<P> We may assume, without loss of generality, that in a Cartesian coordinate system the perpendicular distance between the axes lies along the x-axis and that the center of mass lies at the origin . The moment of inertia relative to the z - axis is </P> <Dl> <Dd> I c m = ∫ (x 2 + y 2) d m . (\ displaystyle I_ (\ mathrm (cm)) = \ int (x ^ (2) + y ^ (2)) \, dm .) </Dd> </Dl> <Dd> I c m = ∫ (x 2 + y 2) d m . (\ displaystyle I_ (\ mathrm (cm)) = \ int (x ^ (2) + y ^ (2)) \, dm .) </Dd> <P> The moment of inertia relative to the axis z ′, which is a perpendicular distance d along the x-axis from the centre of mass, is </P>

When do you use the parallel axis theorem