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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?
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- 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?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?Computation. Consider a stick 1.00 m long and its moments of inertia about axes perpendicular to the stick's length and passing through two different points on the stick: first, a point at its center and second, a point 24 cm from one end. Calculate the ratio I2/11, the ratio of the second moment of inertia to the first. 55 Record your numerical answer below, assuming three significant figures. Remember to include a "_" as necessary. == O Search