Moment of Inertia lab equation

[fisselt]

I'm working on a lab where I have to go into some detail about moment of inertia. I understand the concept and everything but am a little confused by the equation that I found on wikipedia.
I've seen only two equations for this: momentum=torque divided by angular acceleration and
one specifically for a disk: I=.5MR²

On wikipedia I they have the equation: T=ml²$\omega$²
Wikipedia makes sense to me because I understand that as radius decreases momentum decreases at constant angular velocity. Neutron stars for instance maintain similar inertia at reduced radius but much higher angular velocity.

Are all 3 ways true?

 

[Screwdriver]

momentum=torque divided by angular acceleration

I'm assuming you meant that moment of inertia = torque divided by angular acceleration, because what you have there isn't true (just look at the units.)

one specifically for a disk: I=.5MR²

I agree with this.

On wikipedia I they have the equation: T=ml²ω²

I'm assuming that you're referring to this page. You'll note that $T$ is in fact the kinetic energy of the object and not the moment of inertia. You may have been confused just because $T$ is similar to the symbol for torque, $\tau$.