Rotational inertia is additive

For a system composed of several parts, its total rotational inertia is the sum of the rotational inertia of each part of the system.

Conditions:

  1. The rotational inertia is calculated for the same axis for all parts of the system.

Links:

  1. Wikipedia, see second paragraph.

total_rotational_inertia

Total rotational_inertia of the system.

Symbol:

I

Latex:

\(I\)

Dimension:

length**2*mass

index

Index assigned to each part of the system.

rotational_inertia

rotational_inertia of the \(k\)-th part of the system.

Symbol:

I[k]

Latex:

\({I}_{k}\)

Dimension:

length**2*mass

law

I = Sum(I[k], k)

Latex:
\[I = \sum_k {I}_{k}\]