How do we make things rotate?  Apply a force.  But how we apply that force can make differences in how the object rotates.
 

So, what is the relation between torque and angular acceleration?  Look to linear motion, F= ma.  What quantity plays the role of "mass" in rotation? 

When talking about rotation where the mass is located is important, not just what is the total mass.  If the mass is close to the rotational axis then object easily rotates, has a small I.

 
For continuous shapes we replace the summation with an integration and you get results seen in table 8-1.
 
 

Newton's Second Law for rotating systems is:

Given the following configuration of three masses (at the vertices of a 0.5m, 0.4m, 0.64m right triangle).  Find the moment of inertia through the 1 kg mass.  Then through the 2 kg mass (the axis passing through each).