# Formula: Thin Rod (Rotation Perpendicular to Symmetry Axis) Moment of inertia    Mass    Length

## Moment of inertia

Unit
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 we calculate the moment of inertia of a thin rod whose axis of rotation is perpendicular to the axis of symmetry and goes through the center.

## Mass

Unit
Total mass of a thin rod that is homogeneously distributed. The larger the mass, the larger the moment of inertia.

## Length

Unit
Length of the rod. When the length is doubled, the moment of inertia is quadrupled.

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