Question

why does the rotational inertia of the rod with the attached mass closer to your hand compare the way it does with the rotational inertia of the rod with the attached mass farther away? view available hint(s) rotational inertia depends on whether the mass is lower or higher. objects where the mass is higher have a greater rotational inertia. rotational inertia depends on whether the mass is farther or closer to the point of rotation. the farther the mass is, the higher the rotational inertia. rotational inertia depends on whether the mass is farther or closer to the point of rotation. the closer the mass is, the higher the rotational inertia. submit part d is it easier for a circus performer to balance a long rod held vertically with people hanging off the other end, or the same long rod without the people at the other end, and why? view available hint(s) it is easier for the performer to balance a long rod held vertically with people at the other end because the rotational inertia is smaller. it is easier for the performer to balance a long rod held vertically without people at the other end because the rotational inertia is greater. it is easier for the performer to balance a long rod held vertically without people at the other end because the rotational inertia is smaller. it is easier for the performer to balance a long rod held vertically with people at the other end because the rotational inertia is greater.

Explanation:

The rotational inertia formula is $I = \sum_{i}m_ir_i^2$, where $m_i$ is the mass and $r_i$ is the distance from the axis of rotation. The farther the mass is from the axis of rotation, the higher the rotational inertia. For the circus - performer problem, a larger rotational inertia means the rod resists changes in its rotational motion more, giving the performer more time to make adjustments for balance.

Answer:

For the first part: Rotational inertia depends on whether the mass is farther or closer to the point of rotation. The farther the mass is, the higher the rotational inertia.
For the second part: It is easier for the performer to balance a long rod held vertically with people at the other end because the rotational inertia is greater.