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##

Moment of inertia

Newton's second law, Force = mass x acceleration, relates the acceleration
that an object of a certain mass experiences when subject to a given
force. There is an analogous relation between torque and angular
acceleration, which introduces the concept of
**moment of inertia**:

Just as mass is a measure of how readily an object accelerates
due to a given force, the moment of inertia of an object
measures how easily an object rotates about a particular
point of rotation. Thus, objects with a larger moment of inertia
about a given point will be harder to rotate with a set torque.
Correspondingly, a larger torque will cause a larger acceleration
on a particular body.

The moment of inertia of a body, which is always measured relative
to a point of rotation, depends in general on the
object's mass and on its shape. It is perhaps evident that for
a single mass going in a circle of fixed radius, the greater the
radius the harder it is to change the angular velocity. This is
because the actual displacement, and hence linear velocity of
the mass is proportional to the radius, so greater radius, for
a given angular displacement means greater linear displacement.
In an extended object the parts that are further from the axis of
rotation contribute more to the moment of inertia than the parts
closer to the axis. So as a general rule, for two objects with the
same total mass, the object with more of the mass located further from
the axis will have a greater moment of inertia. For example, the moment
of inertia of a solid cylinder of mass *M* and radius *R*
about a line passing through
its center is
*MR*^{2}, whereas a hollow cylinder with the
same mass and radius has a moment of inertia of *MR*^{2}. Similarly
when a spinning figure skater pulls her arms in to her body she places
more of her body weight closer to the axis of rotation and decreases
her moment of inertia.

** Next:** Rotational kinetic energy
**Up:** Torque
** Previous:** Static Equilibrium
*modtech@theory.uwinnipeg.ca *

1999-09-29