Formula Solid cylinder - rotation around the symmetry axis Moment of inertia Mass Radius
$$\class{brown}{I} ~=~ \frac{1}{2} \, m \, {\class{purple}{r}}^2$$ $$\class{brown}{I} ~=~ \frac{1}{2} \, m \, {\class{purple}{r}}^2$$ $$m ~=~ \frac{2\class{brown}{I}}{{\class{purple}{r}}^2}$$ $$\class{purple}{r} ~=~ \sqrt{ \frac{2\class{brown}{I}}{m} }$$
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
$$ \class{brown}{m} $$ 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
$$ \class{purple}{r} $$ Unit $$ \mathrm{m} $$ Radius of the cylinder. If the radius is twice as large, the moment of inertia of the cylinder is quadrupled.