Formula Solid cylinder - rotation around the symmetry axis Moment of inertia Mass Radius
$$I ~=~ \frac{1}{2} \, m \, r^2$$ $$I ~=~ \frac{1}{2} \, m \, r^2$$ $$m ~=~ \frac{2I}{r^2}$$ $$r ~=~ \sqrt{ \frac{2I}{m} }$$
Moment of inertia
$$ \class{brown}{I} $$ Unit $$ \mathrm{kg} \, \mathrm{m}^2 $$ According to \( M ~=~ I \, \alpha \) (\(\alpha\): angular acceleration), the moment of inertia determines how hard it is to exert a torque \(M\) on the body. Moment of inertia \(I\) depends on the mass distribution and on the choice of the axis of rotation. Here, the moment of inertia of a homogeneously filled cylinder is calculated, whose axis of rotation passes through the center, perpendicular to the diameter.
Mass
$$ m $$ Unit $$ \mathrm{kg} $$ Total mass of the cylinder that is homogeneously distributed in the cylinder. The greater the mass, the greater the moment of inertia.
Radius
$$ r $$ Unit $$ \mathrm{m} $$ Radius of the cylinder. If the radius is twice as large, the moment of inertia of the cylinder is quadrupled.