Calculating Moment of Inertia: A Guide for the Falling Mass Method

[willwoll100]

Could anyone help me calculate the moment of inertia of a wheel by the falling mass method, the data I've got is below,

Distance mass falls

Time taken

Mass fallen

Radius of shaft that the wire wraps around which is attached to the mass

Is is just the mass*radius^2? It just doesn't seem right?

Thanks

 

[Doc Al]

I assume you have a light cable wrapped around the wheel shaft with a mass at the end. Then you let the mass fall from rest? And that the purpose of the experiment is to determine the rotational inertia of the wheel?

Given the acceleration of the falling mass you can figure out the rotational inertia of the wheel. You can figure out the acceleration from measurements of the time and distance (using kinematics).

To see how the rotational inertia relates to the acceleration of the falling mass, apply Newton's 2nd law to the wheel and to the falling mass.

 

[willwoll100]

Yes the wire is deemed of no mass and the mass added falls from rest, I've calculated the acceleration which is constant due to the force applied never changing which is 2*S/t^2, I've also calculated the angular acceleration which is acceleration/radius in rad/s^2. Force P acting in the wire is m(9.81-a) I have also calculated as well the torque Which is P*radius of shaft.

 

[Doc Al]

If you've calculated the torque and the angular acceleration, you have all you need to find the rotational inertia: $\tau = I \alpha$.

 

[willwoll100]

I thought of that but was unsure whether I could use that equation for this problem, thanks for your help