Intro to Moment of Inertia Video Lessons

Concept

# Problem: The five 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. Rank the objects based on the maximum height they reach along the curved incline. Rank from largest to smallest. To rank items as equivalent, overlap them.

###### FREE Expert Solution

The objects have both translational and rotational kinetic energy since the objects are rolling.

From the conservation of momentum we have:

$\overline{)\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{I}}{{\mathbf{\omega }}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{m}}{\mathbf{g}}{\mathbf{h}}}$

We solve for h as follows:

$\begin{array}{rcl}\mathbf{h}& \mathbf{=}& \frac{\mathbf{\left(}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{m}{\mathbf{v}}^{\mathbf{2}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{I}{\mathbf{\omega }}^{\mathbf{2}}\mathbf{\right)}}{\mathbf{m}\mathbf{g}}\end{array}$

It is clear that the maximum height reached by the objects depends on the moment of inertia of the objects.

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###### Problem Details

The five 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.

Rank the objects based on the maximum height they reach along the curved incline. Rank from largest to smallest. To rank items as equivalent, overlap them.