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**1. Homework Statement**

A small solid sphere, with radius 0.25 cm and mass 0.68 g rolls without slipping on the inside of a large fixed hemisphere with radius 23 cm and a vertical axis of symmetry. The sphere starts at the top from rest. The moment of inertia of a sphere is I = 2/5 MR

^{2}.

(a) What is its kinetic energy at the bottom?

(b) What fraction of its kinetic energy at the bottom is associated with rotation about an axis through its center of mass?

**2. Homework Equations**

E=U+K=constant

U=mgh

[tex]K=\frac{1}{2}mv^2+\frac{1}{2}I\omega^2[/tex]

**3. The Attempt at a Solution**

For part (a) only:

I started to write up the energy conservation law in great and glorious detail, but then I realized that since K_i=0 and U_f=0, and the question only wants to know K at bottom, I could say

[tex]mgh=K[/tex]

[tex](.00068kg)(9.81m/s^2)(0.23m)=K[/tex]

K=0.00153J

But the correct answer is 0.152J, a rather striking difference. Where did I go wrong?