The Torsional Oscillator --  Part 1

Value of ΔI for added masses

Mathematica can perform calculations with units.  See the help menu for the “Quantity” function.  This makes it easy to do calculations and to check your work.
The values are taken from section 6.1 of the instruction manual.

M = Quantity[0.2145, "Kilograms"];
Ro = (1/2)Quantity[3.72, "Inches"];Ri = (1/2)Quantity[1.72, "Inches"];

ΔI = (1/2)M(Ri^2 + Ro^2) (* Comes out in mixed units *)

UnitConvert[ΔI, "SIBase"] (* Uses kg, m, and s *)