You want to find the moment of inertia of a complicated machine part about an axis through its center of mass. you suspend it from a wire along this axis. the wire has a torsion constant of 0.490 n⋅m/rad. you twist the part a small amount about this axis and let it go, timing 185 oscillations in 225 s.

The time of a torsional harmonic oscillator is computed by:2 pi sqrt (I / kappa), where:I is the moment of inertia; and kappa is the torsion constant (N m per radian); and I is the moment of inertia in kg m^2;

Since Nm = kg m^2 / s^2, the period is in seconds.

In the case at hand, the period is (225/185) seconds, so

(225/185) s = 2 pi sqrt (I / 0.490 N m) 1.2162 s / 2pi = sqrt (I / 0.490 N m) (0.1936 s) ^2 = I / 0.490 N m I = (0.1936) ^2 (0.490) kg m^2 = (0.0375) (0.490) kg m^2 = 0.0184 kg m^2