Formula: Hollow Cylinder (Axis of Rotation Parallel to Radius) Moment of inertia Mass Radius Width
$$\class{brown}{I} ~=~ \frac{1}{2} \, \class{brown}{m} \, \left( r^2 ~+~ \frac{w^2}{6} \right)$$
$$\class{brown}{I} ~=~ \frac{1}{2} \, \class{brown}{m} \, \left( r^2 ~+~ \frac{w^2}{6} \right)$$
$$\class{brown}{m} ~=~ \frac{2\class{brown}{I}}{r^2 + \frac{w^2}{6}}$$
$$r ~=~ \sqrt{ \frac{2}{\class{brown}{m}} \left( \class{brown}{I} - \frac{\class{brown}{m}\, w^2}{12} \right) }$$
$$w ~=~ \sqrt{ \frac{12}{\class{brown}{m}} \left( \class{brown}{I} - \frac{\class{brown}{m}\, r^2}{2} \right) }$$
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 generate 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 hollow cylinder is calculated, whose axis of rotation is parallel to the diameter / radius.
Mass
$$ \class{brown}{m} $$ Unit $$ \mathrm{kg} $$
Total mass of the hollow cylinder. The moment of inertia of the hollow cylinder is larger, the greater its mass.
Radius
$$ r $$ Unit $$ \mathrm{m} $$
Radius of the hollow cylinder. With a larger radius, the mass is located further away from the axis of rotation, i.e. the moment of inertia is larger.
Width
$$ w $$ Unit $$ \mathrm{m} $$
Width of the hollow cylinder. The wider the cylinder, the greater the moment of inertia.