PCh. 16 - At the instant shown rod AB has an angular...Ch. 16 - Peg B on the gear slides freely along the slot in...Ch. 16 - Prob. 144PCh. 16 - A ride in an amusement park consists of a rotating...Ch. 16 - Prob. 146PCh. 16 - If the slider block C is fixed to the disk that...Ch. 16 - Prob. 1RPCh. 16 - Starting at (A)0 = 3 nad/s, when = 0, s = 0,...Ch. 16 - Prob. 3RPCh. 16 - Prob. 4RPCh. 16 - Prob. 5RPCh. 16 - At the instant shown, link AB has an angular...Ch. 16 - Prob. 7RPCh. 16 - At the given instant member AB has the angular...
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- At a given instant the wheel of radius r = 0.8 m is rotating with angular velocity w = 3 rad/s and angular acceleration a = 2 rad/s. The angles shown are OA = 66° and OB = 45°. The distance daB = 0.81 m Determine the angular velocity of link AB and the acceleration of block B at this instant. OB B daB r ω, αarrow_forwardThe center O of the disk has the velocity and acceleration shown in the figure. If the disk rolls without slipping on the horizontal surface, determine the velocity of A and the acceleration of B for the instant represented. Assume a = 5.0 m/s², v = 3.0 m/s, b = 0.2 m, 0 = 45% a Answers: A VA= (i ag= (i b B b V i+i ¡+ i L--x j) m/s j) m/s²arrow_forwardThe disk rotates about the shaft S, while the shaft is turning about the z axis at a rate of ωz = 5.5 rad/s , which is increasing at α = 2.5 rad/s2 . No slipping occurs. Determine the x, y, and z components of the velocity of point B on the disk at the instant shown using scalar notation. Determine the x, y, and z components of the acceleration of point B on the disk at the instant shown using scalar notation.arrow_forward
- End A of the 3.6-ft link has a velocity of 3.7 ft sec in the direction shown. At the same instant, end B has a velocity whose magnitude is 4.4 ft/sec as indicated. Find the angular velocity w of the link in two ways. The angular velocity of the link is positive if counterclockwise, negative if clockwise. A VA = 3.7 ft/sec 40° Answer: w= 3.6' B B VB = 4.4 ft/sec rad/secarrow_forwardThe two rotor blades of 770-mm radius rotate about the shaft at O mounted in the sliding block. The acceleration of the block is aO = 5.2 m/s2. If θ˙θ˙ = 0 and θ¨θ¨ = 4.2 rad/s2 when θ = 0, find the magnitude of the acceleration of the tip A of the blade for this instant..arrow_forwardThe link AB is hinged at A on the gear and at B on the collar moving along the horizontal bar. Note that the rack (toothed rod) is fixed on the ground. At the instant shown, the gear has an angular velocity of 6 rad/sec and an angular acceleration of 12 rad/sec² in the counter-clockwise direction. Determine the magnitude of the angular acceleration of the link AB. Present your answer in rad/sec² using 3 significant figures. @ = 6 rad/s a = 12 rad/s² 3 in. 2 in. 60° B 8 in. Aarrow_forward
- The relative acceleration of point A with respect to point B of the disk in Figure 1 is given as as/B = 3.347i + 1.283j. If the disk rolls without slipping, determine the angular velocity and angular acceleration of the disk at the instant. If, in other case, the disk rolls with slipping and the vM = 2 m/s to the left and vo = 2 m/s to the right, do you think that the process of determining its angular velocity and angular acceleration becomes easier or harder? A 45° B L--x M 0.2 m'0.2 m Figure 1arrow_forwardA motor gives gear A an angular acceleration of αA=0.006θ^2 rad/s2, where θ is in radians. If this gear is initially turning at ωA=10 rad/s, Determine the angular displacement of gear A at the instant at which gear A reaches angular velocity of 35 rad/s. Determine the angular velocity and acceleration of gear B at this instant. Find the magnitude of acceleration of point P on the pitch circle of gear B at this instant.arrow_forwardThe small collar A is sliding on the bent bar with speed u = 1.5 m/s relative to the bar as shown. The distances are L= 2.60 m and d = 0.77 m. Simultaneously, the bar is rotating with angular velocity w = 2.33 rad/s about the fixed pivot B. Take the x-y axes to be fixed to the bar and determine the Coriolis acceleration acor of the slider for the instant represented. Interpret your result. В Answer: acor = ( i i+ i j) m/s? B.arrow_forward
- At the instant represented, the disk rolls without slipping with an angular velocity of 2 rad/s clockwise which changes at the rate of 2 rad/s2 counterclockwise. Determine the corresponding angular acceleration of links AB and BD. At the instant considered, point A is directly above point O.Please provide a clear and complete solution (with figures).The answer must be:α_BD = 0.413 rad/s2 CCWα_AB = 0.146 rad/s2 CWarrow_forwardThe rotor of an electric motor rotates at the constant rate ω1 = 1800 rpm. Determine the angular acceleration of the rotor as the motor is rotated about the y axis with a constant angular velocity ω2 of 6 rpm counterclockwise when viewed from the positive y axis.arrow_forward= The disk has a circular slot with the radius equal to 200 mm, and it is in a pure rotation about O with a constant angular velocity, 15 rad/sec in the direction shown. When the slider A passes the center of the disk O, it has ė = 14 rad/sec and 6 = 0 relative to the disk, in terms of measured in the clockwise direction as shown in the figure. Calculate the magnitude of the acceleration of the slider A when it passes O, by using the body-fixed coordinate system given in the figure. Present your answer in m/sec² using 3 significant figures. A 0. 200 mm-arrow_forward
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