Identify the axis of rotation
Determine the mass of each part of the object
Determine the distance of each part from the axis
Use the formula (I = sum m r^2) for point masses
Use (I = int r^2 , dm) for continuous objects
Break the object into small mass elements if needed
Integrate over the full shape using the correct geometry
Apply the parallel axis theorem if the axis is shifted: (I = I_{text{cm}} + Md^2)
Apply the perpendicular axis theorem for flat laminae when applicable: (I_z = I_x + I_y)
Use standard moment of inertia formulas for common shapes
Add moments of inertia for composite objects
Check units are in ( text{kg} cdot text{m}^2 )