Mechanics 2: Linear and Rotational Dynamics - 3D Math Primer for Graphics and Game Development - page 613

this to linear inertia, where shifting the mass around will not make the
object any easier or harder to accelerate. The only thing that matters for
linear acceleration is the total mass. Furthermore, in three dimensions,
although linear mass can still be quantified with a scalar, the moment of
inertia cannot be described by a single number, due to its dependence on
the distribution of mass.
When we take the limit as the number of mass elements reaches infinity,
Equation (12.25) turns into an integral. Luckily, formulas for the moments
of inertia for many common shapes, such as spheres, cylinders, rings, and
so forth, can be found on the Internet.
Newton's second law, F = ma, has a straightforward rotational equiv-
alent.

Rotational Equivalent of Newton's Second Law

τ = Jα. (12.26)

For rotation in a plane, all of the variables in Equation (12.26) are scalars.
In three dimensions, however, τ and α become vector quantities, and J
becomes a matrix. Section 12.5.3 discusses this.
We've considered torque, the rotational analog to linear force. Now
let's turn our attention to momentum. Remember that linear momentum
is the “quantity of motion” contained in an object. Its analog, angular
momentum, has a similar interpretation. Intuitively, angular momentum
describes how hard it will be to stop the rotation of the object. If the
angular momentum is large, then the magnitude of the applied torque, or
the duration for which it is applied, or both, must be large.
In our discussion of linear momentum, we encountered two ways of
thinking about momentum. The first was to interpret momentum in an
“instantaneous respect” as the product of mass and velocity by using P =
mv. The rotational equivalent is shown in Equation (12.27).

Spin Angular Momentum

Angular momentum (L) is the product of the moment of inertia J and
angular velocity (ω):

L = Jω. (12.27)