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The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is defined relative to a rotational axis. It is the ratio between the torque applied and the resulting angular acceleration about that axis.
In this subsection, we show how to calculate the moment of inertia for several standard types of objects, as well as how to use known moments of inertia to find the moment of inertia for a shifted axis or for a compound object.
The moment of inertia can be derived as getting the moment of inertia of the parts and applying the transfer formula: I = I 0 + Ad 2. We have a comprehensive article explaining the approach to solving the moment of inertia .
2 sie 2023 · Learn how to calculate moment of inertia for different objects and systems using various formulas. Find out the units, dimensions, and applications of moment of inertia in rotational motion.
In this section, we show how to calculate the moment of inertia for several standard types of objects, as well as how to use known moments of inertia to find the moment of inertia for a shifted axis or for a compound object.
Learn the definition, formulas and examples of moment of inertia, the rotational analog of mass for linear motion. Explore the common moments of inertia for different shapes and the general form for any axis.
The formula for the moment of inertia about the $z$-axis of an object is \begin{equation} I =\sum m_i(x_i^2+y_i^2)\notag \end{equation} or \begin{equation} \label{Eq:I:19:4} I =\int(x^2+y^2)\,dm=\int(x^2+y^2)\rho\,dV.
