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## Homework Statement

A hollow, spherical shell with mass 2.50kg rolls without slipping down a slope angled at 35.0 degrees.

i) Find the acceleration

ii) Find the friction force

iii) Find the minimum coefficient of friction to prevent slipping

## Homework Equations

[itex]F=ma[/itex]

[itex]I=\frac{2MR^2}{3}[/itex]

Energy must stay constant:

[itex]E_{p}+E_{kr}+E_{k} = E_{p}+E_{kr}+E_{k}[/itex]

[itex]mgh+\frac{1}{2}Iw^{2}+\frac{1}{2}mv^{2}=mgh+\frac{1}{2}Iw^{2}+\frac{1}{2}mv^{2}[/itex]

## The Attempt at a Solution

I really have no idea where to start, because a radius is not given, so I cannot find the moment of inertia. I was thinking if I used the energies, and said that

[itex]mgh=\frac{1}{2}mv^{2}+\frac{1}{2}Iw^{2}[/itex]

[itex]mgh=\frac{1}{2}mv^{2}+\frac{1}{2}((\frac{2}{3}mR^2)w^{2}[/itex]

because we could use a pretend example, say that the sphere starts at rest at the top of the ramp, and in the end, all the energy is kinetic. But from here, I'm not really sure where to go. Thanks!