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At the instant θ = 60°, the construction lift is rotating about the z axis with an angular velocity of ω1 = 0.5 rad/s and an angular acceleration of
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Engineering Mechanics: Dynamics, Student Value Edition (14th Edition)
- 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=-0.196arrow_forwardWhen the mechanism is in the position shown, the angular speed of the wheel is 2 rad/s clockwise and its angular acceleration is 4 rad/s anti-clockwise, determine αAB Y αBC. Use relative method. The rack is stationary.arrow_forwardBlock E is fixed to a rope wrapped around pulley B, with pulley B fixed to wheel A. Wheel A rotates against wheel C without slipping. Block D is fixed to a rope wrapped around wheel C. Assume that the respective ropes do no not slip on the pulley and wheel.At the instant shown, wheel C has a clockwise angular speed of ω0 = 2.3 rad/s and has a clockwise angular acceleration of αC = 19.7t2 rad/s2, where t is in seconds. Determine the speed (in m/s) of Block E at the instant when t = 1.1 seconds. Take: rA = 0.88 m; rB = 0.2 m; rC = 0.6 m. Choose from the following options: a) 1.505 b) 1.192 c) 2.208 d) 3.889 e) 3.269arrow_forward
- Collars 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_forwardThe smooth bar AB shown rotates in the horizontal plane about point A at the constant rate of 77 rpm. At the instant shown, the 9.4 kg collar C is at r=AC=6.8 m, and it is sliding outward relative to the bar at a speed of 11 m/s. For this instant, the following is required (i) Draw the free body diagram of collar C (ii) Write down the radial and transverse components of the acceleration of the collar C (iii) Write down the equations of motion for collar C (iv) Determine the magnitude of the force(s) exerted by bar AB on the collararrow_forwardThe wheel is spinning about shaft ABAB with an angular velocity of ωs=10rad/sωs=10rad/s, which is increasing at a constant rate of ω˙2=6rad/s2ω˙2=6rad/s2, while the frame precesses about the zzz axis with an angular velocity of ωp=12rad/sωp=12rad/s, which is increasing at a constant rate of ω˙p=3rad/s2ω˙p=3rad/s2. Determine the velocity of point CC located on the rim of the wheel at this instant. Determine the acceleration of point CC located on the rim of the wheel at this instant.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/s^2 counterclockwise. Determine the corresponding angular acceleration of links AB and BD. At the instant considered, point A is directly above point O.arrow_forwardCorner point A of the uniform square plate, with a mass of 25 kg and a side length of = 0.21 m, is pinned freely to the collar, which has an acceleration of a = 4.9 (towards the right) along the fixed horizontal shaft. If the plate has an angular velocity of w = 1.6 rad/s (clockwise) when it swings past the vertical position shown (with G directly below A), what is the magnitude of the angular acceleration (in ) of the plate at this time instant? The xy-plane is vertical. Choose the correct answer. 24.7 23.5 19.8 28.5 21.0arrow_forwardThe pulley is pin-connected to block B at A. As cord CF unwinds from the inner hub with the motion shown, cord DE unwinds from the outer rim. Determine the angular acceleration of the pulley at the instant shown.arrow_forward
- Collars 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 24cm 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 collarB.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- As the hydraulic cylinder elongates, it raises pin B of the mechanism shown below. For the position shown, the velocity of pin B is 80 mm/s. For this instant, determine the angular velocities of bars AD and AEarrow_forward
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