Formula Hollow Cylinder (Axis of Rotation Parallel to Radius) Moment of inertia Mass Radius Width
$$I ~=~ \frac{1}{2} \, m \, \left( r^2 ~+~ \frac{w^2}{6} \right)$$ $$I ~=~ \frac{1}{2} \, m \, \left( r^2 ~+~ \frac{w^2}{6} \right)$$
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
$$ m $$ 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.