PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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A disk oscillates about its axis of rotation given by its angular acceleration of ∝ = -kθ. First determine the value of k for which, ω = 19.3 rad/s when θ = 0 and θ = 6 radians when ω = 0. Then determine the angular velocity when θ = 3 radians.
The 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.
A disk oscillates about its axis of rotation given by its angular acceleration of ∝ = -kθ. First determine the value of k for which, w= 16 rad/s when θ = 0 and θ = 6 radians when w= 0. Then determine the angular velocity when θ = 1.2 radians.
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- The 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_forwardA 3 in radius disk spins at the constant ω1 - 5 radian/s and a constant rate ω2= 4 radians/s. If the angle is 45 degrees, find the absolute acceleration at point P.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 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_forwardThe two rotor blades of 770-mm radius rotate about the shaft at O mounted in the sliding block. The acceleration of the block ao = 5.2 m/s². If Ò = 0 and 0 = 4.2 rad/s² when 0 = 0, find the magnitude of the acceleration of the tip A of the blade for this instant. 770 A mm aoarrow_forwardPoint A of the circular disk is at the angular position 0 = 0 at time t = 0. The disk has angular velocity wo = 0.26 rad/s at t = 0 and subsequently experiences an angular acceleration a = 3.0t where t is in seconds, and a is in radians per second squared. Determine the velocity and acceleration of point A in terms of fixed i and j unit vectors at time t = 1.1 s. Assume r = 185 mm. Answers: VA = 으아 aд = (i (i L. -X i + i i + iarrow_forward
- The relative acceleration of point A with respect to point B of the disk in Figure 1 is given asaA/B = 3.347i + 1.283j. If the disk rolls without slipping, determine the angular velocity andangular acceleration of the disk at the instant. If, in other case, the disk rolls with slipping andthe vM = 2 m/s to the left and vO = 2 m/s to the right, do you think that the process ofdetermining its angular velocity and angular acceleration becomes easier or harder?arrow_forwardThe slender bar is moving in general plane motion with the indicated linear and angular properties. Locate the instantaneous center of zero velocity (distances x to the right of G and y above G) and determine the magnitudes of the velocities of points A and B. A Answers: X = y = VA = 0.30 m VB= i i 4.0 rad/s G 0.30 m -20° 2.0 m/s B 3 m m/s m/sarrow_forwardThe 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° Barrow_forward
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