How does moment of inertia play a role in torque and angular momentum?
Hi Sreeveda!
Moment of Inertia is a lot like mass in linear motion. The more you have of it, the harder it is to change the motion of an object. Also, the more you have, the larger your momentum is.
With some formulas:

<â€” assuming a constant torque, a larger I will result in a smaller angular acceleration

<â€” The greater I is, the more angular momentum you will have. OR (assuming L is constant) the larger I gets, the smaller w gets
I thought that L= mass * lever arm * angular momentum. Does that mean that moment of inertia = mass*lever arm.
Also, I was wondering what exactly happens to the moment of inertia when a ballerina pulls her hands closer to her body?
For a point  I = Mr^2. In general I depends on mass and r^2 usually with some fraction in front of it.
L = Iw => I ~mr^2, w = v/r so we get L = mvr as well.
With the ballerina pulls her arms in, she brings some of her mass inwards, decreasing the radius. This lowers I and allows her to rotate faster because L is conserved.
Lout = L in
I out * w out = I in * w in