Parvinbhai A slender bar of length I and mass m is rigidly attached to the center of a thin circular disk of radius R and mass m. Thecomposite object undergoes a motion in which the bar rotates in the horizontal plane with constant angular velocity woabout the center of mass of the composite object and the disk rolls on the floor.FigurePart ARDerive the expression for wo. (Figure 1)Express your answer in terms of some or all of the variables l, m, R, and gravitation acceleration gΑΣΦ JAM vec?Wα =SubmitRequest AnswerProvide FeedbackNext >1 of 1

The system consists of a slender bar of length l and mass 2m rigidly attached to the center of a…

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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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A 1.6-kg tube AB can slide freely on rod DE which in turn can rotate freely in a horizontal plane. Initially the assembly is rotating with an angular velocity of magnitude w = 5 rad/s and the tube is held in position by a cord. The moment of inertia of the rod and bracket about the vertical axis of rotation is 0.30 kg.m2 and the centroidal moment of inertia of the tube about a vertical axis is 0.0025 kg.m2If the cord suddenly breaks, determine (a) the angular velocity of the assembly after the tube has moved to end E, (b) the energy lost during the plastic impact at E.
A massive sphere, with 10,0cm radius and moment of inertia I=4,00 x 10-3 kg-m² in relation to a straight line passing through the center of mass, rolls without sliding, descending a surface with an inclination of 30º in relation to the horizontal. In a certain initial position the total kinetic energy of the sphere is 17.5j . a Sketch the physical situation by identifying all the forces acting on the sphere in the initial position. (b) How much of this initial kinetic energy is due to rotation? (c)
A uniform, 0.0300 kg rod of length 0.400 m rotates in ahorizontal plane about a fixed axis through its center and perpendicularto the rod. Two small rings, each with mass 0.0200 kg, are mounted sothat they can slide without friction along the rod. They are initially heldby catches at positions 0.0500 m on each side of the center of the rod,and the system is rotating at 48.0 rev/min. With no other changes in thesystem, the catches are released, and the rings slide outward along therod and fly off at the ends. What is the angular speed (a) of the systemat the instant when the rings reach the ends of the rod; (b) of the rodafter the rings leave it?
3.32). As shown in Figure 3, a yo-yo toy is formed by wrapping a massless cord around adisk of radius R= 0.2 m and mass M=3 kg. The cord is vertical and its top end is fixed and the disk isinitially stationary. The cord remains vertical for the entire motion and does not slide on the disk.When the disk is released from rest, it falls down by a distance H=0.8 m, The moment of inertia ofthe disk around its center is I disk=1/2mdiskR^2a . Find the angular acceleration of the disk when it is lowered by a distance H.b . Find the angular velocity of the disk when it is lowered by a distance H.
A load of mass 230 kg is lifted by means of a rope which is wound several times round a drum and which then supports a balance mass of 140 kg. As the load rises, the balance mass falls. The drum has a diameter of 1.2 m and a radius of gyration of 530 mm and its mass is 70 kg. The frictional resistance to the movement of the load is 110 N. and that to the movement of the balance mass 90 N. The frictional torque on the drum shaft is 80 N-m. 2. Find the torque required on the drum, and also the power required, at the instant when the load has an upward velocity of 2.5 m/s and an upward acceleration of 1.2 m/s?. [Ans. 916.2 N-m ; 4.32 kW]
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.
A slender rod is 90.0 cm long and has mass 0.120 kg. A small 0.0200 kg sphere is welded to one end of the rod, and a small 0.0800 kg sphere is welded to the other end. The rod, pivoting about a stationary, frictionless axis at its center, is held horizontal and released from rest. 1) What is the linear speed of the 0.0800 kg sphere as its passes through its lowest point?
Two uniform, solid cylinders of radius R and total mass M are connectedalong their common axis by a short, light rod and rest on a horizontaltabletop. A frictionless ring at the rod’s center is attached toa spring of force constant k; the spring’s other end is fixed. The cylindersare pulled to the left a distance x, stretching the spring, then releasedfrom rest. Due to friction between the tabletop and the cylinders, the cylindersroll without slipping as they oscillate. Show that the motion of thecenter of mass of the cylinders is simple harmonic, and find its period.
A ball of mass M is suspended from a vertical rod by two cables. The system rotates around this rod axis at angular velocity w. Assuming that the tensile strength of the upper cable is 2 times the tension of the lower cable. Draw a free body diagram for this ball
A uniform solid disk of mass 2.0 kg and radius 0.30 m is initially at rest. It is then rotated by a constant torque about an axis through its center of mass until it reached an angular speed of 3.0 rad/s. What is the work done by the constant torque? The moment of inertia through the center of mass is (2/5)MR^2.
A turbine rotor is found to be out of balance to the extent of 1.5 kg at 0.45 m radius in the plane AA and 2kg at 0.6 m radius in the plane BB, the relative angular positions being given in the end view. It is desired to balance these masses by a mass in each of the planes XX and YY at radii of 0.525m and 0.45m respectively. Determine the magnitude and positions of these masses and show their positions in an end view. (Answer: X, 1.42kg, 209.27 degrees from A; y, 2.12KG, 329.1 degrees from A)
(Three-Dimensional Motion) A homogeneous 20-cm-diameter disk has a mass of 1 kg and is placed on apedestal so that the assembly precesses in a horizontal plane as shown. If theprecessional rate is 20i rpm, determine the magnitude and direction of the spinof the disk about its own axle.

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