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- A rigid bar with a mass M and length L is free to rotate about a frictionless hinge at a wall. The bar has a moment of inertia I = 1/3 ML2 about the hinge, and is released from rest when it is in a horizontal position as shown. What is the instantaneous angular acceleration at the moment when the bar has swung down so that it makes an angle of 30° to the vertical?The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ?h=0.421 m and mass 4.32 kg, and two thin crossed rods of mass 7.80 kg each. A farmer would like to replace his wheels with uniform disks ?d=0.0651 mthick, made out of a material with a density of 8290 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?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?
- Let 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 X2. Find the moment of inertia of the object shown for the axis passing through the point shown and perpendicular to the page. Each rod is uniform and has a mass M and a length L. TA rod of mass 3m and length L can pivot about an axis through its center and perpendicular to the length of the rod as shown below. The rod has 2 point masses attached to either end, each of mass m. What is the moment of inertia of the rod + masses system about the axis through the center? Needs Complete typed solution with 100 % accuracy.
- Two uniform, solid spheres (one has a mass M and a radius R and the other has a mass M and a radius 2R) are connected by a thin, uniform rod of length 3R and mass M as shown in the Figure below. Find the moment of inertia about the axis through the center of the rod. 5.91 MR2 15.1 MR2 10.3 MR2 21.3 MR2The wheels of a wagon can be approximated as the combination of a thin outer hoop of radius ?h=0.527 m and mass 5.65 kg, and two thin crossed rods of mass 7.80 kg each. Imagine replacing the wagon wheels with uniform disks that are ?d=5.88 cm thick, made out of a material with a density of 6910 kg/m3. 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?Homework 2: The beam with length L 90 cm is subjected to the loads as shown in below figure. Find the moment at the fixed left end (Point A). The 300N force is at the middle of the beam. 300 N 100 N/m 200 N A -L= 90 cm-
- 3. A thin uniform rod of mass M and length L is bent at its center so that the two segments are perpendicular to each other. Find its moment of inertia about an axis perpendicular to its plane and passing through the point where the two segments meet.A uniform steel rod of length 0.8 m and mass 1.5 kg has two point masses of 1.9 kg each at the two ends. Calculate the moment of inertia of the system about an axis perpendicular to the rod, and passing through its center.The wheels of a wagon can be approximated as the combination of a thin outer hoop of radius rh=0.262 m and mass 4.32 kg, and two thin crossed rods of mass 9.09 kg each. Imagine replacing the wagon wheels with uniform disks that are td=6.51 cm thick, made out of a material with a density of 7370 kg/m3. 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?