Moment of Inertia
When studying rotational dynamics, one must learn
the moment of inertia, I. For simple particles, its moment of inertia is mr2
where r is the distance from the axis of rotation of the particle. However we must also
consider continuous rigid objects composed of many small particles. So, the general
definition for the moment of inertia is:
The above integral is a volume integral. However, it may reduce to a surface integral
for a lamina or a line integral for a wire, the density being then interpreted as mass
per unit area or mass per unit length as the case may be. We should drive some moment
of inertia for simple bodies.
r = M/L
To save you the trouble of doing complicated multivariable calculus, we will give
you the moment of inertia of a sphere which is used everywhere in the following pages:
Sold spheres: I = (2/5)MR2
How do we get the moment of inertia when the axis of rotation is not in the center? We don't
use even more complicated mathematics, but use the Parallel Axis Theorem:
I = Icm + MD2
Sample Problem
The moment of inertia of a disc rotating on its axis is given I = (1/2)MR2.
What is the moment of inertia when the disc rotates on an axis that is at its edge?
