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- RadiusA yo-yo is made of two uniform disks, each of mass M and radius R, which are glued to a smaller central axle of negligible mass and radius 0.5R (see figure). A string is wrapped tightly around the axle. The yo-yo is then released from rest and allowed to drop downwards, as the string unwinds without slipping from the central axle. a) Find the moment of inertia, I, of the yo-yo with respect to an axis through the common centers of the disks, in terms of the mass and radius. b) Calculate the magnitude of the linear velocity V, in meters per second, of the yo-yo after it has fallen a distance 0.46 m.The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ?h=0.421 m and mass 5.46 kg, and two thin crossed rods of mass 7.37 kg each. A farmer would like to replace his wheels with uniform disks ?d=0.0588 mthick, made out of a material with a density of 5990 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be?
- Show complete solution and the fbdLet E be the solid below z = 50 - x² y² and above the square [-5,5] × [-5,5] Given the solid has a constant density of 3, find the moment of inertia of E about the z-axis. 125 XFind the moment of inertia about centroidal X-axis and centroidal Y-axis of the given geometry Figure:
- A uniform thin rod of mass M = 3.37 kg pivots about an axis through its center and perpendicular to its length. Two small bodies, each of mass m = 0.219 kg, are attached to the ends of the rod. What must the length L of the rod be so that the moment of inertia of the three-body system with respect to the described axis is I = 0.975 kg-m? ? L = m M. m m LFind the moment of inertia about the x-axis of the semicircular area. C 20 mm --x' 15 mmFour (4) masses 150 grams each are connected by 4 cords forming a rectangle. Thelength of the cords are 60 cm and 40 cm. determine the moment of inertial of the massesabout the axis of rotation AB (a) if AB is located at the center of longer cords, (b) AB islocated at the center of shorter cords. Ignore the mass of rod.
- Estimate the moment of inertia of a bicycle wheel 67 cm in diameter. The rim and tire have a combined mass of 1.0 kg.The moment of inertia of a uniform circular disc about its diameter is 100gcm2. What is its moment of inertia about its tangent?The baton consists of a metal ball of mass .45 kg and diameter .15m at each end of a slim rod. The rod is .70m long. Find the moment of inertia and radius gyration of the baton about an axis perpendicular to the rod and intersecting it at (a) the middle and (b) .6m from one end of the rod. Assume the rod has negligible mass.