Question

how to calculate the moment of inertia of a solid sphere about a tangent to the sphere?

Answer 1

We know that,

the moment of inertia of a solid sphere about any diameter, I = (2/5) mr²

Now from the theorem of parallel axis,

moment of inertia of sphere about a tangent will be

I' = I + mr² = (2/5)mr² + mr²

^{thus, we get}

^I' = (7/5)mr²