Engineering Mechanics II Two homogeneous bar each of mass m

Engineering Mechanics II

Two homogeneous bar, each of mass m and length l, have been welded together in a T-shape. Find the mass moment of inertia about an axis passing through point O that is perpendicular to the plane of the bars. Use a reference table, not integration, to solve.

Solution

MOI of a bar rotating about its cg = mL² / 12

So, for each of the two rods, MOI about their own cg is mL² / 12

Now we use parallel axis theorem to get the MOI about O for each of the rods.

For the horizontal bar, distance from O to its cg = L/2. Hence,

MOI of horizontal bar about O = (mL² / 12) + m(L/2)² = mL² / 3

Similarly for the verical bar, distance from O to its cg = L. Hence,

MOI of vertical bar about O = (mL² / 12) + m(L)² = (13/12) mL²

Total MOI of assembly of rods about O = (mL² / 3) + (13/12) mL²

MOI_o = (17 / 12) mL²