**Moment of inertia of the objects:**

Solid sphere:

$\overline{){\mathbf{I}}{\mathbf{=}}\frac{\mathbf{2}}{\mathbf{5}}{\mathbf{M}}{{\mathbf{R}}}^{{\mathbf{2}}}}$

Solid cylinder/disk:

$\overline{){\mathbf{I}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{MR}}}^{{\mathbf{2}}}}$

Hoop:

$\overline{){\mathbf{I}}{\mathbf{=}}{{\mathbf{MR}}}^{{\mathbf{2}}}}$

Thin spherical shell/hollow sphere:

$\overline{){\mathbf{I}}{\mathbf{=}}\frac{\mathbf{2}}{\mathbf{3}}{{\mathbf{MR}}}^{{\mathbf{2}}}}$

Gravitational potential energy:

$\overline{){\mathbf{U}}{\mathbf{=}}{\mathbf{m}}{\mathbf{g}}{\mathbf{h}}}$

**The kinetic energy of a rolling object:**

$\overline{){\mathbf{K}}{\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathit{I}}{{\mathbf{\omega}}}^{{\mathbf{2}}}}$

**Angular frequency:**

$\overline{){\mathbf{\omega}}{\mathbf{=}}\frac{\mathbf{v}}{\mathbf{r}}}$

**Conservation of energy:**

Four objects of various masses, each denoted m, all have the same radius. They are all rolling at the same speed as they approach a curved incline as shown below.

Rank the objects based on the maximum height they reach along the curved incline.

Solid disk, m = 0.5 kg

Hollow sphere, m = 0.2 kg

hoop, m = 0.2 kg

Solid cylinder, m = 0.2 kg

solid sphere, m = 1.0 kg

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Conservation of Energy in Rolling Motion concept. You can view video lessons to learn Conservation of Energy in Rolling Motion. Or if you need more Conservation of Energy in Rolling Motion practice, you can also practice Conservation of Energy in Rolling Motion practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Dominguez's class at MDC.