Formula: Steiner's Theorem For Shifting Axes of Rotation Moment of inertia Moment of inertia through CM Distance Mass
$$I ~=~ I_{\text{CM}} ~+~ \class{brown}{m} \, h^2$$
$$I ~=~ I_{\text{CM}} ~+~ \class{brown}{m} \, h^2$$
$$I_{\text{CM}} ~=~ I ~-~ \class{brown}{m} \, h^2$$
$$h ~=~ \sqrt{ \frac{I ~-~ I_{\text{CM}}}{ \class{brown}{m} } }$$
$$\class{brown}{m} ~=~ \frac{I ~-~ I_{\text{CM}}}{ h^2 }$$
Moment of inertia
$$ \class{brown}{I} $$ Unit $$ \mathrm{kg} \, \mathrm{m}^2 $$
Moment of inertia of a rotating body (e.g. a cylinder) whose axis of rotation has been shifted parallel to the axis of rotation through the center of mass. With the Steiner's theorem, there is no need to calculate a complicated integral for the new axis of rotation.
Moment of inertia through CM
$$ I_{\text{CM}} $$ Unit $$ \mathrm{kg} \, \mathrm{m}^2 $$
Moment of inertia of the rotating body whose axis of rotation passes through the center of mass of the body.
Distance
$$ h $$ Unit $$ \mathrm{m} $$
Distance of the new axis of rotation from the axis of rotation through the center of mass
Mass
$$ \class{brown}{m} $$ Unit $$ \mathrm{kg} $$
Total mass of the rotating body.