Angular momentum is very similar to linear momentum except for a couple of things. First,
let me give you the equation for angular momentum and then I'll explain it.
L = I * 
One symbol you should recognize is . We just replaced linear
velocity with angular velocity. Since that is true, it is only logical that I is
angular inertia, right? Well, it is. That's why I didn't just say mass in the
first lesson. Angular inertia has an equation of its own. Actually
it has many, but they all depend on how the object is moving. If the axis of rotation is not
on the object anywhere, then we use the standard equation I = m * r2, where the
radius is the distance from the axis of rotation to the object that is rotating.
Another situation is when the axis of rotation is, in some way going through the object. In
this case, the base equation of I = m * r2 needs to be modified a little. For some
of the more standard modifications refer to the chart below.
Let it also be noted that neither angular inertia nor momentum have the same units as their
linear counterparts. The unit for angular inertia is kgm2, while the unit for angular momentum
is kgm2/s. After the chart, we'll conclude with a sample problem.
A teacher sits on a massless circular platform rotating at 2rad/s. Her arms are extended
0.8m from the axis, each holding a 6kg mass. She pulls the masses in 0.1m toward the axis. If
the moment of inertia for her body with arms extended is 6kgm2 and the final moment of inertia
with arms drawn is 5kgm2 (not including the masses), what is her final angular speed?
Even though we are dealing with angular momentum, momentum is still conserved. In this closed
set, we have three objects, the teacher, and the two weights. All we need to do is to show their
momentum before and afterwards and then solve for the final speed.
Before:
(6kgm2 * 2rad/s) + 2(6kg * (0.8m)2 * 2rad/s)
12kgm2/s + 2(7.68kgm2/s)
27.36kgm2/s
After:
(5kgm2 * ) + 2(6kg * (0.7m)2 * )
(5kgm2 * ) + 2(2.94kgm2 * )
(5kgm2 * ) + (5.88kgm2 * )
10.88kgm2 *
Now, since we know they have to be the same, we just set the two parts equal to each other
and solve.
27.36kgm2/s = 10.88kgm2 *
2.515rad/s =
Work is the main focus of the next section. Not work in the
conventional sense, but physics work.
Momentum and Impulse Sample Problems
