Chapter 13, Problem 77P

The dynamic system is initially at rest. The rod has a mass of m=0.5kg and a length of L=1m. The CG of the rod is located at G, and the rod is rotated about the point O, a distance, h=0.25m, away from point G.  When the rod from above is rotated at the vertical position (swing to 90 degrees counterclockwise), find:  a. Angular velocity  b. Reaction at O

please answer part one of the question

Solve the problem correctly

5. An 80 kg gymnast dismounts from a high bar. He starts the dismount at full extension, then tucks to complete a number of revolutions before landing. His moment of inertia when fully extended can be approximated as a rod of length 1.8 m and when in the tuck a rod of half that length. If his rotation rate at full extension is 1.0 rev/s and he enters the tuck when his center of mass is at 3.0 m height moving horizontally to the floor, how many revolutions can he execute if he comes out of the tuck at 1.8 m height? High bar 1.8 m 3 m ANS. Moment of inertia at full extension, I = 21.6 kg-m^2 Moment of inertia at the tuck I' = 5.4 kg-m^2 Angular velocity at the tuck = 4 rev/sec Time interval in the tuck = 0.5 sec i.e. In 0.5 s, he will be able to execute two revolutions at 4.0 rev/s.

The uniform semicircular bar of radius r = 120 mm and mass m = 3.2 kg rotates freely about a horizontal axis through the pivot O. The bar is initially held in position 1 against the action of the torsional spring and then suddenly released. Determine the spring stiffness kt which will give the bar a counterclockwise angular velocity w = 4.3 rad/s when it reaches position 2, at which the spring is undeformed. KT m 1 2 A' (0)

The slotted circular disk whose mass is 4.9 kg has a radius of gyration about O of 230 mm. The disk carries the four steel balls, each of mass 0.17 kg and located as shown, and rotates freely about a vertical axis through O with an angular speed of 164 rev/min. Each of the small balls is held in place by a latching device not shown. If the balls are released while the disk is rotating and come to rest relative to the disk at the outer ends of the slots, compute the new angular speed N of the disk. Also find the magnitude |ΔE| of the energy loss due to the impact of the balls with the ends of the slots. Neglect the diameter of the balls and discuss this approximation.

The slotted circular disk whose mass is 4.9 kg has a radius of gyration about O of 230 mm. The disk carries the four steel balls, each of mass 0.17 kg and located as shown, and rotates freely about a vertical axis through O with an angular speed of 164 rev/min. Each of the small balls is held in place by a latching device not shown. If the balls are released while the disk is rotating and come to rest relative to the disk at the outer ends of the slots, compute the new angular speed N of the disk. Also find the magnitude |AE| of the energy loss due to the impact of the balls with the ends of the slots. Neglect the diameter of the balls and discuss this approximation. 164 rev/min 145 mm 305 mm

part 2 please

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