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## Homework Statement

A grandfather clock uses a physical pendulum to keep time. The pendulum consists of a uniform thin rod of mass M and length L that is pivoted freely about one end, with a solid sphere of the same mass, M, and a radius of L/2 centered about the free end of the rod.

Obtain an expression for the moment of inertia of the pendulum about its pivot point as a function of M and L.

## Homework Equations

I

_{rod}= ML

^{2}/3

I

_{sphere}= 2MR

^{2}/5

## The Attempt at a Solution

I substituted L/2 in for R, But, the sphere's inertia isn't around the central axis. I can't seem to figure that out. I put L/2 in for R, which becomes L

^{2}/4, and I get rid of the fractions. What else am I supposed to do?

I got to:

I = ML

^{2}/3 + ML

^{2}/10 + 3L

^{2}/4. I simplified and got it wrong. Should I get rid of the fractions first? Am I missing something?