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2 Αυγ 2023 · Moment of inertia, also known as rotational inertia or angular mass, is a physical quantity that resists a rigid body’s rotational motion. It is analogous to mass in translational motion. It determines the torque required to rotate an object by a given angular acceleration.
The quantity \(mr^2\) is called the rotational inertia or moment of inertia of a point mass \(m\) a distance \(r\) from the center of rotation. Figure \(\PageIndex{2}\): An object is supported by a horizontal frictionless table and is attached to a pivot point by a cord that supplies centripetal force.
introduction & theory. Logic behind the moment of inertia: Why do we need this? Definition for point bodies. I = mr2. It's a scalar quantity (like its translational cousin, mass), but has unusual looking units. [kg m 2] Say it, kilogram meter squared and don't say it some other way by accident. For a collection of objects, just add the moments.
Suppose we know the rotational inertias of two separate objects around a common axis. If these two objects are attached so that they rotate together rigidly around that common axis, then the rotational inertia of the combined object is simply the sum of their rotational inertias.
The SI units of rotational inertia are \( kg \cdot{m^2}\). Comparing the expression for linear and angular kinetic energies, we see that rotationalinertia is the rotational analog of mass. The rotational inertia of an object does not depend solely on the amount of mass in the object, but on how this mass is distributed relative to the axis of ...
Rotational inertia depends both on an object’s mass and how the mass is distributed relative to the axis of rotation. Unlike other scenarios in physics where we simplify situations by pretending we have a point mass, the shape of an object determines its rotational inertia.
Rotational Inertia and Moment of Inertia. Before we can consider the rotation of anything other than a point mass like the one in Figure 2, we must extend the idea of rotational inertia to all types of objects.To expand our concept of rotational inertia, we define the moment of inertia [latex]\boldsymbol{I}[/latex]of an object to be the sum of[latex]\boldsymbol{mr^2}[/latex]for all the point ...
