Conservation of Energy in Rolling Motion Video Lessons

Concept

# Problem: An 8.0 cm diameter, 400 g sphere is released from rest ta the tip of a 2.1 m long, 25 degree incline. It rolls, without slipping, to the bottom.What fraction of its kinetic energy is rotational?

###### FREE Expert Solution

Moment of inertia of a sphere:

$\overline{){\mathbf{I}}{\mathbf{=}}\frac{\mathbf{2}}{\mathbf{5}}{\mathbf{m}}{{\mathbf{r}}}^{{\mathbf{2}}}}$

Rotational kinetic energy:

$\overline{){{\mathbf{K}}}_{\mathbf{r}\mathbf{o}\mathbf{t}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{I}}{{\mathbf{\omega }}}^{{\mathbf{2}}}}$

Translational kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}}^{{\mathbf{2}}}}$

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###### Problem Details

An 8.0 cm diameter, 400 g sphere is released from rest ta the tip of a 2.1 m long, 25 degree incline. It rolls, without slipping, to the bottom.

What fraction of its kinetic energy is rotational?