Challenging Physics Question (Mass moment of inertia, pendulum)

AI Thread Summary
The discussion centers on calculating the mass moment of inertia of a baseball bat using pendular motion equations. The user has derived an initial mass moment of inertia (Io) of 1.05 kg*m² but encounters an issue when applying the parallel axis theorem, resulting in a negative value for the moment of inertia about the center of gravity (Icg). This negative result contradicts physical principles, prompting the user to seek clarification on potential errors in their calculations. The user has verified their formulas against textbooks and online resources, indicating confidence in their approach. The challenge lies in resolving the discrepancy while adhering to the requirement of using pendular motion equations.
patrat
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Hello, as you can tell by the hour I have been at this problem for quite some time now.
I am trying to find the mass moment of inertia (rotational inertia) of a baseball bat; by means of using the equations for pendular motion. Here are the equations:

Distance from pendulum pivot to pendulum center of gravity:
Lcg=1.144 meter
Mass of pendulum:
m=0.840 kilogram
Time Period of pendulum:
T=2.1 seconds
Angular speed of pendulum (calculated from period):
w=2.99 radian/second
gravity:
g=9.81 meters/second^2
Mass moment of inertia about pendulum pivot:
Io=what the equations solve (kilogram*meter^2)

The equation is:
Io=(m*g*Lcg)/(w^2)
or equivalently
Io=((T^2)*m*g*Lcg)/(4*pi^2)

for this I get, everytime, Io=1.05 (kilogram*meter^2)

The trouble is coming though
Icg=mass moment of inertia about pendulum's center of gravity
parrallel axis theorem:
Io=Icg+m*Lcg^2
which becomes:
Icg=Io-m*Lcg^2

which spits out: Icg= -0.045 (kilogram*meter^2)

Thats right... a negative number. That violates intuition and the laws of physics for a physical solid. How did I break physics?

What did I do wrong and how do I fix it?
 
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patrat said:
I am trying to find the mass moment of inertia (rotational inertia) of a baseball bat; by means of using the equations for pendular motion.

Does it have to be by this means? If yes, I think it may be related to the 'breaking physics' part you mentioned later.
 
I have to solve the problem using the equations for pendular motion. I checked all my formulas with textbooks and the internet, and all my equations and values seem to line up...
 
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