what is the significance of mass moment of inertia
Moment of inertia The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body is a tensor that determines the torque needed for a desired angular acceleration about a rotational axis. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rotation. It is an extensive (additive) property: For a point mass the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). One of its definitions is the second moment of mass with respect to distance from an axis r,   I = ∫ Q  r 2  d m  {\displaystyle I=\int _{Q}r^{2}\mathrm {d} m} , integrating over the entire mass   Q  {\displaystyle Q} .
Energy–momentum relation The energy–momentum relation (1) is consistent with the familiar mass–energy relation in both its interpretations: E = mc2 relates total energy E to the (total) relativistic mass m (alternatively denoted mrel or mtot ), while E0 = m0c2 relates rest energy E0 to (invariant) rest mass which we denote m0. Unlike either of those equations, the energy–momentum equation (1) relates the total energy to the rest mass m0. All three equations hold true simultaneously.