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.
Irod = ML2/3
Isphere = 2MR2/5
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 L2/4, and I get rid of the fractions. What else am I supposed to do?
I got to:
I = ML2/3 + ML2/10 + 3L2/4. I simplified and got it wrong. Should I get rid of the fractions first? Am I missing something?