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At the instant shown, the arm AB is rotating about the fixed bearing with an angular velocity ω1 = 2 rad/ s and angular acceleration
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Engineering Mechanics: Dynamics (14th Edition)
- At the instant shown, the tower crane rotates about the z axis with an angular velocity ω1=0.25rad/s, which is increasing at 0.6 rad/s2. The boom OA rotates downward with an angular velocityω2=0.4 rad/s, which is increasing at 0.8 rad/s2. Determine,the Velocity Accelerationof point A located at the end of the boom at this instant.arrow_forwardAt the instant shown, the paper is being unrolled with a speed, vp = 7.5m/s and an acceleration ap = 1 m/s2. If, at this instant, the outer radius of the roll is r= 0.75 m, determine the angular velocity ωs and acceleration αs of the rollarrow_forwardAt a given instant, rod AB has the angular motions shown in the previous figure. Determine the angular acceleration of rod CD at this instant if the relative velocity of C with respect to A is 18ft/s and ω CD=9 rad/s.arrow_forward
- For a short time the bucket of the backhoe traces the path of the cardioid r=25(1−cosθ)ft. The boom is rotating with an angular velocity of θ˙omega = 2.3 rad/s and an angular acceleration of θ¨alpha = 0.16 rad/s^2 at the instant shown 1)Determine the magnitude of the velocity of the bucket when θ = 120∘ 2)Determine the magnitude of the acceleration of the bucket when θ = 120∘arrow_forwardA train is moving horizontally to the right with the speed of VT=60 mi/h. Meanwhile, a car is traveling toward the train with the speed of VC=30 mi/h and a 30deg angle with respect to horizontal direction. Select the correct expression of the velocity vector of the train relative to the car ___________mi/h A. (60-30cos30°)-30sin30° B. (60-30cos30°) +30sin30° C. (60+30cos30°)-30sin30° D. (30cos30°-60) +30sin30°arrow_forwardConsider the portion of an excavator shown. At the instant under consideration, the hydraulic cylinder is extending at a rate of 5 in./sec, which is decreasing at the rate of 2 in./sec every second. Simultaneously, the cylinder is rotating about a horizontal axis through O at a constant rate of 13 deg/sec. Determine the velocity v and acceleration a of the clevis attachment at B. Determine the indicated terms used in the velocity and acceleration formulas. Answers: r = __ in. θ = ___ ° r˙ = __in./sec θ˙ = ____ rad/s r¨ = ___ in./sec2 θ¨ = ____rad/s2arrow_forward
- 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.arrow_forwardA disc rolls straight on a flat floor without slipping. The magnitude of the angular velocity ω= 3.0 rad/s, the angular acceleration α=2.0 rad/s2. The radius of the disc is r=1.0 m. Determine e) the magnitude of the acceleration of the point A, aA= ___________m/s2arrow_forwardThe brake drum is attached to a larger flywheel that is not shown. The motion of the brake drum is defined by the relation 0= 36t- 1.6t2 , where 0 is expressed in radians and t in seconds. Determine (a) the angular velocity at t= 2 s, (b) the number of revolutions executed by the brake drum before coming to rest.arrow_forward
- Q2. The peg Pis driven by the sotted link whose motion is defined by theta= 1.5t and r = 0.8theta2. Find Determine the radial and transverse components of velocity and acceleration of the peg P after 1 sec time.arrow_forwardCollars A and B are attached by a rod of length 30 cm, as shown below. The joint at A is a ball-and-socket and at B a pin joint. Collar A moves in the z direction, while the guide bar for collar B is on xy plane. At the instant shown, collar A is at a height of 24 cm and collar B is moving with a speed of 3 m/s towards the x axis. Find the (a) angular velocity of the rod, and (b) the sliding of collar B. Use the image attached to solve the questionarrow_forwardAt the instant shown, slider moves to the left along the horizontal surface with . The collar at is pin connected and rod slides freely through it. At the instant shown, the relative acceleration of point B with respect to point C is a_B/C = a_B - a_C = 3.10 i + 0.634 j ft/s^2. Determine the angular velocity and angular acceleration of rod at this instant.arrow_forward
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