In which situation would an object have the greatest moment of inertia?

The greatest moment of inertia for an object occurs when its mass is distributed further from the axis of rotation. This is because the moment of inertia is mathematically defined as the sum of the products of each mass element of the object and the square of its distance from the axis of rotation. When more mass is positioned far away from this axis, it increases the overall moment of inertia, making it harder to start or stop the rotation.

For instance, if you think of a figure skater spinning with arms extended versus pulled in close, when the arms are extended (mass further from the axis), the moment of inertia is greater, and it becomes more challenging to change their rotational speed. This principle is evident in various practical applications such as in engineering and biomechanics, where controlling rotation is crucial.

In contrast, concentrating mass near the axis of rotation or having lower mass would result in a lower moment of inertia. A situation involving only linear motion does not pertain to rotational dynamics and thus does not factor into the calculation of moment of inertia at all.