reorder the following according to increasing moment of inertia. #1 is the object with the lowest rotational…

Explanation:

Step1: Recall moment - of - inertia formulas

The moment of inertia of a solid sphere about a diameter is $I_{sphere}=\frac{2}{5}mr^{2}$, for a solid cylinder about its symmetry axis is $I_{cylinder}=\frac{1}{2}mr^{2}$, and for a hoop about its symmetry axis is $I_{hoop}=mr^{2}$, where $m$ is the mass and $r$ is the radius.

Step2: Compare the coefficients

We have coefficients $\frac{2}{5}=0.4$ for the solid sphere, $\frac{1}{2} = 0.5$ for the solid cylinder, and $1$ for the hoop. Since $0.4<0.5 < 1$, for the same mass and radius, the solid sphere has the lowest moment of inertia, the solid cylinder has the second - lowest, and the hoop has the highest.

Answer:

1. Solid sphere
2. Solid cylinder
3. Hoop