Determine the mass moment of inertia Izz about the zaxis for

Determine the mass moment of inertia I_zz about the z-axis for the right-circular cylinder with a central longitudinal hole. Use the values m = 8.5 kg, r = 75 mm, and L = 700 mm.

Solution

Align the x-axis with the rod and locate the origin its centre of mass at the centre of the rod, then

Izz = Integral rho*x² dV.........where x is the longitudinal dimension, rho = density and V is volume.

Izz = Integral rho*x² *A dx.......from limits x = -L/2 to L/2...........Here A is the cross-section area.

Izz = rho*A (x³ /3).............from limits x = -L/2 to L/2

Izz = (rho*A/3) (L³ /8 + L³ / 8)

Izz = rho*A*L³ / 12

Izz = mL² / 12.......where m = rho*A*L is the mass of the rod.

Izz = 8.5*0.7² / 12

Izz = 0.347 kg-m2