Torque is force multiplied by the perpendicular distance from the axis of rotation (also called a lever arm.) Torque causes rotation and the size of the torque is directly proportional to the size of the lever arm, meaning that a long lever arm means a big torque. In the video below, I find that Ultimate Physics Tutor does a great job of reinforcing the basics while still expanding on the concept in his second explanation using vectors.
Rotational inertia is the property of an object to resist changes in spin. Since we know that with inertia more mass means more inertia, we also know that the distribution of mass is important when it comes to what makes an object inclined to spin or remain still. A great example of distribution of mass and rotational inertia is in figure skating when the skaters tuck in their arms to spin faster.
Just like linear momentum, angular momentum is conserved. This means that the skater's angular momentum before she tucked in her arms and legs is the same as her angular momentum after. Angular momentum is calculated by multiplying rotational inertia by rotational velocity. Since we know her angular momentum is conserved, we also know that before she tucked her rotational inertia must have been significantly larger than her rotational velocity and that after she tucked her rotational inertia must have been significantly smaller than her rotational velocity.
This quick video has nice explanations and good examples of ways this concept can be demonstrated at home.
