Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 20.4, Problem 39P
To determine
The velocity of point
The acceleration of point
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If the wheel in each case rolls on the circular surface without slipping, determine the acceleration of point C on the wheel momentarily in contact with the circular surface. The wheel has an angular velocity ω = 3.6 rad/s and an angular acceleration α = 5.0 rad/s2. The distances R = 1.5 m and r = 0.6 m.
The disk with radius r = 0.09 m is rotating at a constant angular velocity of ω = 0.9 rad/s (counterclockwise) about the fixed pin support at O. For the instant shown, find the relative acceleration component (aB/A)n, where (aB/A)n = {(ax)i+(ay)j} m/s2.
Choose the correct answer:
a) ax=-0.292; ay=-0.0729
b) ax=0.786; ay=0.196
c) ax=0.292; ay=0.0729
d) ax=0.0182; ay=0.00349
e) ax=-0.786; ay=-0.196
At the instant θ=60∘, the construction lift is rotating about the z axis with an angular velocity of ω1 = 0.55 rad/s and an angular acceleration of ω˙1 = 0.21 rad/s2 while the telescopic boom AB rotates about the pin at A with an angular velocity of ω2 = 0.21 rad/s and angular acceleration of ω˙2 = 6.0×10−2 rad/s2 . Simultaneously, the boom is extending with a velocity of 1.5 ft / s, and it has an acceleration of 0.5 ft / s2, both measured relative to the frame.
Determine the velocity of point B located at the end of the boom at this instant. Enter the x, y, and z components of the velocity separated by comm
Determine the acceleration of point BB located at the end of the boom at this instant.
Chapter 20 Solutions
Engineering Mechanics: Dynamics (14th Edition)
Ch. 20.3 - Prob. 1PCh. 20.3 - Prob. 2PCh. 20.3 - Prob. 3PCh. 20.3 - Prob. 4PCh. 20.3 - Prob. 5PCh. 20.3 - Prob. 6PCh. 20.3 - Prob. 7PCh. 20.3 - The disk rotates about the shaft S, while the...Ch. 20.3 - The electric fan is mounted on a swivel support...Ch. 20.3 - Prob. 11P
Ch. 20.3 - Prob. 12PCh. 20.3 - The right circular cone rotates about the z axis...Ch. 20.3 - Prob. 14PCh. 20.3 - Prob. 15PCh. 20.3 - Prob. 16PCh. 20.3 - Prob. 17PCh. 20.3 - Prob. 18PCh. 20.3 - Prob. 20PCh. 20.3 - Prob. 21PCh. 20.3 - Prob. 22PCh. 20.3 - Prob. 23PCh. 20.3 - Prob. 24PCh. 20.3 - Prob. 25PCh. 20.3 - Rod AB is attached to collars at its ends by using...Ch. 20.3 - Rod AB is attached to collars at its ends by using...Ch. 20.3 - If the rod is attached with ball-and-socket joints...Ch. 20.3 - Prob. 29PCh. 20.3 - If collar A has a speed vA = 4 m/s, determine the...Ch. 20.3 - Prob. 31PCh. 20.3 - If the collar A in Prob. 20-31 has a deceleration...Ch. 20.3 - Prob. 33PCh. 20.3 - Rod CD is attached to the rotating arms using...Ch. 20.3 - Prob. 35PCh. 20.3 - Prob. 36PCh. 20.4 - So1ve Example 20.5 such that the x, y, z axes move...Ch. 20.4 - Prob. 38PCh. 20.4 - Prob. 39PCh. 20.4 - At the instant = 60, the construction lift is...Ch. 20.4 - Prob. 41PCh. 20.4 - Prob. 42PCh. 20.4 - Prob. 43PCh. 20.4 - Prob. 44PCh. 20.4 - Prob. 45PCh. 20.4 - Prob. 46PCh. 20.4 - Prob. 47PCh. 20.4 - At the given instant the rod is turning about the...Ch. 20.4 - Prob. 49PCh. 20.4 - Prob. 50PCh. 20.4 - Prob. 51PCh. 20.4 - Prob. 52PCh. 20.4 - Prob. 53PCh. 20.4 - At the instant shown, the arm AB is rotating about...
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- The shaft of the wheel unit rolls without slipping on the fixed horizontal surface. If the velocity and acceleration of point O are 3 ft/sec to the right and 4 ft/sec2 to the left, respectively, determine the accelerations of points A and D.arrow_forwardGear A is between a stationary gear rack F and the gear rack E, which imoving at VE = 6 ft/s to the right at the instant shown. It is also observed that the acceleration of gear A is 2 ft/s2 also to the right. At this same instant, determine the angular velocity and angular acceleration of disk B. Use RMA for velocity analysis.arrow_forwardb) 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.arrow_forward
- The system has a pin-connected rod AB, rod BC and disk C. At the instant shown, the disc, with center C, rolls without slipping with an angular acceleration of 6 rad/s counterclockwise. If the velocity of C at this instant is 13 m/s to the left,a. what's the total acceleration of C (m/s^2)b. what's the angular acceleration of rod BC (rad/s^2)c. what's the total acceleration at point B (m/s^2)arrow_forwardAt the instant θ = 45, the athlete is running with a constant speed of 2 m/s. Determine the angular velocity at which the camera must turn in order to follow the motionarrow_forwardThe motion of the wheel as it rolls up the fixed rack on its gear hub is controlled through the peripheral cable by the driving wheel D, which turns counter-clockwise at the constant rate ωo=4rad/s for a short interval of motion. By examining the geometry of a small rotation of line AOCB as it pivots momentarily about the contact point C, determine the angular velocity ω of the wheel and the velocity of point A and the center O. Also, find the acceleration of point C.arrow_forward
- If roller A moves to the right with a constant velocity of vA = 3 m/s, determine the angular velocity of the link and the velocity of roller B at the instant Ɵ = 30°.arrow_forward5/125 The disk rotates with angular speed -2 rad/s. The small ball A is moving along the radial slot with speed L= 100 mm/s relative to the disk. Determine the absolute velocity of the ball and state the angle B between this veloc- ity vector and the positive x-axis. 125 mmarrow_forwardBar AB rotates uniformly about the fixed pin A with a constant angular velocity ω. Determine the velocity and acceleration of block C, at the instant Ɵ=60°.arrow_forward
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