Much as in the case of linear momentum, the mistake that tends to be made in the
case of angular momentum is not using the principle of conservation of angular
momentum when it should be used, that is, applying conservation of mechanical
energy in a case in which mechanical energy is not conserved but angular
momentum is. Consider the case, for instance, in which one drops a disk (from a
negligible height) that is not spinning, onto a disk that is spinning, and after the
drop, the two disks spin together as one. The “together as one” part tips you off
that this is a completely inelastic (rotational) collision. Some mechanical energy
is converted into thermal energy (and other forms not accounted for) in the
collision. It’s easy to see that mechanical energy is converted into thermal energy
if the two disks are CD’s and the bottom one is initially spinning quite fast (but is
not being driven). When you drop the top one onto the bottom one, there will be
quite a bit of slipping before the top disk gets up to speed and the two disks spin
as one. During the slipping, it is friction that increases the spin rate of the top
CD and slows the bottom one. Friction converts mechanical energy into thermal
energy. Hence, the mechanical energy prior to the drop is less than the
mechanical energy after the drop.
The angular momentum of an object is a measure of how difficult it is to stop that object from
spinning. For an object rotating about a fixed axis, the angular momentum depends on how fast
the object is spinning, and on the object's rotational inertia (also known as moment of inertia)
with respect to that axis.
Rotational Inertia (a.k.a. Moment of Inertia)
The rotational inertia of an object with respect to a given rotation axis is a measure of the object's
tendency to resist a change in its angular velocity about that axis. The rotational inertia depends
on the mass of the object and how that mass is distributed. You have probably noticed that it is
easier to start a merry-go-round spinning when it has no children on it. When the kids climb on,
the mass of what you are trying to spin is greater, and this means the rotational inertia of the
object you are trying to spin is greater. Have you also noticed that if the kids move in toward the
center of the merry-go-round it is easier to start it spinning than it is when they all sit on the outer
edge of the merry-go-round? It is. The farther, on the average, the mass of an object is
distributed away from the axis of rotation, the greater the object's moment of inertia with respect
to that axis of rotation. The rotational inertia of an object is represented by the symbol I.
During this initial coverage of angular momentum, you will not be required to calculate I from
the shape and mass of the object. You will either be given I or expected to calculate it by
applying conservation of angular momentum (discussed below).
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