0.30 Phy1300: angular momentum -- rotational kinetic energy and  (Page 5/11)

In rotational terms, for a rigid rotating object, the rotational inertia ( I ), is a measure of how hard it is to cause the object to change itsangular velocity.

Finding the rotational inertia

Here are a few tips on how you might go about finding the rotational inertia of an object.

The rotational axis is very important

The rotational inertia for an object depends heavily on the location of the axis of rotation. For example, some vehicles have doors on the back that are hinged on one side.Other vehicles have doors on the back that are hinged at the top. Given a door that has a rectangular shape, but which is not a square, the rotational inertiawhen the door is hinged on the side would be different from when the door is hinged at the top.

Assuming that both doors have the same mass, and are fastened to the vehicle with the same orientation, the center of mass for onearrangement would be further from the hinge than for the other arrangement. The arrangement for which the center of mass is further from the hinge would have thegreater rotational inertia.

A simple experiment

Pick up an eight-foot piece of 2x4 lumber, grasp it near one end, and try swinging it like a baseball bat. You should find that to be relatively difficultbecause it has a large rotational inertia when rotated around its end. (It also has a lot torque due to gravity when supported only at the end. Torque will bethe topic for a future module.)

Then grasp it in the center and rotate it as far as you can without hitting your body. You should find that to be somewhat easier because it has a smallerrotational inertia when rotated around its center than when rotated around its end.

I will have more to say about this later in this module.

The parallel axis theorem

It is possible to determine the rotational inertia of an object about any axis if we can determine the rotational inertia of that same object about aparallel axis that goes through the center of mass of the object.

I will explain this in much more detail in the dumbbell scenario later in this module.