Rotational inertia of arm lifting a cup

[lyl926]

Homework Statement

Doc Holliday takes his last shot of whiskey. His forearm and hand spans 18" and weighs 2lbs. The shotglass and its intoxicating contents weighs 5ozs. (there are 16 ozs in one pound). Doc remains otherwise motionless as his elbow bends, tossing back the whiskey.
Calculate the rotational inertia of the arm + drink.

Homework Equations

τ=Iα (torque=rotational inertia x alpha)

and the equations in the file i attached

The Attempt at a Solution

Since the cup is point mass and that arm I think is rigid mass(?),
I used
I = (1/3)mL² + something
I don't know which of the equations from the file the something should be..
My friend used I=mR² but I'm not sure how that works..

 

[ideasrule]

By definition, the moment of inertia of a point mass is md^2. Every other moment of inertia you've encountered--1/3ML^2, 2/5MR^2, 2/3MR^3, whatever--is derived from I=md^2.