How Can I Calculate the Moment of Inertia for Any Object Using a Simple Setup?

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To calculate the moment of inertia for any object, a simple experimental setup can involve using a pendulum method, where the angular acceleration is measured. The formula J = (mgrθ) / (dω/dt) allows for determining inertia, with known values for mass, gravity, distance from the center of rotation, and angle. A suggestion is to ensure the object has a defined center of rotation and apply a known torque to measure rotational acceleration effectively. Using a mass on a string can help generate a known force to create torque on the object. This approach offers a practical way to deduce moment of inertia without complex equipment.
remz
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Any ideas on a simple experiment I can setup to calculate the moment of inertia for any object (sanity check only).

Another post on PF proposed using a pendulum however unfortunately did not go into enough detail and my google skills are obviously lacking tonight.

Since...

<br /> J = \frac {mgr \theta} {\frac {d \omega} {dt}}<br />

where...

J = inertia of object on end of string
m = mass of object
g = acceleration due to gravity
r = distance of object from centre of rotation
\theta = the angle to which the object is raised (sin \theta \approx \theta for small \theta)
\frac {d \omega} {dt} = angular acceleration of object

So, in this test setup, the inertia can be deduced through measuring the angular acceleration of the object only as the numerator is already fully known.

Is there a flaw in my proposed test or can anyone suggest any alternative solutions.

Regards,

rem
 
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Do the objects have a center of rotation? If so, just make that axis of rotation vertical, and devise a means of applying a known torque and measuring the rotational acceleration. You could use a mass on a string to generate a known force, and translate that down force into a torque on the shaft of your unknown object...
 
Take a look at this:
 
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