Question

which one of the following statements concerning the moment of inertia is false?
the moment of inertia depends on the location of the rotation axis relative to the particles that make up the object.
the moment of inertia depends on the orientation of the rotation axis relative to the particles that make up the object.
of the particles that make up an object, the particle with the smallest mass may contribute the greatest amount to the moment of inertia.
the moment of inertia may be expressed in units of kg·m².
the moment of inertia depends on the angular acceleration of the object as it rotates.

Explanation:

The moment of inertia \(I=\sum_{i}m_{i}r_{i}^{2}\) (for a collection of particles) or \(I = \int r^{2}dm\) (for a continuous object). It depends on the mass distribution relative to the axis of rotation (location and orientation of the axis), and the units are \(kg\cdot m^{2}\). A particle with small mass but large \(r\) (distance from the axis) can contribute a lot to \(I\). However, the moment of inertia is a property of the object's mass - distribution and axis, not related to angular acceleration \(\alpha\). The formula \(\tau=I\alpha\) shows the relationship between torque \(\tau\), moment of inertia \(I\), and angular acceleration \(\alpha\), but \(I\) does not depend on \(\alpha\).

Answer:

The moment of inertia depends on the angular acceleration of the object as it rotates.