Calculate the moment of inertia of each of the following uniform objects about the axes indicated. a) A thin 3.10-kg rod of length 80.0 cm, about an axis perpendicular to it and passing through its center. b) A thin 3.10-kg rod of length 80.0 cm, about an axis perpendicular to it and passing through one end. c) A thin 3.10-kg rod of length 80.0 cm, about an axis parallel to the rod and passing through it. d) A 4.00-kg sphere 31.0 cm in diameter, about an axis through its center, if the sphere is solid. e) A 4.00-kg sphere 31.0 cm in diameter, about an axis through its center, if the sphere is a thin-walled hollow shell. f) An 6.00-kg cylinder, of length 21.0 cm and diameter 22.0 cm , about the central axis of the cylinder, if the cylinder is solid. g) An 6.00-kg cylinder, of length 21.0 cm and diameter 22.0 cm, about the central axis of the cylinder, if the cylinder is thin-walled and hollow.

Solution: Calculate the moment of inertia of each of the following uniform objects about the axes indicated.a) A thin 3.10-kg rod of length 80.0 cm, about an axis perpendicular to it and passing through its cen

Calculate the moment of inertia of each of the following uniform objects about the axes indicated.

a) A thin 3.10-kg rod of length 80.0 cm, about an axis perpendicular to it and passing through its center.

b) A thin 3.10-kg rod of length 80.0 cm, about an axis perpendicular to it and passing through one end.

c) A thin 3.10-kg rod of length 80.0 cm, about an axis parallel to the rod and passing through it.

d) A 4.00-kg sphere 31.0 cm in diameter, about an axis through its center, if the sphere is solid.

e) A 4.00-kg sphere 31.0 cm in diameter, about an axis through its center, if the sphere is a thin-walled hollow shell.

f) An 6.00-kg cylinder, of length 21.0 cm and diameter 22.0 cm , about the central axis of the cylinder, if the cylinder is solid.

g) An 6.00-kg cylinder, of length 21.0 cm and diameter 22.0 cm, about the central axis of the cylinder, if the cylinder is thin-walled and hollow.

a) A thin 3.10-kg rod of length 80.0 cm, about an axis perpendicular to it and passing through its center.

b) A thin 3.10-kg rod of length 80.0 cm, about an axis perpendicular to it and passing through one end.

c) A thin 3.10-kg rod of length 80.0 cm, about an axis parallel to the rod and passing through it.

d) A 4.00-kg sphere 31.0 cm in diameter, about an axis through its center, if the sphere is solid.

e) A 4.00-kg sphere 31.0 cm in diameter, about an axis through its center, if the sphere is a thin-walled hollow shell.

f) An 6.00-kg cylinder, of length 21.0 cm and diameter 22.0 cm , about the central axis of the cylinder, if the cylinder is solid.

g) An 6.00-kg cylinder, of length 21.0 cm and diameter 22.0 cm, about the central axis of the cylinder, if the cylinder is thin-walled and hollow.