Rotational inertia of arm lifting a cup

AI Thread Summary
The discussion revolves around calculating the rotational inertia of Doc Holliday's forearm and the shot glass as he lifts it. Key equations mentioned include τ=Iα, where torque equals rotational inertia times angular acceleration, and the moment of inertia formulas for rigid bodies and point masses. There is confusion regarding which formula to apply, with one participant suggesting I = (1/3)mL² and another referencing I = mR² for point masses. The importance of understanding the derivation of moment of inertia from the basic definition I=md² is emphasized. The conversation highlights the need for clarity on applying the correct equations for different mass distributions.
lyl926
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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..
 

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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.
 
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