# Simple Inertia Test Setup

1. Jun 28, 2007

### remz

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...

$$J = \frac {mgr \theta} {\frac {d \omega} {dt}}$$

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

Last edited: Jun 28, 2007
2. Jun 28, 2007

### Staff: Mentor

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....

3. Jun 29, 2007

### FredGarvin

Take a look at this:

Last edited: Dec 20, 2007