2. A piece of thin uniform wire of mass 7m and length 5b is bent into an equilateral triangle. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices.

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?