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Two 2.6-Ib collars A and B can slide without friction on a frame, consisting of the horizontal rod OE and the vertical rod CD, which is free to rotate about CD. The two collars are connected by a cord running over a pulley that is attached to the frame at O, and a stop prevents collar B from moving. The frame is rotating at the rate
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Vector Mechanics For Engineers
- The device shown is a simplified model of an amusement-park ride in which passengers are rotated about the vertical axis of the central post at an angular speedQ while sitting in a pod which is capable of rotating the occupants 360° about the longitudinal axis of the connecting arm attached to the central collar. Determine the percent increase n in angular velocity between configurations (a) and (b), where the passenger pod has rotated 90° about the connecting arm. For the model, m = 1.7 kg, r = 65 mm, I = 255 mm, and L = 600 mm. The post and connecting arms rotate freely about the z-axis at an initial angular speed 2 = 135 rev/min and have a combined mass moment of inertia about the z-axis of 33(10-3) kg ·m²?. %3D (b) -L- Ω (a) Frame -Pod marrow_forward1. Two children A and B, each having a mass 30kg, sit at the edge of the merry-go-round which is rotating with angular velocity @ = 2 rad/s. Excluding the children, the merry-go-round has a mass 180 kg and a radius of gyration k₂ = 0.8m. Determine the angular velocity of the merry-go-round if A jumps off horizontally in the -n direction (away from the merry-go-gound) with a speed of 3 m/s, measured with respect to the merry-go-round. After A jumps off, B then jumps off horizontally in the +t direction with a speed of 3 m/s, measured with respect to the merry-go-round - what is the merry-go-round's angular velocity now? Neglect friction and the size of each child. 1m 1m B w = 2 rad/sarrow_forwardThe disk with radius r is rolling (without slipping) with angular velocity through the bottom of the circular path of radius R. If @= 2 rad/sec, R = 0.5 m, r = 0.2 m, and the mass of the disk is 3 kg, calculate the magnitude of the normal force exerted by the path on the disk at that instant. Present your answer in Newtons using 3 significant figures. ໙arrow_forward
- An elongated rod of mass 4-kg has a mass of 2-kg at point A to a block moving vertically, 4-kg at point B pinned to a massive disk. The disc rotates without rolling, It is assumed that the block also moves in a frictionless channel. Please pay. The mechanism is released when stationary at θ=60º. Find the angular velocity of the rod when θ=0º.arrow_forwardTwo uniform cylinders, each of mass m= 9.5 kg and radius r= 125 mm, are connected by a belt as shown. The system is released from rest when t = 0. B A Determine the velocity of the center of cylinder A at t = 4.4 s. The velocity of the center of cylinder A is 3 m/s ↓.arrow_forwardThe wheel W of radius R = 1.4 m rolls without slip on a horizontal surface.A bar AB of length L = 3.7 m is pin-connected to the center of the wheel and to a sliderA constrained to move along a vertical guide. Point C is the bar’s midpoint. Determinethe general relation expressing the acceleration of the slider A as a function of θ, L, R,the angular velocity of the wheel αW , and the angular acceleration of the wheel ωW .arrow_forward
- 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.arrow_forwardThe circular concrete culvert rolls with an angular velocity of w = 0.60 rad/s when the man is at the position shown. At this instant the center of gravity of the culvert and the man is located at point G, and the radius of gyration about G is kg = 3.7 ft (Figure 1) Figure 4 ft O 0.5 ft Part A Determine the angular acceleration of the culvert. The combined weight of the culvert and the man is 500 lb Assume that the culvert rolls without slipping, and the man does not move within the culvert. Express your answer to three significant figures and include the appropriate units. α = Submit μÀ Value Provide Feedback X Incorrect; Try Again Units Previous Answers Request Answer ? Units input for part A Next >arrow_forwardThe figure shows a schematic of a simple Watt governor mechanism with the spindle 0102 rotating at an angular velocity w about a vertical axis. The balls at P and S have equal mass. Assume that there is no friction anywhere and all other components are massless and rigid. The vertical distance between the horizontal plane of rotation of the balls and the pivot O₁ is denoted by h. The value of h = 400 mm at a certain w. If w is doubled, the value of h will be mm. (0) g = 9.8 m/s₂ h Spindle O Q Sleeve (QR) Cylindrical Joint R Sarrow_forward
- A particle M1, weighing 2.4 Ibs, is tied to a thread and describes a circular path in a horizontal plane. The thread, of negligible mass, passes through a hole in the center of the circle and descends vertically. Another particle M2 is attached, weighing 5.0 Ibs, as shown in the figure. If M1 describes a uniform circular motion, with angular velocity w 3.1 rad/s, determine the radius R of the circumference in inches.arrow_forwardA 1.8-kg collar A and a 0.7-kg collar B can slide without friction on a frame, consisting of the horizontal rod OE and the vertical rod CD, which is free to rotate about its vertical axis of symmetry. The two collars are connected by a cord running over a pulley that is attached to the frame at O. At the instant shown, the velocity vA of Collar A has a magnitude of 2.1 m/s and a stop prevents collar B from moving. The stop is suddenly removed and collar A moves toward E. As it reaches a distance of 0.12 m from, the magnitude of its velocity is observed to be 2.5 m/s. Determine at that instant the magnitude of the angular velocity of the frame and the moment of inertia of the frame and pulley system about CD.arrow_forwardThe circular concrete culvert rolls with an angular velocity of w = 0.58 rad/s when the man is at the position shown. At this instant the center of gravity of the culvert and the man is located at point G, and the radius of gyration about G is KG = 3.7 ft. (Figure 1) Figure W 4 ft 0.5 ft 1 of 1 Part A Determine the angular acceleration of the culvert. The combined weight of the culvert and the man is 500 lb. Assume that the culvert rolls without slipping, and the man does not move within the culvert. Express your answer to three significant figures and include the appropriate units. α= Submit μA Value Provide Feedback Request Answer Units = ? Next >arrow_forward
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