Problem 2The semicircular disk of mass m and radius r is released from rest at 0 = 0,and rotates freely in the vertical plane about its fixed bearing at O.Note: I = mr² and F = 413 π1. Draw the dynamic free body diagram of the disk in a general positionafter the release. Include inertia forces.2. Write down the dynamic equilibrium equations and determine theangular acceleration of the disk a as a function of 0.3. Calculate the angular velocity of the disk w as a function of

Analysis:1. Dynamic Free Body Diagram:To draw the free body diagram, consider the disk at an…

Answered: Problem 2 The semicircular disk of mass…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Dynamics
Consider the slender rod of length L and mass m that rotates around the point O' in the vertical plane. Its center of mass is at point G. The rod is at rest and forms an angle of 0 with the horizon- tal when a winch is activated to raise the rod. At this instant, the tension (of magnitude T) in the horizontal rope joining the winch to point A causes an angular acceleration, a = Ö. Consider the weight of the rod and assume that the reaction force at point O' is of the form R = Rxî1 + Ryî2. Solve for the tension in the rope and the reaction force components, (T, Rx, Ry). (Hint: Apply E1L for the translation of the center of mass and E2L for the fixed-axis rotation. Make sure you consider the inertia of the slender rod about the rotation point O' not G). Motion A o G L O' B Winch
A drum can rotate about a fixed-point O. The A block is attached to a cord wrapping around the drum. The mass of the drum is md = 100kg and the radius is r = 0.5 m. The radius of gyration of the drum about point O is ko=0.3 m. The mass of the block is mb= 20kg. The block is released from rest. The acceleration due to gravity is g=9.81 m/s2. (3) Calculate the angular acceleration of the drum α= ________ (rad/s2) (two decimal places)
A drum can rotate about a fixed-point O. The A block is attached to a cord wrapping around the drum. The mass of the drum is md = 100kg and the radius is r = 0.5 m. The radius of gyration of the drum about point O is ko=0.3 m. The mass of the block is mb= 20kg. The block is released from rest. The acceleration due to gravity is g=9.81 m/s2. (1) Calculate the mass moment of inertia of the drum about the point O, IO_______(kgm2) (two decimal places)
A drum can rotate about a fixed-point O. The A block is attached to a cord wrapping around the drum. The mass of the drum is md = 100kg and the radius is r = 0.5 m. The radius of gyration of the drum about point O is ko=0.3 m. The mass of the block is mb= 20kg. The block is released from rest. The acceleration due to gravity is g=9.81 m/s2. (1) Calculate the mass moment of inertia of the drum about the point O, IO_______(kgm2) (two decimal places)
A drum can rotate about a fixed-point O. The A block is attached to a cord wrapping around the drum. The mass of the drum is md = 100kg and the radius is r = 0.5 m. The radius of gyration of the drum about point O is ko=0.3 m. The mass of the block is mb= 20kg. The block is released from rest. The acceleration due to gravity is g=9.81 m/s2. (3) Calculate the angular acceleration of the drum α= ________ (rad/s2) (two decimal places)
The spool has mass, m, and a radius of gyration kG. An inextensible cord is attached to the wall at A. The cord is wound around the radius R and the outer radius 2R. The coefficient of friction between the spool and the ground is mu. What it the critical force, Fcrit (force required to cause motion) applied at point B? If force= 2Fcrit what is the linear acceleration of the center of mass? If force= 2Fcrit what is the tension in cord AC?
A momentum wheel for dynamics class demonstration is show. It is basically a bicycle wheel modified with rim band-weighting, handles, and a pulley for cord startup. The heavy rim band causes the radius of gyration of the 3.1 kg wheel tobe 275 mm. If a steady 32 N pull F is applied to the cord, determien the angular acceleration of the wheel. Neglect bearing friciton.
A drum can rotate about a fixed-point O. The A block is attached to a cord wrapping around the drum. The mass of the drum is md = 100kg and the radius is r = 0.5 m. The radius of gyration of the drum about point O is ko=0.3 m. The mass of the block is mb= 20kg. The block is released from rest. The acceleration due to gravity g=9.81 m/s2 . (2) ) If the mass moment of inertia of the drum about point O is IO, and the angular acceleration of the drum is α, select the correct moment equation of the whole drum-block system about the point O._____________ A. mbgr=rmb(rα) B. 0 C. mbgr=Ioα +rmb(rα) D. mbgr=Ioα
The 2-mass system shown below depicts a disk which rotates about its center and has rotational moment of inertia Jo and radius r. The angular displacement of the disk is given by 0. The spring with constant k₂ is attached to the disk at a distance from the center. The mass m has linear displacement & and is subject to an external force u. When the system is at equilibrium, the spring forces due to k₁ and k₂ are zero. Neglect gravity and aerodynamic drag in this problem. You may assume the small angle approximation which implies (i) that the springs and dampers remain in their horizontal / vertical configurations and (ii) that the linear displacement d of a point on the edge of the disk can be approximated by d≈re. Ө K2 www m 4 Cz 777777 Jo Make the following assumptions when analyzing the forces and torques: тв 2 0>0, 0>0, x> > 0, >0 Derive the differential equations of motion for this dynamic system. Start by sketching LARGE and carefully drawn free-body-diagrams for the disk and the…
In a four bar mechanism the link AB rotates with angular velocity of 20rad/s and angular acceleration of 100 rad/s both in clockwise direction when it make an angle of 45° with link AD which is fixed .The length of various linkages are AB=CD=400 mm,BC=500mm and AD=750mm .Neglect the gravitational effect and friction.The mass of link is 5kg/m. Find the torque on output link E (2) (4) A (1) (1)

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