A solid circular disk has a mass of 1.2kg and a radius of .17m. Each of the thre

Question

A solid circular disk has a mass of 1.2kg and a radius of .17m. Each of the three identical thin rods has a mass of .15kg. The rods are attached perpendicularly to the plane of the disk at its outer edge to form a three-legged stool. Find the moment of inertia of the stool with respect to an axis that is perpendicular to the plane of the disk at its center. ( Hint: When considering the moment of inertia of each rod, note that all of the mass of each rod is located at the same perpendicular distance from the axis. )

_______________ kg*m^2

Explanation / Answer

The mass of the dislk is M = 1.2 kg The radius of the disk is R = 0.17 m The mass of the leg is m = 0.15 kg The momont of imertia of the solid disk of mass M and radius R is given by Idisk = 0.5MR2 The moment of inertia of thr rod about the center of the stool is Ileg = mR2 As the theree legs are at same distance R from the center of the disk, The momemt of inertia of the stool about the center of the stool is I = Idisk + 3*Ileg I = 0.5*1.2 kg*(0.17 m)2 + 3*0.15kg*(0.17 m)2 I = 0.030345 kgm2 The moment of inertia of thr rod about the center of the stool is Ileg = mR2 As the theree legs are at same distance R from the center of the disk, The momemt of inertia of the stool about the center of the stool is I = Idisk + 3*Ileg I = 0.5*1.2 kg*(0.17 m)2 + 3*0.15kg*(0.17 m)2 I = 0.030345 kgm2 I = 0.030345 kgm2

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